From efe3af2ba531ec39e72b24910a7f7fdd25dca54e Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Fri, 17 Oct 2025 15:38:54 +0200 Subject: [PATCH 1/9] Add files via upload Commit with the tutorial on Feasibility-Driven trust Region Bayesian Optimization. --- notebooks_community/FuRBO/FuRBO.ipynb | 1011 +++++++++++++++++++++++++ 1 file changed, 1011 insertions(+) create mode 100644 notebooks_community/FuRBO/FuRBO.ipynb diff --git a/notebooks_community/FuRBO/FuRBO.ipynb b/notebooks_community/FuRBO/FuRBO.ipynb new file mode 100644 index 0000000000..98b46fd8b4 --- /dev/null +++ b/notebooks_community/FuRBO/FuRBO.ipynb @@ -0,0 +1,1011 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b5831947-283e-4682-aae4-bd19bcce03e0", + "metadata": {}, + "source": [ + "# Feasible trust Region Bayesian Optimization (FuRBO)\n", + "\n", + "- Contributors: paoloascia, elenaraponi\n", + "- Last update 17 October 2025\n", + "- BoTorch version: 0.12.0\n", + "\n", + "This tutorial shows how to implement Feasible trust Region Bayesian Optimization (FuRBO) with restarts in a closed loop [1].\n", + "\n", + "In this tutorial, we optimize the 10D Ackley function on the domain $[−5,10]^{10}$ subject to two constraint functions $c_1$ and $c_2$. The problem maximizes the Ackley function while the constraints are fulfilled when $c_1(x) \\leq 0$ and $c_2(x) \\leq 0$.\n", + "\n", + "[1] [Ascia, Paolo, Elena Raponi, Thomas Bäck and Fabian Duddeck. \"Feasibility-Driven Trust Region Bayesian Optimization.\" In AutoML 2025 Methods Track.](https://doi.org/10.48550/arXiv.2506.14619)\n", + "\n", + "Since FuRBO is based on Scalable Constrained Bayesian Optimization (SCBO), this tutorial shares part of the same code as the SCBO Tutorial (https://botorch.org/docs/tutorials/scalable_constrained)\n" + ] + }, + { + "cell_type": "markdown", + "id": "762be478-50e4-4af4-aa6d-d3b566649c5e", + "metadata": {}, + "source": [ + "### Objective function\n", + "\n", + "Start by defining the 10D Ackley function for evaluation during the optimization loop." + ] + }, + { + "cell_type": "code", + "execution_count": 170, + "id": "890f1a54-b6cf-4af4-9bfb-1835b2f737a6", + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "from botorch.test_functions import Ackley\n", + "from botorch.utils.transforms import unnormalize\n", + "\n", + "class ack():\n", + " \n", + " def __init__(self, dim, negate, **tkwargs):\n", + " \n", + " self.fun = Ackley(dim = dim, negate = negate).to(**tkwargs)\n", + " self.fun.bounds[0, :].fill_(-5)\n", + " self.fun.bounds[1, :].fill_(10)\n", + " self.dim = self.fun.dim\n", + " self.lb, self.ub = self.fun.bounds\n", + " \n", + " def eval_(self, x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", + " return self.fun(unnormalize(x, [self.lb, self.ub]))" + ] + }, + { + "cell_type": "markdown", + "id": "6b710672-51d0-4fc5-a3e2-ffb3da6f5649", + "metadata": {}, + "source": [ + "### Constraint functions\n", + "\n", + "Define two constraint functions." + ] + }, + { + "cell_type": "markdown", + "id": "64122b23-fc01-4e1a-94de-2fba4839fe72", + "metadata": {}, + "source": [ + "\n", + "1. Constraint $c_1$: enforce the $\\sum_{i=1}^{10} x_i \\leq T$. We will specify $T=0$ later. " + ] + }, + { + "cell_type": "code", + "execution_count": 171, + "id": "228d816a-6452-4078-b3fd-6a42569237c3", + "metadata": {}, + "outputs": [], + "source": [ + "class sum_():\n", + " def __init__(self, threshold, lb, ub):\n", + " \n", + " self.lb = lb\n", + " self.ub = ub\n", + " self.threshold = threshold\n", + " return \n", + " \n", + " def c(self, x):\n", + " \"\"\"This is a helper function we use to unnormalize and evaluate a point\"\"\"\n", + " return x.sum() - self.threshold\n", + " \n", + " def eval_(self, x):\n", + " return self.c(unnormalize(x, [self.lb, self.ub]))" + ] + }, + { + "cell_type": "markdown", + "id": "08472c8a-67de-4206-bf0f-871e40edfe7c", + "metadata": {}, + "source": [ + "2. Constraint $c_2$: enforce the $l_2$ norm $\\| \\mathbb{x}\\|_2 \\leq T$. We will specify $T=0.5$ later." + ] + }, + { + "cell_type": "code", + "execution_count": 172, + "id": "1e0f4e8d-657f-49d8-bb59-eb8c2ff4a9f5", + "metadata": {}, + "outputs": [], + "source": [ + "class norm_():\n", + " def __init__(self, threshold, lb, ub):\n", + " \n", + " self.lb = lb\n", + " self.ub = ub\n", + " self.threshold = threshold\n", + " return \n", + " \n", + " def c(self, x):\n", + " return torch.norm(x, p=2) - self.threshold\n", + " \n", + " def eval_(self, x):\n", + " \"\"\"This is a helper function we use to unnormalize and evaluate a point\"\"\"\n", + " return self.c(unnormalize(x, [self.lb, self.ub]))" + ] + }, + { + "cell_type": "markdown", + "id": "e3c6e1cd-15de-4985-ac6c-bf96c6eafc24", + "metadata": {}, + "source": [ + "### Define FuRBO Class\n", + "Define a class to hold the information needed for the optimization loop. \n", + "\n", + "The state is updated with the samples evaluated at each iteration. \n", + "\n", + "Prior to the class, two utility functions are defined. The first one identifies the current best sample, while the second one fits a GPR model to the current dataset. \n", + "\n", + "The ```Furbo_state``` class features a function to reset the status when restarting. Notice that the state is emptied when restarting. Therefore the samples previously evaluated are extracted and saved (see main optimization loop)." + ] + }, + { + "cell_type": "code", + "execution_count": 173, + "id": "020338e2-9eaf-49cf-9e5c-fd00e1a46835", + "metadata": {}, + "outputs": [], + "source": [ + "import gpytorch\n", + "import numpy as np\n", + "\n", + "from botorch.fit import fit_gpytorch_mll\n", + "from botorch.models import SingleTaskGP\n", + "from botorch.models.transforms.outcome import Standardize\n", + "\n", + "from gpytorch.constraints import Interval\n", + "from gpytorch.kernels import MaternKernel, ScaleKernel\n", + "from gpytorch.likelihoods import GaussianLikelihood\n", + "from gpytorch.mlls import ExactMarginalLogLikelihood\n", + "\n", + "from scipy.stats import invgauss\n", + "from scipy.stats import ecdf\n", + "\n", + "from torch import Tensor\n", + "\n", + "def get_best_index_for_batch(n_tr, Y: Tensor, C: Tensor):\n", + " \"\"\"Return the index for the best point. One for each trust region.\n", + " For reference, see https://botorch.org/docs/tutorials/scalable_constrained_bo/\"\"\"\n", + " is_feas = (C <= 0).all(dim=-1)\n", + " if is_feas.any(): # Choose best feasible candidate\n", + " score = Y.clone()\n", + " score[~is_feas] = -float(\"inf\")\n", + " return torch.topk(score.reshape(-1), k=n_tr).indices\n", + " return torch.topk(C.clamp(min=0).sum(dim=-1), k=n_tr, largest=False).indices # Return smallest violation\n", + "\n", + "def get_fitted_model(X,\n", + " Y,\n", + " dim,\n", + " max_cholesky_size):\n", + " '''Function to fit a GPR to a given set of data.\n", + " For reference, see https://botorch.org/docs/tutorials/scalable_constrained_bo/'''\n", + " likelihood = GaussianLikelihood(noise_constraint=Interval(1e-8, 1e-3))\n", + " covar_module = ScaleKernel( # Use the same lengthscale prior as in the TuRBO paper\n", + " MaternKernel(nu=2.5, ard_num_dims=dim, lengthscale_constraint=Interval(0.005, 4.0))\n", + " )\n", + " model = SingleTaskGP(\n", + " X,\n", + " Y,\n", + " covar_module=covar_module,\n", + " likelihood=likelihood,\n", + " outcome_transform=Standardize(m=1),\n", + " )\n", + " mll = ExactMarginalLogLikelihood(model.likelihood, model)\n", + "\n", + " with gpytorch.settings.max_cholesky_size(max_cholesky_size):\n", + " fit_gpytorch_mll(mll, \n", + " optimizer_kwargs={'method': 'L-BFGS-B'})\n", + "\n", + " return model\n", + "\n", + "from botorch.models.model_list_gp_regression import ModelListGP\n", + "from torch.quasirandom import SobolEngine\n", + "\n", + "class Furbo_state():\n", + " '''Class to track optimization status with restart'''\n", + " # Initialization of the status\n", + " def __init__(self, \n", + " obj, # Objective function\n", + " cons, # Constraints function\n", + " batch_size, # Batch size of each iteration\n", + " n_init, # Number of initial points to evaluate\n", + " n_iteration, # Number of total iterations\n", + " **tkwargs):\n", + " \n", + " # Objective function handle\n", + " self.obj = obj\n", + " \n", + " # Constraints function handle\n", + " self.cons = cons\n", + " \n", + " # Domain bounds\n", + " self.lb = obj.lb\n", + " self.ub = obj.ub\n", + " \n", + " # Problem dimensions\n", + " self.batch_size: int = batch_size # Dimension of the batch at each iteration\n", + " self.n_init: int = n_init # Number of initial samples\n", + " self.dim: int = obj.dim # Dimension of the problem\n", + " \n", + " # Trust regions information\n", + " self.tr_ub: float = torch.ones((1, self.dim), **tkwargs) # Upper bounds of trust region\n", + " self.tr_lb: float = torch.zeros((1, self.dim), **tkwargs) # Lower bounds of trust region\n", + " self.tr_vol: float = torch.prod(self.tr_ub - self.tr_lb, dim=1) # Volume of trust region\n", + " self.radius: float = 1.0 # Percentage around which the trust region is built\n", + " self.radius_min: float = 0.5**7 # Minimum percentage for trust region\n", + "\n", + " # Trust region updating \n", + " self.failure_counter: int = 0 # Counter of failure points to asses how algorithm is going\n", + " self.success_counter: int = 0 # Counter of success points to asses how algorithm is going\n", + " self.success_tolerance: int = 2 # Success tolerance for \n", + " self.failure_tolerance: int = 3 # Failure tolerance for\n", + " \n", + " # Tensor to save current batch information\n", + " self.batch_X: Tensor # Current batch to evaluate: X values\n", + " self.batch_Y: Tensor # Current batch to evaluate: Y value\n", + " self.batch_C: Tensor # Current batch to evaluate: C values\n", + " \n", + " # Stopping criteria information\n", + " self.n_iteration: int = n_iteration # Maximum number of iterations allowed\n", + " self.it_counter: int = 0 # Counter of iterations for stopping\n", + " self.finish_trigger: bool = False # Trigger to stop optimization\n", + " self.failed_GP : bool = False # Flag to pass to failed_GP in FuRBORestart\n", + " \n", + " # Restart criteria information\n", + " self.restart_trigger: bool = False\n", + " \n", + " # Sobol sampler engine\n", + " self.sobol = SobolEngine(dimension=self.dim, scramble=True, seed=1)\n", + " \n", + " # Update the status\n", + " def update(self,\n", + " X_next, # Samples X (input values) to update the status\n", + " Y_next, # Samples Y (objective value) to update the status\n", + " C_next, # Samples C (constraints values) to update the status\n", + " **tkwargs):\n", + " \n", + " '''Function to update optimization status'''\n", + " \n", + " # Merge current batch with previously evaluated samples\n", + " if not hasattr(self, 'X'):\n", + " # If there are no previous samples, declare the Tensors\n", + " self.X = X_next\n", + " self.Y = Y_next\n", + " self.C = C_next\n", + " else:\n", + " # Else, concatenate the new batch to the previous samples\n", + " self.X = torch.cat((self.X, X_next), dim=0)\n", + " self.Y = torch.cat((self.Y, Y_next), dim=0)\n", + " self.C = torch.cat((self.C, C_next), dim=0)\n", + "\n", + " # update GPR surrogates\n", + " try:\n", + " self.Y_model = get_fitted_model(self.X, self.Y, self.dim, max_cholesky_size = float(\"inf\"))\n", + " self.C_model = ModelListGP(*[get_fitted_model(self.X, C.reshape([C.shape[0],1]), self.dim, max_cholesky_size = float(\"inf\")) for C in self.C.t()])\n", + " except:\n", + " # If update fail, flag to stop entire optimization\n", + " self.failed_GP = True\n", + " \n", + " # Update batch information \n", + " self.batch_X = X_next\n", + " self.batch_Y = Y_next\n", + " self.batch_C = C_next\n", + " \n", + " # Update best value\n", + " # Find the best value among the candidates\n", + " best_id = get_best_index_for_batch(n_tr=1, Y=self.Y, C=self.C)\n", + " \n", + " # Update success and failure counters for trust region update\n", + " # If attribute 'best_X' does not exist, DoE was just evaluated -> no update on counters\n", + " if hasattr(self, 'best_X'):\n", + " if (self.C[best_id] <= 0).all():\n", + " # At least one new candidate is feasible\n", + " if (self.Y[best_id] > self.best_Y).any() or (self.best_C > 0).any():\n", + " self.success_counter += 1\n", + " self.failure_counter = 0 \n", + " else:\n", + " self.success_counter = 0\n", + " self.failure_counter += 1\n", + " else:\n", + " # No new candidate is feasible\n", + " total_violation_next = self.C[best_id].clamp(min=0).sum(dim=-1)\n", + " total_violation_center = self.best_C.clamp(min=0).sum(dim=-1)\n", + " if total_violation_next < total_violation_center:\n", + " self.success_counter += 1\n", + " self.failure_counter = 0\n", + " else:\n", + " self.success_counter = 0\n", + " self.failure_counter += 1\n", + " \n", + " # Update best values\n", + " self.best_X = self.X[best_id]\n", + " self.best_Y = self.Y[best_id]\n", + " self.best_C = self.C[best_id]\n", + " \n", + " # Update iteration counter\n", + " self.it_counter += 1\n", + " \n", + " def reset_status(self,\n", + " **tkwargs):\n", + " '''Function to reset the status for the restart'''\n", + " \n", + " # Reset trust regions size\n", + " self.tr_ub: float = torch.ones((1, self.dim), **tkwargs) # Upper bounds of trust region\n", + " self.tr_lb: float = torch.zeros((1, self.dim), **tkwargs) # Lower bounds of trust region\n", + " self.tr_vol: float = torch.prod(self.tr_ub - self.tr_lb, dim=1) # Volume of trust region\n", + " self.radius: float = 1.0 # Percentage around which the trust region is built\n", + " self.radius_min: float = 0.5**7 # Minimum percentage for trust region\n", + "\n", + " # Reset counters to change trust region size \n", + " self.failure_counter: int = 0 # Counter of failure points to asses how algorithm is going\n", + " self.success_counter: int = 0 # Counter of success points to asses how algorithm is going\n", + " \n", + " # Reset restart criteria trigger\n", + " self.restart_trigger: bool = False # Trigger to restart optimization\n", + " self.failed_GP: bool = False # Reset GPR failure trigger\n", + " \n", + " # Delete tensors with samples for training GPRs\n", + " if hasattr(self, 'X'):\n", + " del self.X\n", + " del self.Y\n", + " del self.C\n", + " \n", + " # Delete tensors with best value so far\n", + " if hasattr(self, 'best_X'):\n", + " del self.best_X\n", + " del self.best_Y\n", + " del self.best_C\n", + " \n", + " # Clear GPU memory\n", + " if tkwargs[\"device\"] == \"cuda\":\n", + " torch.cuda.empty_cache() " + ] + }, + { + "cell_type": "markdown", + "id": "58fee9fb-ca01-4024-8859-1fc3d9d4aea4", + "metadata": {}, + "source": [ + "### Define trust region\n", + "\n", + "Define a set of functions to evaluate the trust region. First sample according to a Multinormal distribution the GPR surrogates (both objective and constraints). Rank the samples according to both the objective and violation estimation. Take the top $10\\%$ of the samples according to the rank. The trust region is defined as a hyperbox enclosing the picked samples. " + ] + }, + { + "cell_type": "code", + "execution_count": 174, + "id": "3d36cf01-c5be-44ee-96bb-12564225bd7b", + "metadata": {}, + "outputs": [], + "source": [ + "def multivariate_circular(centre, # Centre of the multivariate distribution\n", + " radius, # Radius of the multivariate distribution\n", + " n_samples, # Number of samples to evaluate\n", + " lb = None, # Domain lower bound\n", + " ub = None, # Domain upper bound\n", + " **tkwargs):\n", + " '''Function to generate multivariate distribution of given radius and centre within a given domain.'''\n", + " # Dimension of the design domain\n", + " dim = centre.shape[0]\n", + " \n", + " # Generate a multivariate normal distribution centered at 0\n", + " multivariate_normal = torch.distributions.multivariate_normal.MultivariateNormal(torch.zeros(dim, **tkwargs), 0.025*torch.eye(dim, **tkwargs))\n", + " \n", + " # Draw samples torch.distributions.multivariate_normal import MultivariateNormal\n", + " samples = multivariate_normal.sample(sample_shape=torch.Size([n_samples]))\n", + " \n", + " # Normalize each sample to have unit norm, then scale by the radius\n", + " norms = torch.norm(samples, dim=1, keepdim=True) # Euclidean norms\n", + " normalized_samples = samples / norms # Normalize to unit hypersphere\n", + " scaled_samples = normalized_samples * torch.rand(n_samples, 1, **tkwargs) * radius # Scale by random factor within radius\n", + " \n", + " # Translate samples to be centered at centre\n", + " samples = scaled_samples + centre\n", + " \n", + " \n", + " # Trim samples outside domain\n", + " for dim in range(len(lb)):\n", + " samples = samples[torch.where(samples[:,dim]>=lb[dim])]\n", + " samples = samples[torch.where(samples[:,dim]<=ub[dim])]\n", + " \n", + " return samples\n", + "\n", + "def update_tr(state, # FuRBO state\n", + " percentage = 0.1, # Percentage to define trust region (default 10%)\n", + " **tkwargs):\n", + " '''Function to sample Multinormal Distribution of GPRs and define trust region'''\n", + " # Update the trust regions based on the feasible region\n", + " n_samples = 1000 * state.dim\n", + " lb = torch.zeros(state.dim, **tkwargs)\n", + " ub = torch.ones(state.dim, **tkwargs)\n", + " \n", + " # Update radius dimension\n", + " if state.success_counter == state.success_tolerance: # Expand trust region\n", + " state.radius = min(2.0 * state.radius, 1.0)\n", + " state.success_counter = 0\n", + " elif state.failure_counter == state.failure_tolerance: # Shrink trust region\n", + " state.radius /= 2.0\n", + " state.failure_counter = 0\n", + " \n", + " for ind, x_candidate in enumerate(state.best_X):\n", + " # Generate the samples to evaluathe the feasible area on\n", + " radius = state.radius\n", + " samples = multivariate_circular(x_candidate, radius, n_samples, lb=lb, ub=ub, **tkwargs)\n", + " \n", + " # Evaluate samples on the models of the objective -> yy Tensor\n", + " state.Y_model.eval()\n", + " with torch.no_grad():\n", + " posterior = state.Y_model.posterior(samples)\n", + " samples_yy = posterior.mean.squeeze()\n", + " \n", + " # Evaluate samples on the models of the constraints -> yy Tensor\n", + " state.C_model.eval()\n", + " with torch.no_grad():\n", + " posterior = state.C_model.posterior(samples)\n", + " samples_cc = posterior.mean\n", + " \n", + " # Combine the constraints values\n", + " # Normalize\n", + " samples_cc /= torch.abs(samples_cc).max(dim=0).values\n", + " samples_cc = torch.max(samples_cc, dim=1).values\n", + " \n", + " # Take the best X% of the drawn samples to define the trust region\n", + " n_samples_tr = int(n_samples * percentage)\n", + " \n", + " # Order the samples for feasibility and for best objective\n", + " if torch.any(samples_cc < 0):\n", + " \n", + " feasible_samples_id = torch.where(samples_cc <= 0)[0]\n", + " infeasible_samples_id = torch.where(samples_cc > 0)[0]\n", + " \n", + " feasible_cc = -1 * samples_yy[feasible_samples_id]\n", + " infeasible_cc = samples_cc[infeasible_samples_id]\n", + " \n", + " feasible_sorted, feasible_sorted_id = torch.sort(feasible_cc)\n", + " infeasible_sorted, infeasible_sorted_id = torch.sort(infeasible_cc)\n", + " \n", + " original_feasible_sorted_indices = feasible_samples_id[feasible_sorted_id]\n", + " original_infeasible_sorted_indices = infeasible_samples_id[infeasible_sorted_id]\n", + " \n", + " top_indices = torch.cat((original_feasible_sorted_indices, original_infeasible_sorted_indices))[:n_samples_tr]\n", + " \n", + " else:\n", + " \n", + " if n_samples_tr > len(samples_cc):\n", + " n_samples_tr = len(samples_cc)\n", + " \n", + " if n_samples_tr < 4:\n", + " n_samples_tr = 4\n", + " \n", + " top_values, top_indices = torch.topk(samples_cc, n_samples_tr, largest=False)\n", + " \n", + " # Set the box around the selected samples\n", + " state.tr_lb[ind] = torch.min(samples[top_indices], dim=0).values\n", + " state.tr_ub[ind] = torch.max(samples[top_indices], dim=0).values\n", + " \n", + " # Update volume of trust region\n", + " state.tr_vol[ind] = torch.prod(state.tr_ub[ind] - state.tr_lb[ind])\n", + " \n", + " # return updated status with new trust regions\n", + " return state" + ] + }, + { + "cell_type": "markdown", + "id": "f49690e5-6505-47df-89f7-1a56f9b087b2", + "metadata": {}, + "source": [ + "### Sampling strategies\n", + "\n", + "Define a function to generate an initial experimental design using Sobol sampling strategy, similarly to SCBO (https://botorch.org/docs/tutorials/scalable_constrained_bo/)." + ] + }, + { + "cell_type": "code", + "execution_count": 175, + "id": "0116ca79-7555-4da3-bfd4-69941926eb11", + "metadata": {}, + "outputs": [], + "source": [ + "def get_initial_points(state,\n", + " **tkwargs):\n", + " '''Function to generate the initial experimental design'''\n", + " X_init = state.sobol.draw(n=state.n_init).to(**tkwargs)\n", + " return X_init" + ] + }, + { + "cell_type": "markdown", + "id": "55726979-92f6-488f-869c-2fa6140f6b85", + "metadata": {}, + "source": [ + "Define a function to identify the best next candidate point, similar to SCBO(https://botorch.org/docs/tutorials/scalable_constrained_bo/)." + ] + }, + { + "cell_type": "code", + "execution_count": 176, + "id": "2d969ea7-2f1e-4433-b3b4-53413546c2f2", + "metadata": {}, + "outputs": [], + "source": [ + "from botorch.generation.sampling import ConstrainedMaxPosteriorSampling\n", + "\n", + "def generate_batch(state,\n", + " n_candidates,\n", + " **tkwargs):\n", + " '''Function to find net candidate optimum'''\n", + " assert state.X.min() >= 0.0 and state.X.max() <= 1.0 and torch.all(torch.isfinite(state.Y))\n", + "\n", + " # Initialize tensor with samples to evaluate\n", + " X_next = torch.ones((state.batch_size, state.dim), **tkwargs)\n", + " \n", + " # Iterate over the several trust regions\n", + "\n", + " tr_lb = state.tr_lb[0]\n", + " tr_ub = state.tr_ub[0]\n", + "\n", + " # Thompson Sampling w/ Constraints (like SCBO)\n", + " pert = state.sobol.draw(n_candidates).to(**tkwargs)\n", + " pert = tr_lb + (tr_ub - tr_lb) * pert\n", + "\n", + " # Create a perturbation mask\n", + " prob_perturb = min(20.0 / state.dim, 1.0)\n", + " mask = torch.rand(n_candidates, state.dim, **tkwargs) <= prob_perturb\n", + " ind = torch.where(mask.sum(dim=1) == 0)[0]\n", + " mask[ind, torch.randint(0, state.dim - 1, size=(len(ind),), device=tkwargs['device'])] = 1\n", + "\n", + " # Create candidate points from the perturbations and the mask\n", + " X_cand = state.best_X[0].expand(n_candidates, state.dim).clone()\n", + " X_cand[mask] = pert[mask]\n", + " \n", + " # Sample on the candidate points using Constrained Max Posterior Sampling\n", + " constrained_thompson_sampling = ConstrainedMaxPosteriorSampling(\n", + " model=state.Y_model, constraint_model=state.C_model, replacement=False\n", + " )\n", + " with torch.no_grad():\n", + " X_next[0*state.batch_size:0*state.batch_size+state.batch_size, :] = constrained_thompson_sampling(X_cand, num_samples=state.batch_size)\n", + " \n", + " return X_next" + ] + }, + { + "cell_type": "markdown", + "id": "024e10f4-4de9-433b-8827-c58a7177784f", + "metadata": {}, + "source": [ + "### Stopping criterion\n", + "\n", + "Define a function to detect when the maximum number of iterations is met." + ] + }, + { + "cell_type": "code", + "execution_count": 177, + "id": "189aae72-f033-49db-bcc8-0e791774bd76", + "metadata": {}, + "outputs": [], + "source": [ + "def stopping_criterion(state, n_iteration):\n", + " '''Function to evaluate if the maximum number of allowed iterations is reached.'''\n", + " if state.it_counter <= n_iteration:\n", + " return False\n", + " return True" + ] + }, + { + "cell_type": "markdown", + "id": "44f15711-8503-4226-8ee0-171f26f7b8f4", + "metadata": {}, + "source": [ + "### Restart criterion\n", + "\n", + "Detect when the GPR fitting process fails to stop the optimization.curve" + ] + }, + { + "cell_type": "code", + "execution_count": 178, + "id": "f0d2b342-601b-4d07-9fe3-459f28ecead2", + "metadata": {}, + "outputs": [], + "source": [ + "def GP_restart_criterion(state):\n", + " '''Function to evaluate if a GPR failed during the optimization.'''\n", + " if state.failed_GP:\n", + " print(\"GPR failed.\")\n", + " return True\n", + " return False" + ] + }, + { + "cell_type": "markdown", + "id": "476bada4", + "metadata": {}, + "source": [ + "Detect when the radius becomes too small." + ] + }, + { + "cell_type": "code", + "execution_count": 179, + "id": "81f9bd26", + "metadata": {}, + "outputs": [], + "source": [ + "def restart_criterion(state, radius_min):\n", + " '''Function to evaluate if MND radius is smaller than the minimum allowed radius'''\n", + " if state.radius < radius_min:\n", + " return True\n", + " return False" + ] + }, + { + "cell_type": "markdown", + "id": "a80c7b75-a62d-46c2-aa80-28f6f29501be", + "metadata": {}, + "source": [ + "### Main optimization loop" + ] + }, + { + "cell_type": "code", + "execution_count": 180, + "id": "b9d52417-aaa5-40b6-bf07-12c074460283", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0) No feasible point yet! Smallest total violation: 5.72e-01, MND radius: 1.0\n", + "1) Best value: -1.72e+00, MND radius: 1.0\n", + "2) Best value: -1.72e+00, MND radius: 1.0\n", + "3) Best value: -7.71e-01, MND radius: 1.0\n", + "4) Best value: -7.71e-01, MND radius: 1.0\n", + "5) Best value: -7.71e-01, MND radius: 1.0\n", + "6) Best value: -2.39e-01, MND radius: 1.0\n", + "7) Best value: -2.37e-01, MND radius: 1.0\n", + "8) Best value: -2.37e-01, MND radius: 1.0\n", + "9) Best value: -8.69e-02, MND radius: 1.0\n", + "10) Best value: -8.32e-02, MND radius: 1.0\n", + "11) Best value: -8.32e-02, MND radius: 1.0\n", + "12) Best value: -8.32e-02, MND radius: 1.0\n", + "13) Best value: -8.32e-02, MND radius: 1.0\n", + "14) Best value: -8.32e-02, MND radius: 0.5\n", + "15) Best value: -8.32e-02, MND radius: 0.5\n", + "16) Best value: -2.84e-02, MND radius: 0.5\n", + "17) Best value: -2.84e-02, MND radius: 0.5\n", + "18) Best value: -2.84e-02, MND radius: 0.5\n", + "19) Best value: -2.84e-02, MND radius: 0.5\n", + "20) Best value: -2.84e-02, MND radius: 0.25\n", + "21) Best value: -2.84e-02, MND radius: 0.25\n", + "22) Best value: -2.84e-02, MND radius: 0.25\n", + "23) Best value: -2.21e-02, MND radius: 0.125\n", + "24) Best value: -1.57e-02, MND radius: 0.125\n", + "25) Best value: -1.57e-02, MND radius: 0.25\n", + "26) Best value: -1.57e-02, MND radius: 0.25\n", + "27) Best value: -1.57e-02, MND radius: 0.25\n", + "28) Best value: -1.57e-02, MND radius: 0.125\n", + "29) Best value: -1.57e-02, MND radius: 0.125\n", + "30) Best value: -1.56e-02, MND radius: 0.125\n", + "31) Best value: -1.56e-02, MND radius: 0.125\n", + "32) Best value: -1.56e-02, MND radius: 0.125\n", + "33) Best value: -1.56e-02, MND radius: 0.125\n", + "34) Best value: -1.46e-02, MND radius: 0.0625\n", + "35) Best value: -1.46e-02, MND radius: 0.0625\n", + "36) Best value: -1.39e-02, MND radius: 0.0625\n", + "37) Best value: -1.16e-02, MND radius: 0.0625\n", + "38) Best value: -1.16e-02, MND radius: 0.125\n", + "39) Best value: -1.16e-02, MND radius: 0.125\n", + "40) Best value: -1.16e-02, MND radius: 0.125\n", + "41) Best value: -1.16e-02, MND radius: 0.0625\n", + "42) Best value: -1.16e-02, MND radius: 0.0625\n", + "43) Best value: -7.18e-03, MND radius: 0.0625\n", + "44) Best value: -7.18e-03, MND radius: 0.0625\n", + "45) Best value: -7.18e-03, MND radius: 0.0625\n", + "46) Best value: -7.18e-03, MND radius: 0.0625\n", + "47) Best value: -3.63e-03, MND radius: 0.03125\n", + "48) Best value: -3.63e-03, MND radius: 0.03125\n", + "GPR failed.\n", + "49) No feasible point yet! Smallest total violation: 4.53e-01, MND radius: 1.0\n", + "50) Best value: -2.94e+00, MND radius: 1.0\n", + "51) Best value: -2.94e+00, MND radius: 1.0\n", + "52) Best value: -2.94e+00, MND radius: 1.0\n", + "53) Best value: -2.94e+00, MND radius: 1.0\n", + "54) Best value: -1.44e+00, MND radius: 0.5\n", + "55) Best value: -2.58e-01, MND radius: 0.5\n", + "56) Best value: -2.58e-01, MND radius: 1.0\n", + "57) Best value: -7.49e-02, MND radius: 1.0\n", + "58) Best value: -7.49e-02, MND radius: 1.0\n", + "59) Best value: -6.21e-02, MND radius: 1.0\n", + "60) Best value: -6.21e-02, MND radius: 1.0\n", + "61) Best value: -6.21e-02, MND radius: 1.0\n", + "62) Best value: -6.21e-02, MND radius: 1.0\n", + "63) Best value: -6.21e-02, MND radius: 0.5\n", + "64) Best value: -6.21e-02, MND radius: 0.5\n", + "65) Best value: -2.03e-02, MND radius: 0.5\n", + "66) Best value: -2.03e-02, MND radius: 0.5\n", + "67) Best value: -2.03e-02, MND radius: 0.5\n", + "68) Best value: -2.03e-02, MND radius: 0.5\n", + "69) Best value: -2.03e-02, MND radius: 0.25\n", + "70) Best value: -2.03e-02, MND radius: 0.25\n", + "71) Best value: -2.03e-02, MND radius: 0.25\n", + "72) Best value: -1.33e-02, MND radius: 0.125\n", + "73) Best value: -1.33e-02, MND radius: 0.125\n", + "74) Best value: -1.33e-02, MND radius: 0.125\n", + "75) Best value: -1.33e-02, MND radius: 0.125\n", + "76) Best value: -3.34e-03, MND radius: 0.125\n", + "77) Best value: -3.34e-03, MND radius: 0.125\n", + "78) Best value: -3.34e-03, MND radius: 0.125\n", + "79) Best value: -3.34e-03, MND radius: 0.125\n", + "80) Best value: -1.99e-03, MND radius: 0.0625\n", + "81) Best value: -1.99e-03, MND radius: 0.0625\n", + "82) Best value: -1.99e-03, MND radius: 0.0625\n", + "83) Best value: -1.99e-03, MND radius: 0.0625\n", + "84) Best value: -1.99e-03, MND radius: 0.03125\n", + "85) Best value: -1.99e-03, MND radius: 0.03125\n", + "86) Best value: -1.99e-03, MND radius: 0.03125\n", + "87) Best value: -1.99e-03, MND radius: 0.015625\n", + "88) Best value: -1.99e-03, MND radius: 0.015625\n", + "89) Best value: -1.99e-03, MND radius: 0.015625\n", + "90) Best value: -1.99e-03, MND radius: 0.0078125\n", + "91) Best value: -1.99e-03, MND radius: 0.0078125\n", + "92) Best value: -1.99e-03, MND radius: 0.0078125\n", + "93) No feasible point yet! Smallest total violation: 2.07e+00, MND radius: 1.0\n", + "94) Best value: -3.47e+00, MND radius: 1.0\n", + "95) Best value: -3.47e+00, MND radius: 1.0\n", + "96) Best value: -2.16e+00, MND radius: 1.0\n", + "97) Best value: -2.16e+00, MND radius: 1.0\n", + "98) Best value: -2.16e+00, MND radius: 1.0\n", + "99) Best value: -2.16e+00, MND radius: 1.0\n", + "100) Best value: -4.88e-01, MND radius: 0.5\n" + ] + } + ], + "source": [ + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + " \n", + "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n", + "dtype = torch.double\n", + "tkwargs = {\"device\": device, \"dtype\": dtype}\n", + "\n", + "# Initialize FuRBO\n", + "obj = ack(dim = 2,\n", + " negate=True,\n", + " **tkwargs)\n", + "cons = list([sum_(threshold = 0,\n", + " lb = obj.lb,\n", + " ub = obj.ub), \n", + " norm_(threshold = 0.5, \n", + " lb = obj.lb, \n", + " ub = obj.ub)])\n", + "batch_size = int(1)#3 * obj.dim)\n", + "n_init = int(10)# * obj.dim)\n", + "n_iteration = int(100)# * obj.dim)\n", + "N_CANDIDATES = 2000\n", + "\n", + "# FuRBO state initialization\n", + "FuRBO_status = Furbo_state(obj = obj, # Objective function\n", + " cons = cons, # Constraints function\n", + " batch_size = batch_size, # Batch size of each iteration\n", + " n_init = n_init, # Number of initial points to evaluate\n", + " n_iteration = n_iteration, # Number of iterations\n", + " **tkwargs)\n", + "\n", + "# Initiate lists to save samples over the restarts\n", + "X_best, Y_best, C_best = [], [], []\n", + "X_all, Y_all, C_all = [], [], []\n", + "\n", + "# Continue optimization the stopping criterions isn't triggered\n", + "while not FuRBO_status.finish_trigger: \n", + " \n", + " # Reset status for restarting\n", + " FuRBO_status.reset_status(**tkwargs)\n", + " \n", + " # generate intial batch of X\n", + " X_next = get_initial_points(FuRBO_status, **tkwargs)\n", + " \n", + " # Reset and restart optimization\n", + " while not FuRBO_status.restart_trigger and not FuRBO_status.finish_trigger:\n", + " \n", + " # Evaluate current batch (samples in X_next)\n", + " Y_next = []\n", + " C_next = []\n", + " for x in X_next:\n", + " # Evaluate batch on obj ...\n", + " Y_next.append(FuRBO_status.obj.eval_(x))\n", + " # ... and constraints\n", + " C_next.append([c.eval_(x) for c in FuRBO_status.cons])\n", + " \n", + " # process vector for PyTorch\n", + " Y_next = torch.tensor(Y_next).unsqueeze(-1).to(**tkwargs)\n", + " C_next = torch.tensor(C_next).to(**tkwargs)\n", + " \n", + " # Update FuRBO status with newly evaluated batch\n", + " FuRBO_status.update(X_next, Y_next, C_next, **tkwargs) \n", + " \n", + " # Printing current best\n", + " # If a feasible has been evaluated -> print current optimum (feasible sample with best objective value)\n", + " if (FuRBO_status.best_C <= 0).all():\n", + " best = FuRBO_status.best_Y.amax()\n", + " print(f\"{FuRBO_status.it_counter-1}) Best value: {best:.2e},\"\n", + " f\" MND radius: {FuRBO_status.radius}\")\n", + " \n", + " # Else, if no feasible has been evaluated -> print smallest violation (the sample that violatest the least all constraints)\n", + " else:\n", + " violation = FuRBO_status.best_C.clamp(min=0).sum()\n", + " print(f\"{FuRBO_status.it_counter-1}) No feasible point yet! Smallest total violation: \"\n", + " f\"{violation:.2e}, MND radius: {FuRBO_status.radius}\")\n", + " \n", + " # Update Trust regions\n", + " FuRBO_status = update_tr(FuRBO_status,\n", + " **tkwargs)\n", + " \n", + " # generate next batch to evaluate \n", + " X_next = generate_batch(FuRBO_status, N_CANDIDATES, **tkwargs)\n", + " \n", + " # Check if stopping criterion is met (budget exhausted and if GP failed)\n", + " FuRBO_status.finish_trigger = stopping_criterion(FuRBO_status, n_iteration) \n", + " \n", + " # Check if restart criterion is met\n", + " FuRBO_status.restart_trigger = (restart_criterion(FuRBO_status, FuRBO_status.radius_min) or GP_restart_criterion(FuRBO_status))\n", + "\n", + " # Save samples evaluated before resetting the status\n", + " X_all.append(FuRBO_status.X)\n", + " Y_all.append(FuRBO_status.Y)\n", + " C_all.append(FuRBO_status.C)\n", + "\n", + " # Save best sample of this run\n", + " X_best.append(FuRBO_status.best_X)\n", + " Y_best.append(FuRBO_status.best_Y)\n", + " C_best.append(FuRBO_status.best_C)" + ] + }, + { + "cell_type": "markdown", + "id": "a3d28f6c-5940-4d56-a3b5-4635980db76f", + "metadata": {}, + "source": [ + "### Printing result and plotting convergence curve\n", + "\n", + "Print the best-evaluated sample (over all restarts) and the objective value (if a feasible sample was found) or the smallest violation (if no feasible sample was found)." + ] + }, + { + "cell_type": "code", + "execution_count": 181, + "id": "027a9ec9-930a-48d0-b481-ffe9e9ca0d90", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimization finished \n", + "\t Optimum: -1.99e-03, \n", + "\t X: tensor([[0.3333, 0.3333]], dtype=torch.float64)\n" + ] + } + ], + "source": [ + "# Print best value found so far\n", + "# Ri-elaborate for processing\n", + "X_best = torch.stack(X_best).to(**tkwargs)\n", + "Y_best = torch.stack(Y_best).to(**tkwargs)\n", + "C_best = torch.stack(C_best).to(**tkwargs)\n", + "\n", + "# If a feasible has been evaluated -> print current optimum sample and yielded value\n", + "if (C_best <= 0).any():\n", + " best = Y_best.amax()\n", + " bext = X_best[Y_best.argmax()]\n", + " print(\"Optimization finished \\n\"\n", + " f\"\\t Optimum: {best:.2e}, \\n\"\n", + " f\"\\t X: {bext}\")\n", + " \n", + "# Else, if no feasible has been evaluated -> print sample with smallest violation and the violation value\n", + "else:\n", + " violation = C_best.sum(dim=2).amin()\n", + " violaxion = X_best[C_best.sum(dim=2).argmin()]\n", + " \n", + " print(\"Optimization failed \\n\"\n", + " f\"\\t Smallest violation: {violation:.2e}, \\n\"\n", + " f\"\\t X: {violaxion}\")" + ] + }, + { + "cell_type": "markdown", + "id": "db5ae248-3f04-4173-a98a-6c0738e38510", + "metadata": {}, + "source": [ + "Plot the monotonic convergence curve" + ] + }, + { + "cell_type": "code", + "execution_count": 189, + "id": "671ec5e5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from matplotlib import rc\n", + "\n", + "def ensure_tensor(x, tkwargs, dim=0):\n", + " \"\"\"Helper function to concatenate or convert to tensor to handle potential multiple restarts.\"\"\"\n", + " if isinstance(x, (list, tuple)):\n", + " # flatten if there's only one element\n", + " if len(x) == 1:\n", + " x = x[0]\n", + " else:\n", + " x = torch.cat([xi if torch.is_tensor(xi) else torch.as_tensor(xi) for xi in x], dim=dim)\n", + " # ensure final type is tensor\n", + " if not torch.is_tensor(x):\n", + " x = torch.as_tensor(x)\n", + " return x.to(**tkwargs)\n", + "\n", + "Y_all = ensure_tensor(Y_all, tkwargs)\n", + "C_all = ensure_tensor(C_all, tkwargs)\n", + "\n", + "\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "score = Y_all.clone()\n", + "# Set infeasible to -inf\n", + "score[~(C_all <= 0).all(dim=-1)] = float(\"-inf\")\n", + "fx = np.maximum.accumulate(score.cpu())\n", + "plt.plot(fx, marker=\"\", lw=3)\n", + "\n", + "plt.plot([0, len(Y_all)], [obj.fun.optimal_value, obj.fun.optimal_value], \"k--\", lw=3)\n", + "plt.ylabel(\"Function value\", fontsize=18)\n", + "plt.xlabel(\"Number of evaluations\", fontsize=18)\n", + "plt.title(\"10D Ackley with 2 outcome constraints\", fontsize=20)\n", + "plt.xlim([0, len(Y_all)])\n", + "plt.ylim([np.floor(min(fx[(C_all <= 0).all(dim=-1)])), 1]) \n", + "\n", + "plt.grid(True)\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.15" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From d067dccbe998d8bce7dcc8c1d90c6de383ff686a Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Fri, 17 Oct 2025 15:40:17 +0200 Subject: [PATCH 2/9] Update FuRBO.ipynb Title update --- notebooks_community/FuRBO/FuRBO.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/notebooks_community/FuRBO/FuRBO.ipynb b/notebooks_community/FuRBO/FuRBO.ipynb index 98b46fd8b4..dce65f077e 100644 --- a/notebooks_community/FuRBO/FuRBO.ipynb +++ b/notebooks_community/FuRBO/FuRBO.ipynb @@ -5,13 +5,13 @@ "id": "b5831947-283e-4682-aae4-bd19bcce03e0", "metadata": {}, "source": [ - "# Feasible trust Region Bayesian Optimization (FuRBO)\n", + "# Feasibility-Driven trust Region Bayesian Optimization (FuRBO)\n", "\n", "- Contributors: paoloascia, elenaraponi\n", "- Last update 17 October 2025\n", "- BoTorch version: 0.12.0\n", "\n", - "This tutorial shows how to implement Feasible trust Region Bayesian Optimization (FuRBO) with restarts in a closed loop [1].\n", + "This tutorial shows how to implement Feasibility-Driven trust Region Bayesian Optimization (FuRBO) with restarts in a closed loop [1].\n", "\n", "In this tutorial, we optimize the 10D Ackley function on the domain $[−5,10]^{10}$ subject to two constraint functions $c_1$ and $c_2$. The problem maximizes the Ackley function while the constraints are fulfilled when $c_1(x) \\leq 0$ and $c_2(x) \\leq 0$.\n", "\n", From e396692ea7781e6b3e003198236907c00e34ebee Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Fri, 17 Oct 2025 15:41:10 +0200 Subject: [PATCH 3/9] Update FuRBO.ipynb SCBO url update --- notebooks_community/FuRBO/FuRBO.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notebooks_community/FuRBO/FuRBO.ipynb b/notebooks_community/FuRBO/FuRBO.ipynb index dce65f077e..f7cb6f6925 100644 --- a/notebooks_community/FuRBO/FuRBO.ipynb +++ b/notebooks_community/FuRBO/FuRBO.ipynb @@ -17,7 +17,7 @@ "\n", "[1] [Ascia, Paolo, Elena Raponi, Thomas Bäck and Fabian Duddeck. \"Feasibility-Driven Trust Region Bayesian Optimization.\" In AutoML 2025 Methods Track.](https://doi.org/10.48550/arXiv.2506.14619)\n", "\n", - "Since FuRBO is based on Scalable Constrained Bayesian Optimization (SCBO), this tutorial shares part of the same code as the SCBO Tutorial (https://botorch.org/docs/tutorials/scalable_constrained)\n" + "Since FuRBO is based on Scalable Constrained Bayesian Optimization (SCBO), this tutorial shares part of the same code as the SCBO Tutorial (https://botorch.org/docs/tutorials/scalable_constrained_bo/)\n" ] }, { From f1a3bbd246be478a8f58e8bb245655e746d547a6 Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Fri, 17 Oct 2025 15:41:43 +0200 Subject: [PATCH 4/9] Update FuRBO.ipynb Title update --- notebooks_community/FuRBO/FuRBO.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/notebooks_community/FuRBO/FuRBO.ipynb b/notebooks_community/FuRBO/FuRBO.ipynb index f7cb6f6925..f5580dd09c 100644 --- a/notebooks_community/FuRBO/FuRBO.ipynb +++ b/notebooks_community/FuRBO/FuRBO.ipynb @@ -5,13 +5,13 @@ "id": "b5831947-283e-4682-aae4-bd19bcce03e0", "metadata": {}, "source": [ - "# Feasibility-Driven trust Region Bayesian Optimization (FuRBO)\n", + "# Feasibility-driven trust Region Bayesian Optimization (FuRBO)\n", "\n", "- Contributors: paoloascia, elenaraponi\n", "- Last update 17 October 2025\n", "- BoTorch version: 0.12.0\n", "\n", - "This tutorial shows how to implement Feasibility-Driven trust Region Bayesian Optimization (FuRBO) with restarts in a closed loop [1].\n", + "This tutorial shows how to implement Feasibility-driven trust Region Bayesian Optimization (FuRBO) with restarts in a closed loop [1].\n", "\n", "In this tutorial, we optimize the 10D Ackley function on the domain $[−5,10]^{10}$ subject to two constraint functions $c_1$ and $c_2$. The problem maximizes the Ackley function while the constraints are fulfilled when $c_1(x) \\leq 0$ and $c_2(x) \\leq 0$.\n", "\n", From 0af79b74c51adfc7b5dc09af8dd4faea6e551c96 Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Thu, 4 Dec 2025 13:56:32 +0100 Subject: [PATCH 5/9] Review FuRBO.ipynb Review of the FuRBO tutorial after the changes requested. --- notebooks_community/FuRBO/FuRBO.ipynb | 1712 +++++++++++++++++++------ 1 file changed, 1300 insertions(+), 412 deletions(-) diff --git a/notebooks_community/FuRBO/FuRBO.ipynb b/notebooks_community/FuRBO/FuRBO.ipynb index f5580dd09c..1c13811606 100644 --- a/notebooks_community/FuRBO/FuRBO.ipynb +++ b/notebooks_community/FuRBO/FuRBO.ipynb @@ -8,31 +8,48 @@ "# Feasibility-driven trust Region Bayesian Optimization (FuRBO)\n", "\n", "- Contributors: paoloascia, elenaraponi\n", - "- Last update 17 October 2025\n", + "- Last update 04 December 2025\n", "- BoTorch version: 0.12.0\n", "\n", - "This tutorial shows how to implement Feasibility-driven trust Region Bayesian Optimization (FuRBO) with restarts in a closed loop [1].\n", + "In this tutorial, we show how to implement the Feasibility-driven trust Region Bayesian Optimization (FuRBO) [1] algorithm in a closed loop, with restarts. This is a Bayesian optimization (BO) algorithm developed specifically to handle severely constrained problems, while still performing well in simpler settings. \n", "\n", - "In this tutorial, we optimize the 10D Ackley function on the domain $[−5,10]^{10}$ subject to two constraint functions $c_1$ and $c_2$. The problem maximizes the Ackley function while the constraints are fulfilled when $c_1(x) \\leq 0$ and $c_2(x) \\leq 0$.\n", + "The key feature of FuRBO is the new definition of the trust region. At each iteration, we define the trust regions as a hyper-rectangle encapsulating subregions of the search space predicted to be promising by the Gaussian process regression (GPR) models of the objective and constraints. Compared to other trust-region-based methods, such as Scalable Constrained Bayesian Optimization (SCBO) [2], FuRBO offers higher flexibility in how the trust region evolves. Its position and shape adapt dynamically to the regions predicted to be both feasible and optimal, allowing the search to align with the structure of the GP models.\n", "\n", - "[1] [Ascia, Paolo, Elena Raponi, Thomas Bäck and Fabian Duddeck. \"Feasibility-Driven Trust Region Bayesian Optimization.\" In AutoML 2025 Methods Track.](https://doi.org/10.48550/arXiv.2506.14619)\n", + "In case of mildly constrained scenarios, the new definition of the trust region is advantageous when several samples are evaluated at each iteration (batches). \n", "\n", - "Since FuRBO is based on Scalable Constrained Bayesian Optimization (SCBO), this tutorial shares part of the same code as the SCBO Tutorial (https://botorch.org/docs/tutorials/scalable_constrained_bo/)\n" + "Therefore, we recommend using FuRBO when solving:\n", + " - high-dimensional constrained black-box problems;\n", + " - severely constrained black-box problems of any dimension D;\n", + " - constrained problems evaluated with large batch sizes (i.e., bigger than 1D).\n", + "\n", + "[1] [Paolo Ascia, Elena Raponi, Thomas Bäck and Fabian Duddeck. \"Feasibility-Driven Trust Region Bayesian Optimization.\" In AutoML 2025 Methods Track.](https://doi.org/10.48550/arXiv.2506.14619)\n", + "\n", + "[2] [David Eriksson and Matthias Poloczek. Scalable constrained Bayesian optimization. In International Conference on Artificial Intelligence and Statistics, pages 730–738. PMLR, 2021.](https://doi.org/10.48550/arxiv.2002.08526)\n" ] }, { "cell_type": "markdown", - "id": "762be478-50e4-4af4-aa6d-d3b566649c5e", + "id": "ba4aa821", + "metadata": {}, + "source": [ + "## Tutorial on FuRBO\n", + "\n", + "Tho show the implementation of FuRBO, we use a 20D Ackley function on the domain $[−5,10]^{10}$ subject to two constraint functions $c_1$ and $c_2$. The problem maximizes the Ackley function under the constraints $c_1(x) \\leq 0$ and $c_2(x) \\leq 0$. The Ackley function is translated in every dimension, so that the optimum of the unconstrained problem lies outside of the feasible area. Since this problem presents only two constraints, we showcase the performance with a batch of $q = 3D = 30$." + ] + }, + { + "cell_type": "markdown", + "id": "ba051b56", "metadata": {}, "source": [ "### Objective function\n", "\n", - "Start by defining the 10D Ackley function for evaluation during the optimization loop." + "In this block, we define a handle to evaluate the objective function." ] }, { "cell_type": "code", - "execution_count": 170, + "execution_count": 1, "id": "890f1a54-b6cf-4af4-9bfb-1835b2f737a6", "metadata": {}, "outputs": [], @@ -41,19 +58,23 @@ "from botorch.test_functions import Ackley\n", "from botorch.utils.transforms import unnormalize\n", "\n", - "class ack():\n", - " \n", - " def __init__(self, dim, negate, **tkwargs):\n", - " \n", - " self.fun = Ackley(dim = dim, negate = negate).to(**tkwargs)\n", - " self.fun.bounds[0, :].fill_(-5)\n", - " self.fun.bounds[1, :].fill_(10)\n", - " self.dim = self.fun.dim\n", - " self.lb, self.ub = self.fun.bounds\n", - " \n", - " def eval_(self, x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", - " return self.fun(unnormalize(x, [self.lb, self.ub]))" + "import warnings\n", + "\n", + "# Setting up the device\n", + "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n", + "dtype = torch.double\n", + "tkwargs = {\"device\": device, \"dtype\": dtype}\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "# Defining objective function\n", + "fun = Ackley(dim=10, negate=True).to(**tkwargs)\n", + "fun.bounds[0, :].fill_(-5)\n", + "fun.bounds[1, :].fill_(10)\n", + "\n", + "def eval_objective(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", + " return fun(unnormalize(x - 0.3, fun.bounds))\n" ] }, { @@ -63,7 +84,7 @@ "source": [ "### Constraint functions\n", "\n", - "Define two constraint functions." + "The problem is constrained by two functions, $c_1$ and $c_2$. In this block, we define the constriant functions and a handle to call when evaluating the constraints." ] }, { @@ -72,30 +93,22 @@ "metadata": {}, "source": [ "\n", - "1. Constraint $c_1$: enforce the $\\sum_{i=1}^{10} x_i \\leq T$. We will specify $T=0$ later. " + "1. Constraint $c_1$: enforce the $\\sum_{i=1}^{10} x_i \\leq 0$. " ] }, { "cell_type": "code", - "execution_count": 171, + "execution_count": 2, "id": "228d816a-6452-4078-b3fd-6a42569237c3", "metadata": {}, "outputs": [], "source": [ - "class sum_():\n", - " def __init__(self, threshold, lb, ub):\n", - " \n", - " self.lb = lb\n", - " self.ub = ub\n", - " self.threshold = threshold\n", - " return \n", - " \n", - " def c(self, x):\n", - " \"\"\"This is a helper function we use to unnormalize and evaluate a point\"\"\"\n", - " return x.sum() - self.threshold\n", + "def c1(x):\n", + " return x.sum()\n", " \n", - " def eval_(self, x):\n", - " return self.c(unnormalize(x, [self.lb, self.ub]))" + "def eval_c1(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint c1\"\"\"\n", + " return c1(unnormalize(x, fun.bounds))" ] }, { @@ -103,30 +116,22 @@ "id": "08472c8a-67de-4206-bf0f-871e40edfe7c", "metadata": {}, "source": [ - "2. Constraint $c_2$: enforce the $l_2$ norm $\\| \\mathbb{x}\\|_2 \\leq T$. We will specify $T=0.5$ later." + "2. Constraint $c_2$: enforce the $l_2$ norm $\\| \\mathbb{x}\\|_2 \\leq 0.5$." ] }, { "cell_type": "code", - "execution_count": 172, + "execution_count": 3, "id": "1e0f4e8d-657f-49d8-bb59-eb8c2ff4a9f5", "metadata": {}, "outputs": [], "source": [ - "class norm_():\n", - " def __init__(self, threshold, lb, ub):\n", - " \n", - " self.lb = lb\n", - " self.ub = ub\n", - " self.threshold = threshold\n", - " return \n", - " \n", - " def c(self, x):\n", - " return torch.norm(x, p=2) - self.threshold\n", + "def c2(x):\n", + " return torch.norm(x, p=2) - 5\n", " \n", - " def eval_(self, x):\n", - " \"\"\"This is a helper function we use to unnormalize and evaluate a point\"\"\"\n", - " return self.c(unnormalize(x, [self.lb, self.ub]))" + "def eval_c2(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint c2\"\"\"\n", + " return c2(unnormalize(x, fun.bounds))" ] }, { @@ -134,37 +139,37 @@ "id": "e3c6e1cd-15de-4985-ac6c-bf96c6eafc24", "metadata": {}, "source": [ - "### Define FuRBO Class\n", - "Define a class to hold the information needed for the optimization loop. \n", + "### FuRBO Class\n", + "We define a class to hold the information needed for the optimization loop. \n", "\n", - "The state is updated with the samples evaluated at each iteration. \n", + "The state is updated with the samples evaluated at each iteration. Therefore, the class presents a method for self-updating.\n", "\n", "Prior to the class, two utility functions are defined. The first one identifies the current best sample, while the second one fits a GPR model to the current dataset. \n", "\n", - "The ```Furbo_state``` class features a function to reset the status when restarting. Notice that the state is emptied when restarting. Therefore the samples previously evaluated are extracted and saved (see main optimization loop)." + "The ```FurboState``` class features a function to reset the status when restarting. Notice that the state is emptied when restarting. Therefore the samples previously evaluated are extracted and saved (see main optimization loop)." ] }, { "cell_type": "code", - "execution_count": 173, + "execution_count": 4, "id": "020338e2-9eaf-49cf-9e5c-fd00e1a46835", "metadata": {}, "outputs": [], "source": [ "import gpytorch\n", - "import numpy as np\n", "\n", "from botorch.fit import fit_gpytorch_mll\n", + "\n", "from botorch.models import SingleTaskGP\n", "from botorch.models.transforms.outcome import Standardize\n", + "from botorch.models.model_list_gp_regression import ModelListGP\n", "\n", "from gpytorch.constraints import Interval\n", "from gpytorch.kernels import MaternKernel, ScaleKernel\n", "from gpytorch.likelihoods import GaussianLikelihood\n", "from gpytorch.mlls import ExactMarginalLogLikelihood\n", "\n", - "from scipy.stats import invgauss\n", - "from scipy.stats import ecdf\n", + "from torch.quasirandom import SobolEngine\n", "\n", "from torch import Tensor\n", "\n", @@ -178,10 +183,7 @@ " return torch.topk(score.reshape(-1), k=n_tr).indices\n", " return torch.topk(C.clamp(min=0).sum(dim=-1), k=n_tr, largest=False).indices # Return smallest violation\n", "\n", - "def get_fitted_model(X,\n", - " Y,\n", - " dim,\n", - " max_cholesky_size):\n", + "def get_fitted_model(X, Y, dim):\n", " '''Function to fit a GPR to a given set of data.\n", " For reference, see https://botorch.org/docs/tutorials/scalable_constrained_bo/'''\n", " likelihood = GaussianLikelihood(noise_constraint=Interval(1e-8, 1e-3))\n", @@ -197,51 +199,41 @@ " )\n", " mll = ExactMarginalLogLikelihood(model.likelihood, model)\n", "\n", - " with gpytorch.settings.max_cholesky_size(max_cholesky_size):\n", - " fit_gpytorch_mll(mll, \n", - " optimizer_kwargs={'method': 'L-BFGS-B'})\n", + " fit_gpytorch_mll(mll)\n", "\n", " return model\n", "\n", - "from botorch.models.model_list_gp_regression import ModelListGP\n", - "from torch.quasirandom import SobolEngine\n", + "class FurboState():\n", + " '''\n", + " Class to track optimization state and update it with newly evaluated samples\n", "\n", - "class Furbo_state():\n", - " '''Class to track optimization status with restart'''\n", - " # Initialization of the status\n", - " def __init__(self, \n", - " obj, # Objective function\n", - " cons, # Constraints function\n", - " batch_size, # Batch size of each iteration\n", - " n_init, # Number of initial points to evaluate\n", - " n_iteration, # Number of total iterations\n", - " **tkwargs):\n", + " Args:\n", + " fcn: objective function class\n", + " batch_size: batch size\n", + " n_init: number of initial points to evaluate\n", + " n_iteration: number of total iterations\n", " \n", - " # Objective function handle\n", - " self.obj = obj\n", - " \n", - " # Constraints function handle\n", - " self.cons = cons\n", + " '''\n", + " # Initialization of the status\n", + " def __init__(self, fcn, batch_size, n_init, max_budget, **tkwargs):\n", " \n", " # Domain bounds\n", - " self.lb = obj.lb\n", - " self.ub = obj.ub\n", + " self.lb, self.ub = fcn.bounds\n", " \n", " # Problem dimensions\n", " self.batch_size: int = batch_size # Dimension of the batch at each iteration\n", " self.n_init: int = n_init # Number of initial samples\n", - " self.dim: int = obj.dim # Dimension of the problem\n", + " self.dim: int = fcn.dim # Dimension of the problem\n", " \n", " # Trust regions information\n", " self.tr_ub: float = torch.ones((1, self.dim), **tkwargs) # Upper bounds of trust region\n", " self.tr_lb: float = torch.zeros((1, self.dim), **tkwargs) # Lower bounds of trust region\n", " self.tr_vol: float = torch.prod(self.tr_ub - self.tr_lb, dim=1) # Volume of trust region\n", " self.radius: float = 1.0 # Percentage around which the trust region is built\n", - " self.radius_min: float = 0.5**7 # Minimum percentage for trust region\n", "\n", " # Trust region updating \n", - " self.failure_counter: int = 0 # Counter of failure points to asses how algorithm is going\n", - " self.success_counter: int = 0 # Counter of success points to asses how algorithm is going\n", + " self.failure_counter: int = 0 # Counter for failure points to asses how algorithm is going\n", + " self.success_counter: int = 0 # Counter for success points to asses how algorithm is going\n", " self.success_tolerance: int = 2 # Success tolerance for \n", " self.failure_tolerance: int = 3 # Failure tolerance for\n", " \n", @@ -251,25 +243,29 @@ " self.batch_C: Tensor # Current batch to evaluate: C values\n", " \n", " # Stopping criteria information\n", - " self.n_iteration: int = n_iteration # Maximum number of iterations allowed\n", - " self.it_counter: int = 0 # Counter of iterations for stopping\n", + " self.it_counter: int = 0 # Counter for iterations\n", + " self.n_counter: int = 0 # Counter for sampled evaluated\n", + " self.max_budget = max_budget # Maximum number of samples allowed to be evaluated\n", " self.finish_trigger: bool = False # Trigger to stop optimization\n", - " self.failed_GP : bool = False # Flag to pass to failed_GP in FuRBORestart\n", " \n", " # Restart criteria information\n", - " self.restart_trigger: bool = False\n", + " self.radius_min: float = 0.5**9 # Minimum percentage for trust region\n", + " self.restart_trigger: bool = False # Trigger to stop optimization\n", " \n", " # Sobol sampler engine\n", - " self.sobol = SobolEngine(dimension=self.dim, scramble=True, seed=1)\n", + " self.sobol = SobolEngine(dimension=self.dim, scramble=True)\n", " \n", " # Update the status\n", - " def update(self,\n", - " X_next, # Samples X (input values) to update the status\n", - " Y_next, # Samples Y (objective value) to update the status\n", - " C_next, # Samples C (constraints values) to update the status\n", - " **tkwargs):\n", + " def update(self, X_next, Y_next, C_next, **tkwargs):\n", + " '''\n", + " Function to update optimization status\n", " \n", - " '''Function to update optimization status'''\n", + " Args:\n", + " X_next: samples X (input values) to update the status\n", + " Y_next: samples Y (objective value) to update the status\n", + " C_next: Samples C (constraints values) to update the status\n", + "\n", + " '''\n", " \n", " # Merge current batch with previously evaluated samples\n", " if not hasattr(self, 'X'):\n", @@ -284,12 +280,8 @@ " self.C = torch.cat((self.C, C_next), dim=0)\n", "\n", " # update GPR surrogates\n", - " try:\n", - " self.Y_model = get_fitted_model(self.X, self.Y, self.dim, max_cholesky_size = float(\"inf\"))\n", - " self.C_model = ModelListGP(*[get_fitted_model(self.X, C.reshape([C.shape[0],1]), self.dim, max_cholesky_size = float(\"inf\")) for C in self.C.t()])\n", - " except:\n", - " # If update fail, flag to stop entire optimization\n", - " self.failed_GP = True\n", + " self.Y_model = get_fitted_model(self.X, self.Y, self.dim)\n", + " self.C_model = ModelListGP(*[get_fitted_model(self.X, C.reshape(-1, 1), self.dim) for C in self.C.t()])\n", " \n", " # Update batch information \n", " self.batch_X = X_next\n", @@ -329,9 +321,9 @@ " \n", " # Update iteration counter\n", " self.it_counter += 1\n", + " self.n_counter += len(Y_next)\n", " \n", - " def reset_status(self,\n", - " **tkwargs):\n", + " def reset_status(self, **tkwargs):\n", " '''Function to reset the status for the restart'''\n", " \n", " # Reset trust regions size\n", @@ -347,7 +339,6 @@ " \n", " # Reset restart criteria trigger\n", " self.restart_trigger: bool = False # Trigger to restart optimization\n", - " self.failed_GP: bool = False # Reset GPR failure trigger\n", " \n", " # Delete tensors with samples for training GPRs\n", " if hasattr(self, 'X'):\n", @@ -371,25 +362,56 @@ "id": "58fee9fb-ca01-4024-8859-1fc3d9d4aea4", "metadata": {}, "source": [ - "### Define trust region\n", + "### Trust region\n", + "\n", + "In this block contains the trust region definition, according to the following steps:\n", "\n", - "Define a set of functions to evaluate the trust region. First sample according to a Multinormal distribution the GPR surrogates (both objective and constraints). Rank the samples according to both the objective and violation estimation. Take the top $10\\%$ of the samples according to the rank. The trust region is defined as a hyperbox enclosing the picked samples. " + "1. Sample GPR surrogates
\n", + " - Draw ```n_samples``` with a uniform distribution in a sphere centred in $x_{best}$ and of radius $\\mathcal{R}$
\n", + " - Evaluate the samples on the GPR surrogates
\n", + "2. Rank samples
\n", + " - Rank the samples based on optimality and feasibility:
\n", + " - first come all feasible samples in order of optimality
\n", + " - second come the infeasible samples ranked based on the total violation
\n", + "3. Define trust region
\n", + " - Select the top P% ranked samples
\n", + " - Find the samllest hyper-rectangle that includes all selected samples
\n", + "\n", + "Step 1 is performed by the function ```multivariate_circular```. ```update_tr``` calls ```multivariate_circular``` and performs steps 2 and 3.\n", + "\n", + "This definition yields two main properties:\n", + "1. The trust region can jump across the entire domain since it is defined based on the posterior of the GPR models instead of the current best evaluated sample, as SCBO[2] or TuRBO[3].\n", + "2. The trust region shape adapts to the most promising area according to the GPR models of objective and constraints, e.g., if the promising area is narrow and long, the trust region will also be narrow and long. \n", + "\n", + "Note that the trust region is defined with its sides parallel to the axes. Further improvements could be expected by allowing the trust region to rotate and allign with the feasible area.\n", + "\n", + "[2] [David Eriksson and Matthias Poloczek. Scalable constrained Bayesian optimization. In International Conference on Artificial Intelligence and Statistics, pages 730–738. PMLR, 2021.](https://doi.org/10.48550/arxiv.2002.08526)\n", + "\n", + "[3] [David Eriksson, Michael Pearce, Jacob Gardner, Ryan D Turner, Matthias Poloczek. Scalable global optimization via local Bayesian optimization. Advances in Neural Information Processing Systems. 2019](https://proceedings.neurips.cc/paper_files/paper/2019/file/6c990b7aca7bc7058f5e98ea909e924b-Paper.pdf)" ] }, { "cell_type": "code", - "execution_count": 174, + "execution_count": 5, "id": "3d36cf01-c5be-44ee-96bb-12564225bd7b", "metadata": {}, "outputs": [], "source": [ - "def multivariate_circular(centre, # Centre of the multivariate distribution\n", - " radius, # Radius of the multivariate distribution\n", - " n_samples, # Number of samples to evaluate\n", - " lb = None, # Domain lower bound\n", - " ub = None, # Domain upper bound\n", - " **tkwargs):\n", - " '''Function to generate multivariate distribution of given radius and centre within a given domain.'''\n", + "def multivariate_circular(centre, radius, n_samples, lb = None, ub = None, **tkwargs):\n", + " '''\n", + " Function to generate distribution of given radius and centre within a given domain.\n", + " \n", + " Args:\n", + " centre: centre of the hypersphere\n", + " radius: radius of the hypersphere\n", + " n_samples: number of samples to evaluate\n", + " lb: (optional) domain lower bound\n", + " ub: (optional) domain upper bound\n", + "\n", + " Return: \n", + " samples: samples generated inside the radius given\n", + " \n", + " '''\n", " # Dimension of the design domain\n", " dim = centre.shape[0]\n", " \n", @@ -406,8 +428,7 @@ " \n", " # Translate samples to be centered at centre\n", " samples = scaled_samples + centre\n", - " \n", - " \n", + "\n", " # Trim samples outside domain\n", " for dim in range(len(lb)):\n", " samples = samples[torch.where(samples[:,dim]>=lb[dim])]\n", @@ -415,10 +436,18 @@ " \n", " return samples\n", "\n", - "def update_tr(state, # FuRBO state\n", - " percentage = 0.1, # Percentage to define trust region (default 10%)\n", - " **tkwargs):\n", - " '''Function to sample Multinormal Distribution of GPRs and define trust region'''\n", + "def update_tr(state, percentage = 0.1, **tkwargs):\n", + " '''\n", + " Function to sample Multinormal Distribution of GPRs and define trust region\n", + " \n", + " Args:\n", + " state: FurboState object\n", + " percentage: percentage of inspectors defining the trust region\n", + " \n", + " Return:\n", + " state: updated FurboState with new trust region\n", + "\n", + " '''\n", " # Update the trust regions based on the feasible region\n", " n_samples = 1000 * state.dim\n", " lb = torch.zeros(state.dim, **tkwargs)\n", @@ -438,13 +467,11 @@ " samples = multivariate_circular(x_candidate, radius, n_samples, lb=lb, ub=ub, **tkwargs)\n", " \n", " # Evaluate samples on the models of the objective -> yy Tensor\n", - " state.Y_model.eval()\n", " with torch.no_grad():\n", " posterior = state.Y_model.posterior(samples)\n", " samples_yy = posterior.mean.squeeze()\n", " \n", " # Evaluate samples on the models of the constraints -> yy Tensor\n", - " state.C_model.eval()\n", " with torch.no_grad():\n", " posterior = state.C_model.posterior(samples)\n", " samples_cc = posterior.mean\n", @@ -474,6 +501,7 @@ " \n", " top_indices = torch.cat((original_feasible_sorted_indices, original_infeasible_sorted_indices))[:n_samples_tr]\n", " \n", + " # If no feasible point is found\n", " else:\n", " \n", " if n_samples_tr > len(samples_cc):\n", @@ -502,18 +530,19 @@ "source": [ "### Sampling strategies\n", "\n", - "Define a function to generate an initial experimental design using Sobol sampling strategy, similarly to SCBO (https://botorch.org/docs/tutorials/scalable_constrained_bo/)." + "In this block, we define sampling functions for:\n", + "\n", + "1. Generating an initial experimental design using Sobol sampling strategy. We use this function when a restart is triggered." ] }, { "cell_type": "code", - "execution_count": 175, + "execution_count": 6, "id": "0116ca79-7555-4da3-bfd4-69941926eb11", "metadata": {}, "outputs": [], "source": [ - "def get_initial_points(state,\n", - " **tkwargs):\n", + "def get_initial_points(state, **tkwargs):\n", " '''Function to generate the initial experimental design'''\n", " X_init = state.sobol.draw(n=state.n_init).to(**tkwargs)\n", " return X_init" @@ -524,22 +553,30 @@ "id": "55726979-92f6-488f-869c-2fa6140f6b85", "metadata": {}, "source": [ - "Define a function to identify the best next candidate point, similar to SCBO(https://botorch.org/docs/tutorials/scalable_constrained_bo/)." + "2. Identifing the best next candidate point using Thompson sampling. Definitions 1 and 2 are the same as in the SCBO tutorial (https://botorch.org/docs/tutorials/scalable_constrained_bo/)." ] }, { "cell_type": "code", - "execution_count": 176, + "execution_count": 7, "id": "2d969ea7-2f1e-4433-b3b4-53413546c2f2", "metadata": {}, "outputs": [], "source": [ "from botorch.generation.sampling import ConstrainedMaxPosteriorSampling\n", "\n", - "def generate_batch(state,\n", - " n_candidates,\n", - " **tkwargs):\n", - " '''Function to find net candidate optimum'''\n", + "def generate_batch(state, n_candidates, **tkwargs):\n", + " '''Function to find net candidate optimum\n", + " \n", + " Args:\n", + " state: FurboState object\n", + " n_candidates: number of candidates to draw\n", + "\n", + " Return:\n", + " X_next: n_candidates to be evaluated\n", + "\n", + " '''\n", + "\n", " assert state.X.min() >= 0.0 and state.X.max() <= 1.0 and torch.all(torch.isfinite(state.Y))\n", "\n", " # Initialize tensor with samples to evaluate\n", @@ -581,21 +618,19 @@ "source": [ "### Stopping criterion\n", "\n", - "Define a function to detect when the maximum number of iterations is met." + "This function detects when the maximum number of samples evaluated is met and returns a flag to stop the optimization." ] }, { "cell_type": "code", - "execution_count": 177, + "execution_count": 8, "id": "189aae72-f033-49db-bcc8-0e791774bd76", "metadata": {}, "outputs": [], "source": [ - "def stopping_criterion(state, n_iteration):\n", + "def stopping_criterion(state):\n", " '''Function to evaluate if the maximum number of allowed iterations is reached.'''\n", - " if state.it_counter <= n_iteration:\n", - " return False\n", - " return True" + " return state.n_counter > state.max_budget" ] }, { @@ -603,340 +638,1167 @@ "id": "44f15711-8503-4226-8ee0-171f26f7b8f4", "metadata": {}, "source": [ - "### Restart criterion\n", + "### Restart criterion" + ] + }, + { + "cell_type": "markdown", + "id": "476bada4", + "metadata": {}, + "source": [ + "This function triggers a restart when $\\mathcal{R} < \\mathcal{R}_{\\min}$." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "81f9bd26", + "metadata": {}, + "outputs": [], + "source": [ + "def restart_criterion(state):\n", + " '''Function to evaluate if MND radius is smaller than the minimum allowed radius'''\n", + " return state.radius < state.radius_min" + ] + }, + { + "cell_type": "markdown", + "id": "a80c7b75-a62d-46c2-aa80-28f6f29501be", + "metadata": {}, + "source": [ + "### Main optimization loop\n", "\n", - "Detect when the GPR fitting process fails to stop the optimization.curve" + "This function runs the main optimization loop of FuRBO. " ] }, { "cell_type": "code", - "execution_count": 178, - "id": "f0d2b342-601b-4d07-9fe3-459f28ecead2", + "execution_count": 10, + "id": "b9d52417-aaa5-40b6-bf07-12c074460283", "metadata": {}, "outputs": [], "source": [ - "def GP_restart_criterion(state):\n", - " '''Function to evaluate if a GPR failed during the optimization.'''\n", - " if state.failed_GP:\n", - " print(\"GPR failed.\")\n", - " return True\n", - " return False" + "def furbo_optimize(fcn, objective, constraints, X_ini, batch_size = 1, n_init = 10, max_budget = 200, N_CANDIDATES = 2000):\n", + " '''Function to optimize an objective under a set of given constraints using FuRBO\n", + " \n", + " Args:\n", + " objective: handle to evaluate objective\n", + " constraints: list of handles to evaluate constraints\n", + " X_ini: initial DoE (needed for reproducibility)\n", + " batch_size: size of the batch to evaluate at each iteration\n", + " n_init: number of initial samples\n", + " n_iterations: computational budget (maximum number of iterations)\n", + "\n", + " Return:\n", + " X_all: samples evaluated\n", + " Y_all: objective values of the samples evaluated\n", + " C_all: constraints values of the samples evaluated\n", + "\n", + " '''\n", + "\n", + " # FuRBO state initialization\n", + " state = FurboState(fcn,\n", + " batch_size = batch_size, # Batch size of each iteration\n", + " n_init = n_init, # Number of initial points to evaluate\n", + " max_budget = max_budget, # Maximum number of evaluations allowed\n", + " **tkwargs)\n", + "\n", + " # Initiate lists to save samples over the restarts\n", + " X_all, Y_all, C_all = [], [], []\n", + "\n", + " # Continue optimization the stopping criterions isn't triggered\n", + " while not state.finish_trigger: \n", + " \n", + " # Reset status for restarting\n", + " state.reset_status(**tkwargs)\n", + " \n", + " # generate intial batch of X\n", + " X_next = X_ini \n", + " \n", + " # Reset and restart optimization\n", + " while not state.restart_trigger and not state.finish_trigger:\n", + " \n", + " # Evaluate current batch (samples in X_next)\n", + " Y_next = []\n", + " C_next = []\n", + " for x in X_next:\n", + " # Evaluate batch on obj ...\n", + " Y_next.append(objective(x))\n", + " # ... and constraints\n", + " C_next.append([c(x) for c in constraints])\n", + " \n", + " # process vector for PyTorch\n", + " Y_next = torch.tensor(Y_next).unsqueeze(-1).to(**tkwargs)\n", + " C_next = torch.tensor(C_next).to(**tkwargs)\n", + " \n", + " # Update FuRBO status with newly evaluated batch\n", + " state.update(X_next, Y_next, C_next, **tkwargs) \n", + " \n", + " # Printing current best\n", + " # If a feasible has been evaluated -> print current optimum (feasible sample with best objective value)\n", + " if (state.best_C <= 0).all():\n", + " best = state.best_Y.amax()\n", + " print(f\"Samples evaluated: {state.n_counter} | Best value: {best:.2e},\"\n", + " f\" MND radius: {state.radius}\")\n", + " \n", + " # Else, if no feasible has been evaluated -> print smallest violation (the sample that violatest the least all constraints)\n", + " else:\n", + " violation = state.best_C.clamp(min=0).sum()\n", + " print(f\"Samples evaluated: {state.n_counter} | No feasible point yet! Smallest total violation: \"\n", + " f\"{violation:.2e}, MND radius: {state.radius}\")\n", + " \n", + " # Update Trust regions\n", + " state = update_tr(state, **tkwargs)\n", + " \n", + " # generate next batch to evaluate \n", + " X_next = generate_batch(state, N_CANDIDATES, **tkwargs)\n", + " \n", + " # Check if stopping criterion is met (budget exhausted and if GP failed)\n", + " state.finish_trigger = stopping_criterion(state) \n", + " \n", + " # Check if restart criterion is met\n", + " state.restart_trigger = restart_criterion(state)\n", + "\n", + " # Save samples evaluated before resetting the status\n", + " X_all.append(state.X)\n", + " Y_all.append(state.Y)\n", + " C_all.append(state.C)\n", + "\n", + " # Ri-elaborate for processing\n", + " X_all = torch.cat(X_all)\n", + " Y_all = torch.cat(Y_all)\n", + " C_all = torch.cat(C_all)\n", + "\n", + " return X_all, Y_all, C_all" ] }, { "cell_type": "markdown", - "id": "476bada4", + "id": "28e7acb3", "metadata": {}, "source": [ - "Detect when the radius becomes too small." + "### Post-processing\n", + "\n", + "In this block, we define two functions for post-processing the optimization data, print the optimum sample and its value, and plot the monotonic convergence curve. " ] }, { "cell_type": "code", - "execution_count": 179, - "id": "81f9bd26", + "execution_count": 11, + "id": "17675f23", "metadata": {}, "outputs": [], "source": [ - "def restart_criterion(state, radius_min):\n", - " '''Function to evaluate if MND radius is smaller than the minimum allowed radius'''\n", - " if state.radius < radius_min:\n", - " return True\n", - " return False" + "import numpy as np\n", + "\n", + "def print_results(X_all, Y_all, C_all):\n", + " '''Function to print the best sample evaluated from the optimization.'''\n", + " best_id = get_best_index_for_batch(n_tr=1, Y=Y_all, C=C_all)\n", + "\n", + " X_best = X_all[best_id]\n", + " Y_best = Y_all[best_id]\n", + " C_best = C_all[best_id]\n", + "\n", + " # If a feasible has been evaluated -> print current optimum sample and yielded value\n", + " if (C_best <= 0).all():\n", + " print(\"Optimization finished \\n\"\n", + " f\"\\t Optimum: {Y_best.item():.2e}, \\n\"\n", + " f\"\\t X: {X_best.cpu().numpy()}\")\n", + " \n", + " # Else, if no feasible has been evaluated -> print sample with smallest violation and the violation value\n", + " else:\n", + " violation = C_best.sum()\n", + " print(\"Optimization failed \\n\"\n", + " f\"\\t Smallest violation: {violation:.2e}, \\n\"\n", + " f\"\\t X: {X_best.cpu().numpy()}\")\n", + " \n", + " return\n", + "\n", + "def plot_results(ax, color, Y_all, C_all):\n", + " '''Function to plot the convergence curve of the sample evaluated on a given plot.'''\n", + "\n", + " score = Y_all.clone()\n", + " # Set infeasible to -inf\n", + " score[~(C_all <= 0).all(dim=-1)] = float(\"-inf\")\n", + " fx = np.maximum.accumulate(score.cpu())\n", + " ax.plot(fx, marker=\"\", lw=3, color=color)\n", + "\n", + " return" ] }, { "cell_type": "markdown", - "id": "a80c7b75-a62d-46c2-aa80-28f6f29501be", + "id": "a3d28f6c-5940-4d56-a3b5-4635980db76f", "metadata": {}, "source": [ - "### Main optimization loop" + "### Evaluating FuRBO\n", + "\n", + "We run the optimization with a batch size of 60, an initial DoE of 10 samples over 50 iteration." ] }, { "cell_type": "code", - "execution_count": 180, - "id": "b9d52417-aaa5-40b6-bf07-12c074460283", + "execution_count": 12, + "id": "027a9ec9-930a-48d0-b481-ffe9e9ca0d90", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "0) No feasible point yet! Smallest total violation: 5.72e-01, MND radius: 1.0\n", - "1) Best value: -1.72e+00, MND radius: 1.0\n", - "2) Best value: -1.72e+00, MND radius: 1.0\n", - "3) Best value: -7.71e-01, MND radius: 1.0\n", - "4) Best value: -7.71e-01, MND radius: 1.0\n", - "5) Best value: -7.71e-01, MND radius: 1.0\n", - "6) Best value: -2.39e-01, MND radius: 1.0\n", - "7) Best value: -2.37e-01, MND radius: 1.0\n", - "8) Best value: -2.37e-01, MND radius: 1.0\n", - "9) Best value: -8.69e-02, MND radius: 1.0\n", - "10) Best value: -8.32e-02, MND radius: 1.0\n", - "11) Best value: -8.32e-02, MND radius: 1.0\n", - "12) Best value: -8.32e-02, MND radius: 1.0\n", - "13) Best value: -8.32e-02, MND radius: 1.0\n", - "14) Best value: -8.32e-02, MND radius: 0.5\n", - "15) Best value: -8.32e-02, MND radius: 0.5\n", - "16) Best value: -2.84e-02, MND radius: 0.5\n", - "17) Best value: -2.84e-02, MND radius: 0.5\n", - "18) Best value: -2.84e-02, MND radius: 0.5\n", - "19) Best value: -2.84e-02, MND radius: 0.5\n", - "20) Best value: -2.84e-02, MND radius: 0.25\n", - "21) Best value: -2.84e-02, MND radius: 0.25\n", - "22) Best value: -2.84e-02, MND radius: 0.25\n", - "23) Best value: -2.21e-02, MND radius: 0.125\n", - "24) Best value: -1.57e-02, MND radius: 0.125\n", - "25) Best value: -1.57e-02, MND radius: 0.25\n", - "26) Best value: -1.57e-02, MND radius: 0.25\n", - "27) Best value: -1.57e-02, MND radius: 0.25\n", - "28) Best value: -1.57e-02, MND radius: 0.125\n", - "29) Best value: -1.57e-02, MND radius: 0.125\n", - "30) Best value: -1.56e-02, MND radius: 0.125\n", - "31) Best value: -1.56e-02, MND radius: 0.125\n", - "32) Best value: -1.56e-02, MND radius: 0.125\n", - "33) Best value: -1.56e-02, MND radius: 0.125\n", - "34) Best value: -1.46e-02, MND radius: 0.0625\n", - "35) Best value: -1.46e-02, MND radius: 0.0625\n", - "36) Best value: -1.39e-02, MND radius: 0.0625\n", - "37) Best value: -1.16e-02, MND radius: 0.0625\n", - "38) Best value: -1.16e-02, MND radius: 0.125\n", - "39) Best value: -1.16e-02, MND radius: 0.125\n", - "40) Best value: -1.16e-02, MND radius: 0.125\n", - "41) Best value: -1.16e-02, MND radius: 0.0625\n", - "42) Best value: -1.16e-02, MND radius: 0.0625\n", - "43) Best value: -7.18e-03, MND radius: 0.0625\n", - "44) Best value: -7.18e-03, MND radius: 0.0625\n", - "45) Best value: -7.18e-03, MND radius: 0.0625\n", - "46) Best value: -7.18e-03, MND radius: 0.0625\n", - "47) Best value: -3.63e-03, MND radius: 0.03125\n", - "48) Best value: -3.63e-03, MND radius: 0.03125\n", - "GPR failed.\n", - "49) No feasible point yet! Smallest total violation: 4.53e-01, MND radius: 1.0\n", - "50) Best value: -2.94e+00, MND radius: 1.0\n", - "51) Best value: -2.94e+00, MND radius: 1.0\n", - "52) Best value: -2.94e+00, MND radius: 1.0\n", - "53) Best value: -2.94e+00, MND radius: 1.0\n", - "54) Best value: -1.44e+00, MND radius: 0.5\n", - "55) Best value: -2.58e-01, MND radius: 0.5\n", - "56) Best value: -2.58e-01, MND radius: 1.0\n", - "57) Best value: -7.49e-02, MND radius: 1.0\n", - "58) Best value: -7.49e-02, MND radius: 1.0\n", - "59) Best value: -6.21e-02, MND radius: 1.0\n", - "60) Best value: -6.21e-02, MND radius: 1.0\n", - "61) Best value: -6.21e-02, MND radius: 1.0\n", - "62) Best value: -6.21e-02, MND radius: 1.0\n", - "63) Best value: -6.21e-02, MND radius: 0.5\n", - "64) Best value: -6.21e-02, MND radius: 0.5\n", - "65) Best value: -2.03e-02, MND radius: 0.5\n", - "66) Best value: -2.03e-02, MND radius: 0.5\n", - "67) Best value: -2.03e-02, MND radius: 0.5\n", - "68) Best value: -2.03e-02, MND radius: 0.5\n", - "69) Best value: -2.03e-02, MND radius: 0.25\n", - "70) Best value: -2.03e-02, MND radius: 0.25\n", - "71) Best value: -2.03e-02, MND radius: 0.25\n", - "72) Best value: -1.33e-02, MND radius: 0.125\n", - "73) Best value: -1.33e-02, MND radius: 0.125\n", - "74) Best value: -1.33e-02, MND radius: 0.125\n", - "75) Best value: -1.33e-02, MND radius: 0.125\n", - "76) Best value: -3.34e-03, MND radius: 0.125\n", - "77) Best value: -3.34e-03, MND radius: 0.125\n", - "78) Best value: -3.34e-03, MND radius: 0.125\n", - "79) Best value: -3.34e-03, MND radius: 0.125\n", - "80) Best value: -1.99e-03, MND radius: 0.0625\n", - "81) Best value: -1.99e-03, MND radius: 0.0625\n", - "82) Best value: -1.99e-03, MND radius: 0.0625\n", - "83) Best value: -1.99e-03, MND radius: 0.0625\n", - "84) Best value: -1.99e-03, MND radius: 0.03125\n", - "85) Best value: -1.99e-03, MND radius: 0.03125\n", - "86) Best value: -1.99e-03, MND radius: 0.03125\n", - "87) Best value: -1.99e-03, MND radius: 0.015625\n", - "88) Best value: -1.99e-03, MND radius: 0.015625\n", - "89) Best value: -1.99e-03, MND radius: 0.015625\n", - "90) Best value: -1.99e-03, MND radius: 0.0078125\n", - "91) Best value: -1.99e-03, MND radius: 0.0078125\n", - "92) Best value: -1.99e-03, MND radius: 0.0078125\n", - "93) No feasible point yet! Smallest total violation: 2.07e+00, MND radius: 1.0\n", - "94) Best value: -3.47e+00, MND radius: 1.0\n", - "95) Best value: -3.47e+00, MND radius: 1.0\n", - "96) Best value: -2.16e+00, MND radius: 1.0\n", - "97) Best value: -2.16e+00, MND radius: 1.0\n", - "98) Best value: -2.16e+00, MND radius: 1.0\n", - "99) Best value: -2.16e+00, MND radius: 1.0\n", - "100) Best value: -4.88e-01, MND radius: 0.5\n" + "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 1.01e+01, MND radius: 1.0\n", + "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 1.90e+00, MND radius: 1.0\n", + "Samples evaluated: 30 | No feasible point yet! Smallest total violation: 1.90e+00, MND radius: 1.0\n", + "Samples evaluated: 40 | Best value: -1.46e+01, MND radius: 1.0\n", + "Samples evaluated: 50 | Best value: -1.41e+01, MND radius: 1.0\n", + "Samples evaluated: 60 | Best value: -1.37e+01, MND radius: 1.0\n", + "Samples evaluated: 70 | Best value: -1.35e+01, MND radius: 1.0\n", + "Samples evaluated: 80 | Best value: -1.35e+01, MND radius: 1.0\n", + "Samples evaluated: 90 | Best value: -1.35e+01, MND radius: 1.0\n", + "Samples evaluated: 100 | Best value: -1.35e+01, MND radius: 1.0\n", + "Samples evaluated: 110 | Best value: -1.30e+01, MND radius: 0.5\n", + "Samples evaluated: 120 | Best value: -1.30e+01, MND radius: 0.5\n", + "Samples evaluated: 130 | Best value: -1.30e+01, MND radius: 0.5\n", + "Samples evaluated: 140 | Best value: -1.30e+01, MND radius: 0.5\n", + "Samples evaluated: 150 | Best value: -1.30e+01, MND radius: 0.25\n", + "Samples evaluated: 160 | Best value: -1.30e+01, MND radius: 0.25\n", + "Samples evaluated: 170 | Best value: -1.30e+01, MND radius: 0.25\n", + "Samples evaluated: 180 | Best value: -1.30e+01, MND radius: 0.125\n", + "Samples evaluated: 190 | Best value: -1.30e+01, MND radius: 0.125\n", + "Samples evaluated: 200 | Best value: -1.27e+01, MND radius: 0.125\n", + "Samples evaluated: 210 | Best value: -1.27e+01, MND radius: 0.125\n", + "Samples evaluated: 220 | Best value: -1.27e+01, MND radius: 0.125\n", + "Samples evaluated: 230 | Best value: -1.25e+01, MND radius: 0.125\n", + "Samples evaluated: 240 | Best value: -1.25e+01, MND radius: 0.125\n", + "Samples evaluated: 250 | Best value: -1.25e+01, MND radius: 0.125\n", + "Samples evaluated: 260 | Best value: -1.23e+01, MND radius: 0.125\n", + "Samples evaluated: 270 | Best value: -1.23e+01, MND radius: 0.125\n", + "Samples evaluated: 280 | Best value: -1.23e+01, MND radius: 0.25\n", + "Samples evaluated: 290 | Best value: -1.23e+01, MND radius: 0.25\n", + "Samples evaluated: 300 | Best value: -1.23e+01, MND radius: 0.25\n", + "Samples evaluated: 310 | Best value: -1.23e+01, MND radius: 0.125\n", + "Samples evaluated: 320 | Best value: -1.22e+01, MND radius: 0.125\n", + "Samples evaluated: 330 | Best value: -1.22e+01, MND radius: 0.125\n", + "Samples evaluated: 340 | Best value: -1.21e+01, MND radius: 0.125\n", + "Samples evaluated: 350 | Best value: -1.21e+01, MND radius: 0.125\n", + "Samples evaluated: 360 | Best value: -1.21e+01, MND radius: 0.125\n", + "Samples evaluated: 370 | Best value: -1.21e+01, MND radius: 0.125\n", + "Samples evaluated: 380 | Best value: -1.21e+01, MND radius: 0.0625\n", + "Samples evaluated: 390 | Best value: -1.21e+01, MND radius: 0.0625\n", + "Samples evaluated: 400 | Best value: -1.21e+01, MND radius: 0.125\n", + "Samples evaluated: 410 | Best value: -1.21e+01, MND radius: 0.125\n", + "Samples evaluated: 420 | Best value: -1.21e+01, MND radius: 0.125\n", + "Samples evaluated: 430 | Best value: -1.21e+01, MND radius: 0.0625\n", + "Samples evaluated: 440 | Best value: -1.21e+01, MND radius: 0.0625\n", + "Samples evaluated: 450 | Best value: -1.21e+01, MND radius: 0.0625\n", + "Samples evaluated: 460 | Best value: -1.21e+01, MND radius: 0.03125\n", + "Samples evaluated: 470 | Best value: -1.21e+01, MND radius: 0.03125\n", + "Samples evaluated: 480 | Best value: -1.21e+01, MND radius: 0.03125\n", + "Samples evaluated: 490 | Best value: -1.21e+01, MND radius: 0.015625\n", + "Samples evaluated: 500 | Best value: -1.21e+01, MND radius: 0.015625\n", + "Samples evaluated: 510 | Best value: -1.21e+01, MND radius: 0.03125\n", + "Optimization finished \n", + "\t Optimum: -1.21e+01, \n", + "\t X: [[0.30068576 0.36640939 0.2989651 0.23413855 0.30010012 0.43401068\n", + " 0.36672435 0.3660089 0.23313606 0.43276746]]\n" ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "import warnings\n", + "import matplotlib.pyplot as plt\n", "\n", - "warnings.filterwarnings(\"ignore\")\n", + "# Evaluate optimization\n", + "batch_size = 1 * fun.dim\n", + "n_init = int(10)\n", + "max_budget = 500\n", + "N_CANDIDATES = 2000 # Number of candidates used during the Thompson sampling\n", + "\n", + "# First generate initial DoE\n", + "X_ini = SobolEngine(dimension=fun.dim, scramble=True, seed=1).draw(n=n_init).to(**tkwargs)\n", + "\n", + "# Run optimization loop \n", + "X_all, Y_all, C_all = furbo_optimize(fun,\n", + " eval_objective, \n", + " [eval_c1, eval_c2],\n", + " X_ini,\n", + " batch_size = batch_size,\n", + " n_init = n_init,\n", + " max_budget = max_budget,\n", + " N_CANDIDATES = N_CANDIDATES) \n", + "\n", + "# Print optimization result\n", + "print_results(X_all, Y_all, C_all)\n", + "\n", + "# Plotting monotic convergence curve\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "plot_results(ax, \"darkgreen\", Y_all, C_all)\n", + "\n", + "# Adding description\n", + "plt.ylabel(\"Function value\", fontsize=18)\n", + "plt.xlabel(\"Number of evaluations\", fontsize=18)\n", + "plt.title(\"10D Ackley with 2 constraints (Batch 1D)\", fontsize=20)\n", + "plt.xlim([0, len(Y_all)])\n", + "\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "9ff0989b", + "metadata": {}, + "source": [ + "## Comparison with SCBO\n", + "\n", + "In this section, we compare the performance of SCBO [2] and FuRBO in two scenarios:\n", + "1. 20D Ackley function with 2 cosntraints and large batch (batch size = 3D = 60)\n", + "2. Speed reducer volume minimization problem [4], a severely constrained black-box problem (7 dimensions and 11 constraints).\n", + "\n", + "For a more in-depth comparison of FuRBO with other algorithms, please refer to [1] or to the data published on [GitHub](https://github.com/paoloascia/FuRBO).\n", + "\n", + "[1] [Paolo Ascia, Elena Raponi, Thomas Bäck and Fabian Duddeck. \"Feasibility-Driven Trust Region Bayesian Optimization.\" In AutoML 2025 Methods Track.](https://doi.org/10.48550/arXiv.2506.14619)\n", + "\n", + "[2] [David Eriksson and Matthias Poloczek. Scalable constrained Bayesian optimization. In International Conference on Artificial Intelligence and Statistics, pages 730–738. PMLR, 2021.](https://doi.org/10.48550/arxiv.2002.08526)\n", + "\n", + "[4] [Afonso C.C. Lemonge, Helio J.C. Barbosa, Carlos C.H. Borges and Francilene B.S. Silva. \"Constrained optimization problems in mechanical engineering design using a real-coded steady-state genetic algorithm.\" Mecánica Computacional, 29(95):9287–9303, 2010.](http://venus.ceride.gov.ar/ojs/index.php/mc/article/viewFile/3669/3581)" + ] + }, + { + "cell_type": "markdown", + "id": "8a75e708", + "metadata": {}, + "source": [ + "### SCBO class and other utility functions" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "faf1d844", + "metadata": {}, + "outputs": [], + "source": [ + "class ScboState():\n", + " '''\n", + " Class to track SCBO optimization state and update it with newly evaluated samples\n", + "\n", + " Args:\n", + " fcn: objective function class\n", + " batch_size: batch size\n", + " n_init: number of initial points to evaluate\n", + " n_iteration: number of total iterations\n", " \n", - "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n", - "dtype = torch.double\n", - "tkwargs = {\"device\": device, \"dtype\": dtype}\n", + " '''\n", + " # Initialization of the status\n", + " def __init__(self, fcn, batch_size, n_init, max_budget, **tkwargs):\n", + " \n", + " # Domain bounds\n", + " self.lb, self.ub = fcn.bounds\n", + " \n", + " # Problem dimensions\n", + " self.batch_size: int = batch_size # Dimension of the batch at each iteration\n", + " self.n_init: int = n_init # Number of initial samples\n", + " self.dim: int = fcn.dim # Dimension of the problem\n", + " \n", + " # Trust regions information # Lower bounds of trust region\n", + " self.tr_length: float = 0.8 # side length of trust region\n", + " self.tr_length_max: float = 0.8\n", + " self.tr_lb = torch.clamp(0.5*torch.ones(self.dim, **tkwargs) - self.tr_length / 2.0, 0.0, 1.0)\n", + " self.tr_ub = torch.clamp(0.5*torch.ones(self.dim, **tkwargs) + self.tr_length / 2.0, 0.0, 1.0)\n", + " self.tr_vol = torch.prod(self.tr_ub - self.tr_lb)\n", "\n", - "# Initialize FuRBO\n", - "obj = ack(dim = 2,\n", - " negate=True,\n", - " **tkwargs)\n", - "cons = list([sum_(threshold = 0,\n", - " lb = obj.lb,\n", - " ub = obj.ub), \n", - " norm_(threshold = 0.5, \n", - " lb = obj.lb, \n", - " ub = obj.ub)])\n", - "batch_size = int(1)#3 * obj.dim)\n", - "n_init = int(10)# * obj.dim)\n", - "n_iteration = int(100)# * obj.dim)\n", - "N_CANDIDATES = 2000\n", + " # Trust region updating \n", + " self.failure_counter: int = 0 # Counter for failure points to asses how algorithm is going\n", + " self.success_counter: int = 0 # Counter for success points to asses how algorithm is going\n", + " self.success_tolerance: int = 2 # Success tolerance \n", + " self.failure_tolerance: int = 3 # Failure tolerance \n", + " \n", + " # Tensor to save current batch information\n", + " self.batch_X: Tensor # Current batch to evaluate: X values\n", + " self.batch_Y: Tensor # Current batch to evaluate: Y value\n", + " self.batch_C: Tensor # Current batch to evaluate: C values\n", + " \n", + " # Stopping criteria information\n", + " self.it_counter: int = 0 # Counter for iterations\n", + " self.n_counter: int = 0 # Counter for samples evaluated\n", + " self.max_budget: int = max_budget # Maximum number of evaluations allowed\n", + " self.finish_trigger: bool = False # Trigger to stop optimization\n", + " \n", + " # Restart criteria information\n", + " self.tr_length_min: float = 0.5**7 # Minimum volume allowed for trust region\n", + " self.restart_trigger: bool = False # Trigger to stop optimization\n", + " \n", + " # Sobol sampler engine\n", + " self.sobol = SobolEngine(dimension=self.dim, scramble=True, seed=1)\n", + " \n", + " # Update the status\n", + " def update(self, X_next, Y_next, C_next, **tkwargs):\n", + " '''\n", + " Function to update optimization status\n", + " \n", + " Args:\n", + " X_next: samples X (input values) to update the status\n", + " Y_next: samples Y (objective value) to update the status\n", + " C_next: Samples C (constraints values) to update the status\n", + "\n", + " '''\n", + " \n", + " # Merge current batch with previously evaluated samples\n", + " if not hasattr(self, 'X'):\n", + " # If there are no previous samples, declare the Tensors\n", + " self.X = X_next\n", + " self.Y = Y_next\n", + " self.C = C_next\n", + " else:\n", + " # Else, concatenate the new batch to the previous samples\n", + " self.X = torch.cat((self.X, X_next), dim=0)\n", + " self.Y = torch.cat((self.Y, Y_next), dim=0)\n", + " self.C = torch.cat((self.C, C_next), dim=0)\n", + "\n", + " # update GPR surrogates\n", + " self.Y_model = get_fitted_model(self.X, self.Y, self.dim)\n", + " self.C_model = ModelListGP(*[get_fitted_model(self.X, C.reshape(-1, 1), self.dim) for C in self.C.t()])\n", + " \n", + " # Update batch information \n", + " self.batch_X = X_next\n", + " self.batch_Y = Y_next\n", + " self.batch_C = C_next\n", + " \n", + " # Update best value\n", + " # Find the best value among the candidates\n", + " best_id = get_best_index_for_batch(n_tr=1, Y=self.Y, C=self.C)\n", + " \n", + " # Update success and failure counters for trust region update\n", + " # If attribute 'best_X' does not exist, DoE was just evaluated -> no update on counters\n", + " if hasattr(self, 'best_X'):\n", + " if (self.C[best_id] <= 0).all():\n", + " # At least one new candidate is feasible\n", + " if (self.Y[best_id] > self.best_Y).any() or (self.best_C > 0).any():\n", + " self.success_counter += 1\n", + " self.failure_counter = 0 \n", + " else:\n", + " self.success_counter = 0\n", + " self.failure_counter += 1\n", + " else:\n", + " # No new candidate is feasible\n", + " total_violation_next = self.C[best_id].clamp(min=0).sum(dim=-1)\n", + " total_violation_center = self.best_C.clamp(min=0).sum(dim=-1)\n", + " if total_violation_next < total_violation_center:\n", + " self.success_counter += 1\n", + " self.failure_counter = 0\n", + " else:\n", + " self.success_counter = 0\n", + " self.failure_counter += 1\n", + " \n", + " # Update best values\n", + " self.best_X = self.X[best_id]\n", + " self.best_Y = self.Y[best_id]\n", + " self.best_C = self.C[best_id]\n", + " \n", + " # Update iteration counter\n", + " self.it_counter += 1\n", + " self.n_counter += len(Y_next)\n", + " \n", + " def reset_status(self, **tkwargs):\n", + " '''Function to reset the status for the restart'''\n", + " \n", + " # Reset trust regions size\n", + " self.tr_length: float = 0.8 # side length of trust region\n", + " self.tr_length_max: float = 0.8\n", + " self.tr_lb = torch.clamp(0.5*torch.ones(self.dim, **tkwargs) - self.tr_length / 2.0, 0.0, 1.0)\n", + " self.tr_ub = torch.clamp(0.5*torch.ones(self.dim, **tkwargs) + self.tr_length / 2.0, 0.0, 1.0)\n", + " self.tr_vol = torch.prod(self.tr_ub - self.tr_lb)\n", + "\n", + " # Reset counters to change trust region size \n", + " self.failure_counter: int = 0 # Counter of failure points to asses how algorithm is going\n", + " self.success_counter: int = 0 # Counter of success points to asses how algorithm is going\n", + " \n", + " # Reset restart criteria trigger\n", + " self.restart_trigger: bool = False # Trigger to restart optimization\n", + " \n", + " # Delete tensors with samples for training GPRs\n", + " if hasattr(self, 'X'):\n", + " del self.X\n", + " del self.Y\n", + " del self.C\n", + " \n", + " # Delete tensors with best value so far\n", + " if hasattr(self, 'best_X'):\n", + " del self.best_X\n", + " del self.best_Y\n", + " del self.best_C\n", + " \n", + " # Clear GPU memory\n", + " if tkwargs[\"device\"] == \"cuda\":\n", + " torch.cuda.empty_cache() \n", + "\n", + "def scbo_update_tr(state, **tkwargs):\n", + " \"\"\"\n", + " Function to update the side length of the trust region\n", + "\n", + " Args:\n", + " state: ScboState object\n", + "\n", + " \"\"\"\n", + " if state.success_counter == state.success_tolerance: # Expand trust region\n", + " state.tr_length = min(2.0 * state.tr_length, state.tr_length_max)\n", + " state.success_counter = 0\n", + " elif state.failure_counter == state.failure_tolerance: # Shrink trust region\n", + " state.tr_length /= 2.0\n", + " state.failure_counter = 0\n", + " \n", + " state.tr_lb = torch.clamp(state.best_X - state.tr_length / 2.0, 0.0, 1.0)\n", + " state.tr_ub = torch.clamp(state.best_X + state.tr_length / 2.0, 0.0, 1.0)\n", + "\n", + " state.tr_vol = torch.prod(state.tr_ub - state.tr_lb)\n", + " return state\n", + "\n", + "def scbo_generate_batch(state, n_candidates, **tkwargs):\n", + " \"\"\"\n", + " Function to compute next candidate to evaluate\n", + "\n", + " Args:\n", + " state: ScboState object\n", + " n_candidates: number of candidates inspecting the surrogates\n", + "\n", + " \"\"\"\n", + "\n", + " assert state.X.min() >= 0.0 and state.X.max() <= 1.0 and torch.all(torch.isfinite(state.Y))\n", + "\n", + " # Create the TR bounds\n", + " tr_lb = state.tr_lb\n", + " tr_ub = state.tr_ub\n", "\n", - "# FuRBO state initialization\n", - "FuRBO_status = Furbo_state(obj = obj, # Objective function\n", - " cons = cons, # Constraints function\n", - " batch_size = batch_size, # Batch size of each iteration\n", - " n_init = n_init, # Number of initial points to evaluate\n", - " n_iteration = n_iteration, # Number of iterations\n", - " **tkwargs)\n", + " # Thompson Sampling w/ Constraints (SCBO)\n", + " dim = state.X.shape[-1]\n", + " pert = state.sobol.draw(n_candidates).to(dtype=tkwargs['dtype'], device=tkwargs['device'])\n", + " pert = tr_lb + (tr_ub - tr_lb) * pert\n", + "\n", + " # Create a perturbation mask\n", + " prob_perturb = min(20.0 / dim, 1.0)\n", + " mask = torch.rand(n_candidates, dim, **tkwargs) <= prob_perturb\n", + " ind = torch.where(mask.sum(dim=1) == 0)[0]\n", + " mask[ind, torch.randint(0, dim - 1, size=(len(ind),), device=tkwargs['device'])] = 1\n", + "\n", + " # Create candidate points from the perturbations and the mask\n", + " X_cand = state.best_X.expand(n_candidates, dim).clone()\n", + " X_cand[mask] = pert[mask]\n", + "\n", + " # Sample on the candidate points using Constrained Max Posterior Sampling\n", + " constrained_thompson_sampling = ConstrainedMaxPosteriorSampling(\n", + " model=state.Y_model, constraint_model=state.C_model, replacement=False\n", + " )\n", + " with torch.no_grad():\n", + " X_next = constrained_thompson_sampling(X_cand, num_samples=state.batch_size)\n", + "\n", + " return X_next\n", + "\n", + "def scbo_stopping_criterion(state):\n", + " '''Function to evaluate if the maximum number of allowed iterations is reached.'''\n", + " return state.n_counter > state.max_budget\n", + "\n", + "def scbo_restart_criterion(state):\n", + " '''Function to evaluate if the minimum side length of the trust region is reached.'''\n", + " return state.tr_length < state.tr_length_min\n", + "\n", + "def scbo_optimize(fcn, objective, constraints, X_ini, batch_size = 1, n_init = 10, max_budget = 200, N_CANDIDATES = 2000):\n", + " '''Function to optimize an objective under a set of given constraints using SCBO\n", + " \n", + " Args:\n", + " objective: handle to evaluate objective\n", + " constraints: list of handles to evaluate constraints\n", + " batch_size: size of the batch to evaluate at each iteration\n", + " n_init: number of initial samples\n", + " max_budget: maximum number of evaluations allowed\n", "\n", - "# Initiate lists to save samples over the restarts\n", - "X_best, Y_best, C_best = [], [], []\n", - "X_all, Y_all, C_all = [], [], []\n", + " Return:\n", + " X_all: samples evaluated\n", + " Y_all: objective values of the samples evaluated\n", + " C_all: constraints values of the samples evaluated\n", "\n", - "# Continue optimization the stopping criterions isn't triggered\n", - "while not FuRBO_status.finish_trigger: \n", + " '''\n", + " # SCBO state initialization\n", + " state = ScboState(fcn,\n", + " batch_size = batch_size, # Batch size of each iteration\n", + " n_init = n_init, # Number of initial points to evaluate\n", + " max_budget = max_budget, # Number of iterations\n", + " **tkwargs)\n", + "\n", + " # Initiate lists to save samples over the restarts\n", + " X_all, Y_all, C_all = [], [], []\n", + "\n", + " # Continue optimization the stopping criterions isn't triggered\n", + " while not state.finish_trigger: \n", " \n", - " # Reset status for restarting\n", - " FuRBO_status.reset_status(**tkwargs)\n", + " # Reset status for restarting\n", + " state.reset_status(**tkwargs)\n", " \n", - " # generate intial batch of X\n", - " X_next = get_initial_points(FuRBO_status, **tkwargs)\n", + " # generate intial batch of X\n", + " X_next = X_ini # Use same initial DoE of FuRBO\n", " \n", - " # Reset and restart optimization\n", - " while not FuRBO_status.restart_trigger and not FuRBO_status.finish_trigger:\n", + " # Reset and restart optimization\n", + " while not state.restart_trigger and not state.finish_trigger:\n", " \n", - " # Evaluate current batch (samples in X_next)\n", - " Y_next = []\n", - " C_next = []\n", - " for x in X_next:\n", - " # Evaluate batch on obj ...\n", - " Y_next.append(FuRBO_status.obj.eval_(x))\n", - " # ... and constraints\n", - " C_next.append([c.eval_(x) for c in FuRBO_status.cons])\n", + " # Evaluate current batch (samples in X_next)\n", + " Y_next = []\n", + " C_next = []\n", + " for x in X_next:\n", + " # Evaluate batch on obj ...\n", + " Y_next.append(objective(x))\n", + " # ... and constraints\n", + " C_next.append([c(x) for c in constraints])\n", " \n", - " # process vector for PyTorch\n", - " Y_next = torch.tensor(Y_next).unsqueeze(-1).to(**tkwargs)\n", - " C_next = torch.tensor(C_next).to(**tkwargs)\n", + " # process vector for PyTorch\n", + " Y_next = torch.tensor(Y_next).unsqueeze(-1).to(**tkwargs)\n", + " C_next = torch.tensor(C_next).to(**tkwargs)\n", " \n", - " # Update FuRBO status with newly evaluated batch\n", - " FuRBO_status.update(X_next, Y_next, C_next, **tkwargs) \n", + " # Update SCBO status with newly evaluated batch\n", + " state.update(X_next, Y_next, C_next, **tkwargs) \n", " \n", - " # Printing current best\n", - " # If a feasible has been evaluated -> print current optimum (feasible sample with best objective value)\n", - " if (FuRBO_status.best_C <= 0).all():\n", - " best = FuRBO_status.best_Y.amax()\n", - " print(f\"{FuRBO_status.it_counter-1}) Best value: {best:.2e},\"\n", - " f\" MND radius: {FuRBO_status.radius}\")\n", - " \n", - " # Else, if no feasible has been evaluated -> print smallest violation (the sample that violatest the least all constraints)\n", - " else:\n", - " violation = FuRBO_status.best_C.clamp(min=0).sum()\n", - " print(f\"{FuRBO_status.it_counter-1}) No feasible point yet! Smallest total violation: \"\n", - " f\"{violation:.2e}, MND radius: {FuRBO_status.radius}\")\n", + " # Printing current best\n", + " # If a feasible has been evaluated -> print current optimum (feasible sample with best objective value)\n", + " if (state.best_C <= 0).all():\n", + " best = state.best_Y.amax()\n", + " print(f\"Samples evaluated: {state.n_counter} | Best value: {best:.2e},\"\n", + " f\" TR volume: {state.tr_vol}\")\n", + " \n", + " # Else, if no feasible has been evaluated -> print smallest violation (the sample that violatest the least all constraints)\n", + " else:\n", + " violation = state.best_C.clamp(min=0).sum()\n", + " print(f\"Samples evaluated: {state.n_counter} | No feasible point yet! Smallest total violation: \"\n", + " f\"{violation:.2e}, TR volume: {state.tr_vol}\")\n", " \n", - " # Update Trust regions\n", - " FuRBO_status = update_tr(FuRBO_status,\n", - " **tkwargs)\n", + " # Update Trust region\n", + " state = scbo_update_tr(state, **tkwargs)\n", " \n", - " # generate next batch to evaluate \n", - " X_next = generate_batch(FuRBO_status, N_CANDIDATES, **tkwargs)\n", + " # generate next batch to evaluate \n", + " X_next = scbo_generate_batch(state, N_CANDIDATES, **tkwargs)\n", " \n", - " # Check if stopping criterion is met (budget exhausted and if GP failed)\n", - " FuRBO_status.finish_trigger = stopping_criterion(FuRBO_status, n_iteration) \n", + " # Check if stopping criterion is met (budget exhausted and if GP failed)\n", + " state.finish_trigger = scbo_stopping_criterion(state) \n", " \n", - " # Check if restart criterion is met\n", - " FuRBO_status.restart_trigger = (restart_criterion(FuRBO_status, FuRBO_status.radius_min) or GP_restart_criterion(FuRBO_status))\n", + " # Check if restart criterion is met\n", + " state.restart_trigger = scbo_restart_criterion(state)\n", + "\n", + " # Save samples evaluated before resetting the status\n", + " X_all.append(state.X)\n", + " Y_all.append(state.Y)\n", + " C_all.append(state.C)\n", "\n", - " # Save samples evaluated before resetting the status\n", - " X_all.append(FuRBO_status.X)\n", - " Y_all.append(FuRBO_status.Y)\n", - " C_all.append(FuRBO_status.C)\n", + " # Ri-elaborate for processing\n", + " X_all = torch.cat(X_all)\n", + " Y_all = torch.cat(Y_all)\n", + " C_all = torch.cat(C_all)\n", "\n", - " # Save best sample of this run\n", - " X_best.append(FuRBO_status.best_X)\n", - " Y_best.append(FuRBO_status.best_Y)\n", - " C_best.append(FuRBO_status.best_C)" + " return X_all, Y_all, C_all" ] }, { "cell_type": "markdown", - "id": "a3d28f6c-5940-4d56-a3b5-4635980db76f", + "id": "96d1dc88", "metadata": {}, "source": [ - "### Printing result and plotting convergence curve\n", + "### Scenario 1: 20D Ackley function\n", "\n", - "Print the best-evaluated sample (over all restarts) and the objective value (if a feasible sample was found) or the smallest violation (if no feasible sample was found)." + "The problem maximizes the Ackley function in 20D" ] }, { "cell_type": "code", - "execution_count": 181, - "id": "027a9ec9-930a-48d0-b481-ffe9e9ca0d90", + "execution_count": 14, + "id": "05045730", + "metadata": {}, + "outputs": [], + "source": [ + "fun20 = Ackley(dim=20, negate=True).to(**tkwargs)\n", + "fun20.bounds[0, :].fill_(-5)\n", + "fun20.bounds[1, :].fill_(10)\n", + "\n", + "def eval_objective(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", + " return fun20(unnormalize(x - 0.3, fun20.bounds))" + ] + }, + { + "cell_type": "markdown", + "id": "c150dd70", + "metadata": {}, + "source": [ + "With two constraint functions: \n", + "\n", + "$c_1 = \\sum_{i=1}^{20} x_i \\leq 0$\n", + "\n", + "$c_2 = \\| \\mathbb{x}\\|_2 \\leq 0.5$" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "3abb68dd", + "metadata": {}, + "outputs": [], + "source": [ + "def c1(x):\n", + " return x.sum()\n", + "\n", + "def c2(x):\n", + " return torch.norm(x, p=2) - 5\n", + " \n", + "def eval_c1(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint c1\"\"\"\n", + " return c1(unnormalize(x, fun20.bounds))\n", + "\n", + "def eval_c2(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint c2\"\"\"\n", + " return c2(unnormalize(x, fun20.bounds))" + ] + }, + { + "cell_type": "markdown", + "id": "b4c5059b", + "metadata": {}, + "source": [ + "#### Evaluate algorithms" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "63e1529c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ + "FuRBO on 20D Ackley function\n", + "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 1.24e+01, MND radius: 1.0\n", + "Samples evaluated: 80 | No feasible point yet! Smallest total violation: 8.11e+00, MND radius: 1.0\n", + "Samples evaluated: 140 | No feasible point yet! Smallest total violation: 4.24e+00, MND radius: 1.0\n", + "Samples evaluated: 200 | No feasible point yet! Smallest total violation: 1.52e+00, MND radius: 1.0\n", + "Samples evaluated: 260 | Best value: -1.37e+01, MND radius: 1.0\n", + "Samples evaluated: 320 | Best value: -1.35e+01, MND radius: 1.0\n", + "Samples evaluated: 380 | Best value: -1.35e+01, MND radius: 1.0\n", + "Samples evaluated: 440 | Best value: -1.35e+01, MND radius: 1.0\n", + "Samples evaluated: 500 | Best value: -1.34e+01, MND radius: 1.0\n", + "Samples evaluated: 560 | Best value: -1.34e+01, MND radius: 1.0\n", + "Samples evaluated: 620 | Best value: -1.34e+01, MND radius: 1.0\n", + "Samples evaluated: 680 | Best value: -1.34e+01, MND radius: 1.0\n", + "Samples evaluated: 740 | Best value: -1.34e+01, MND radius: 1.0\n", + "Samples evaluated: 800 | Best value: -1.34e+01, MND radius: 1.0\n", + "Samples evaluated: 860 | Best value: -1.34e+01, MND radius: 0.5\n", + "Samples evaluated: 920 | Best value: -1.34e+01, MND radius: 0.5\n", + "Samples evaluated: 980 | Best value: -1.33e+01, MND radius: 0.5\n", + "Samples evaluated: 1040 | Best value: -1.33e+01, MND radius: 0.5\n", + "Samples evaluated: 1100 | Best value: -1.33e+01, MND radius: 0.5\n", + "Samples evaluated: 1160 | Best value: -1.33e+01, MND radius: 0.5\n", + "Samples evaluated: 1220 | Best value: -1.33e+01, MND radius: 0.25\n", + "Samples evaluated: 1280 | Best value: -1.30e+01, MND radius: 0.25\n", + "Samples evaluated: 1340 | Best value: -1.30e+01, MND radius: 0.25\n", + "Samples evaluated: 1400 | Best value: -1.30e+01, MND radius: 0.25\n", + "Samples evaluated: 1460 | Best value: -1.30e+01, MND radius: 0.25\n", + "Samples evaluated: 1520 | Best value: -1.27e+01, MND radius: 0.25\n", + "Samples evaluated: 1580 | Best value: -1.27e+01, MND radius: 0.5\n", + "Samples evaluated: 1640 | Best value: -1.27e+01, MND radius: 0.5\n", + "Samples evaluated: 1700 | Best value: -1.27e+01, MND radius: 0.5\n", + "Samples evaluated: 1760 | Best value: -1.27e+01, MND radius: 0.25\n", + "Samples evaluated: 1820 | Best value: -1.27e+01, MND radius: 0.25\n", + "Samples evaluated: 1880 | Best value: -1.27e+01, MND radius: 0.25\n", + "Samples evaluated: 1940 | Best value: -1.25e+01, MND radius: 0.125\n", + "Samples evaluated: 2000 | Best value: -1.24e+01, MND radius: 0.125\n", + "Samples evaluated: 2060 | Best value: -1.24e+01, MND radius: 0.25\n", "Optimization finished \n", - "\t Optimum: -1.99e-03, \n", - "\t X: tensor([[0.3333, 0.3333]], dtype=torch.float64)\n" + "\t Optimum: -1.24e+01, \n", + "\t X: [[0.29986496 0.22883195 0.36632051 0.36075071 0.29621583 0.3632648\n", + " 0.29325852 0.2913269 0.36938339 0.29182121 0.22704174 0.29191579\n", + " 0.50050442 0.30535068 0.36156627 0.30391326 0.36148896 0.42429123\n", + " 0.42693231 0.297737 ]]\n", + "\n", + " SCBO on 20D Ackley function\n", + "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 1.24e+01, TR volume: 0.011529215046068493\n", + "Samples evaluated: 80 | No feasible point yet! Smallest total violation: 8.80e+00, TR volume: 4.448000994609387e-05\n", + "Samples evaluated: 140 | No feasible point yet! Smallest total violation: 5.27e+00, TR volume: 0.00012368295952370722\n", + "Samples evaluated: 200 | No feasible point yet! Smallest total violation: 3.98e+00, TR volume: 0.0005001296693795576\n", + "Samples evaluated: 260 | No feasible point yet! Smallest total violation: 3.98e+00, TR volume: 0.0005404477468218018\n", + "Samples evaluated: 320 | No feasible point yet! Smallest total violation: 3.79e+00, TR volume: 0.0005404477468218018\n", + "Samples evaluated: 380 | No feasible point yet! Smallest total violation: 3.79e+00, TR volume: 0.0006255176611259401\n", + "Samples evaluated: 440 | No feasible point yet! Smallest total violation: 3.79e+00, TR volume: 0.0006255176611259401\n", + "Samples evaluated: 500 | No feasible point yet! Smallest total violation: 3.79e+00, TR volume: 0.0006255176611259401\n", + "Samples evaluated: 560 | No feasible point yet! Smallest total violation: 6.08e-01, TR volume: 6.171161145432459e-09\n", + "Samples evaluated: 620 | No feasible point yet! Smallest total violation: 2.51e-01, TR volume: 9.820559727080237e-09\n", + "Samples evaluated: 680 | No feasible point yet! Smallest total violation: 2.51e-01, TR volume: 0.00065009265457945\n", + "Samples evaluated: 740 | No feasible point yet! Smallest total violation: 2.51e-01, TR volume: 0.00065009265457945\n", + "Samples evaluated: 800 | No feasible point yet! Smallest total violation: 2.51e-01, TR volume: 0.00065009265457945\n", + "Samples evaluated: 860 | Best value: -1.40e+01, TR volume: 9.989878884692766e-09\n", + "Samples evaluated: 920 | Best value: -1.40e+01, TR volume: 1.0995116277760021e-08\n", + "Samples evaluated: 980 | Best value: -1.40e+01, TR volume: 1.0995116277760021e-08\n", + "Samples evaluated: 1040 | Best value: -1.40e+01, TR volume: 1.0995116277760021e-08\n", + "Samples evaluated: 1100 | Best value: -1.33e+01, TR volume: 1.0485760000000007e-14\n", + "Samples evaluated: 1160 | Best value: -1.33e+01, TR volume: 1.048575999999999e-14\n", + "Samples evaluated: 1220 | Best value: -1.33e+01, TR volume: 1.048575999999999e-14\n", + "Samples evaluated: 1280 | Best value: -1.33e+01, TR volume: 1.048575999999999e-14\n", + "Samples evaluated: 1340 | Best value: -1.33e+01, TR volume: 9.999999999999956e-21\n", + "Samples evaluated: 1400 | Best value: -1.33e+01, TR volume: 9.999999999999956e-21\n", + "Samples evaluated: 1460 | Best value: -1.33e+01, TR volume: 9.999999999999956e-21\n", + "Samples evaluated: 1520 | Best value: -1.32e+01, TR volume: 9.53674316406265e-27\n", + "Samples evaluated: 1580 | Best value: -1.31e+01, TR volume: 9.536743164062644e-27\n", + "Samples evaluated: 1640 | Best value: -1.31e+01, TR volume: 9.999999999999956e-21\n", + "Samples evaluated: 1700 | Best value: -1.31e+01, TR volume: 9.999999999999956e-21\n", + "Samples evaluated: 1760 | Best value: -1.31e+01, TR volume: 9.999999999999956e-21\n", + "Samples evaluated: 1820 | Best value: -1.29e+01, TR volume: 9.536743164062637e-27\n", + "Samples evaluated: 1880 | Best value: -1.29e+01, TR volume: 9.536743164062644e-27\n", + "Samples evaluated: 1940 | Best value: -1.29e+01, TR volume: 9.999999999999963e-21\n", + "Samples evaluated: 2000 | Best value: -1.29e+01, TR volume: 9.999999999999963e-21\n", + "Samples evaluated: 2060 | Best value: -1.29e+01, TR volume: 9.999999999999963e-21\n", + "Optimization finished \n", + "\t Optimum: -1.29e+01, \n", + "\t X: [[0.30035487 0.31809956 0.30696511 0.23543128 0.30153329 0.42668045\n", + " 0.43635181 0.41619196 0.28313953 0.29624711 0.2341553 0.37516172\n", + " 0.25547553 0.30038809 0.29715446 0.31140388 0.36711527 0.43834427\n", + " 0.31500617 0.44621602]]\n" ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "# Print best value found so far\n", - "# Ri-elaborate for processing\n", - "X_best = torch.stack(X_best).to(**tkwargs)\n", - "Y_best = torch.stack(Y_best).to(**tkwargs)\n", - "C_best = torch.stack(C_best).to(**tkwargs)\n", - "\n", - "# If a feasible has been evaluated -> print current optimum sample and yielded value\n", - "if (C_best <= 0).any():\n", - " best = Y_best.amax()\n", - " bext = X_best[Y_best.argmax()]\n", - " print(\"Optimization finished \\n\"\n", - " f\"\\t Optimum: {best:.2e}, \\n\"\n", - " f\"\\t X: {bext}\")\n", + "from matplotlib import patches\n", + "\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "# Defining settings\n", + "batch_size = 3 * fun20.dim\n", + "n_init = fun20.dim\n", + "max_budget = 2000\n", + "N_CANDIDATES = 2000\n", + "\n", + "# Generate initial DoE\n", + "X_ini = SobolEngine(dimension=fun20.dim, scramble=True, seed=1).draw(n=n_init).to(**tkwargs)\n", + "\n", + "# Evaluate FuRBO optimization \n", + "print(\"FuRBO on 20D Ackley function\")\n", + "X_all, Y_all, C_all = furbo_optimize(fun20,\n", + " eval_objective, \n", + " [eval_c1, eval_c2],\n", + " X_ini,\n", + " batch_size = batch_size,\n", + " n_init = n_init,\n", + " max_budget = max_budget,\n", + " N_CANDIDATES = N_CANDIDATES) \n", + "\n", + "# Print optimization result\n", + "print_results(X_all, Y_all, C_all)\n", + "\n", + "# Plot FuRBO convergence curve\n", + "plot_results(ax, \"darkgreen\", Y_all, C_all)\n", + "\n", + "# Evaluate SCBO optimization \n", + "print(\"\\n SCBO on 20D Ackley function\")\n", + "X_all, Y_all, C_all = scbo_optimize(fun20,\n", + " eval_objective, \n", + " [eval_c1, eval_c2],\n", + " X_ini,\n", + " batch_size = batch_size,\n", + " n_init = n_init,\n", + " max_budget = max_budget,\n", + " N_CANDIDATES = N_CANDIDATES) \n", + "\n", + "# Print optimization result\n", + "print_results(X_all, Y_all, C_all)\n", + "\n", + "# Plot SCBO convergence curve\n", + "plot_results(ax, \"darkorange\", Y_all, C_all)\n", + "\n", + "plt.xlim([0, len(Y_all)])\n", + "\n", + "patchList = []\n", + "patchList.append(patches.Patch(color='darkgreen', label='FuRBO'))\n", + "patchList.append(patches.Patch(color='darkorange', label='SCBO'))\n", + "ax.legend(handles=patchList, loc='lower right')\n", + "\n", + "ax.set_title(\"20D Ackley function with 2 constraints (Batch 3D)\")\n", + "\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "378feaab", + "metadata": {}, + "source": [ + "### Scenario 2: Speed Reducer Objective function\n", + "\n", + "The problem minimizes the weight $W$ of a speed reducer:\n", + "\n", + "$W = 0.7854x_1x_2^2(3.3333x_e^2+14.9334x_3-43.0934)-1.508x_1(x_6^2+x_7^2)+7.4777(x_6^3+x_7^3)+0.7854(x_4x_6^2+x_5x_7^2)$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "5a56a1e4", + "metadata": {}, + "outputs": [], + "source": [ + "class speedReducer():\n", + "\n", + " def __init__(self):\n", + " self.lower_bounds = torch.Tensor([2.6, 0.7, 17., 7.3, 7.3, 2.9, 4.9])\n", + " self.upper_bounds = torch.Tensor([3.6, 0.8, 28., 8.3, 8.3, 3.9, 5.9])\n", + " self.bounds = [self.lower_bounds, self.upper_bounds]\n", + "\n", + " self.dim: int = 7\n", + "\n", + " return\n", " \n", - "# Else, if no feasible has been evaluated -> print sample with smallest violation and the violation value\n", - "else:\n", - " violation = C_best.sum(dim=2).amin()\n", - " violaxion = X_best[C_best.sum(dim=2).argmin()]\n", - " \n", - " print(\"Optimization failed \\n\"\n", - " f\"\\t Smallest violation: {violation:.2e}, \\n\"\n", - " f\"\\t X: {violaxion}\")" + " def __call__(self, x):\n", + " x1, x2, x3, x4, x5, x6, x7 = x\n", + " \n", + " term1 = 0.7854 * x1 * x2**2 * (3.3333 * x3**2 + 14.9334 * x3 - 43.0934)\n", + " term2 = 1.508 * x1 * (x6**2 + x7**2)\n", + " term3 = 7.4777 * (x6**3 + x7**3)\n", + " term4 = 0.7854 * (x4 * x6**2 + x5 * x7**2)\n", + " \n", + " return term1 - term2 + term3 + term4 \n", + " \n", + "funS = speedReducer()\n", + "\n", + "def eval_objective(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", + " return -1 * funS(unnormalize(x, funS.bounds))" ] }, { "cell_type": "markdown", - "id": "db5ae248-3f04-4173-a98a-6c0738e38510", + "id": "8634f6c8", "metadata": {}, "source": [ - "Plot the monotonic convergence curve" + "#### Speed Reducer Constraint functions\n", + "\n", + "The problem is constrained by 11 functions.\n", + "\n", + "$g_1(x) = 27x^{−1}_1 x^{−2}_2 x^{−1}_3 \\leq 1$\n", + "\n", + "$g_2(x)=397.5x^{−1}_1 x^{−2}_2 x^{−2}_3 \\leq 1$\n", + "\n", + "$g_3(x)=1.93x^{−1}_2 x^{−1}_3 x^3_4 x^{−4}_6 \\leq 1$\n", + "\n", + "$g_4(x)=1.93x^{−1}_2 x^{−1}_3 x^3_5 x^{−4}_7 \\leq 1$\n", + "\n", + "$g_5(x)= \\frac{1}{0.1x^3_6} \\sqrt{\\left( \\frac{745x_4}{x_2x_3} \\right)^2 + 16.9 \\cdot 10^6} \\leq 1100$\n", + "\n", + "$g_6(x)= \\frac{1}{0.1x^3_7} \\sqrt{\\left( \\frac{745x5}{x_2x_3} \\right)^2 + 157.5 \\cdot 10^6} \\leq 850$\n", + "\n", + "$g_7(x)=x_2x_3 \\leq 40$\n", + "\n", + "$g_8(x)=\\frac{x_1}{x_2} \\geq 5$\n", + "\n", + "$g_9(x)=\\frac{x_1}{x_2} \\leq 12$\n", + "\n", + "$g_{10}(x)=(1.5x_6 + 1.9)x^{−1}_4 \\leq 1$\n", + "\n", + "$g_{11}(x)=(1.1x_7 + 1.9)x^{−1}_5 \\leq 1$" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "695f8690", + "metadata": {}, + "outputs": [], + "source": [ + "def g1(x):\n", + " return 27.0 / (x[0] * x[1]**2 * x[2]) - 1\n", + "\n", + "def g2(x):\n", + " return 397.5 / (x[0] * x[1]**2 * x[2]**2) - 1\n", + "\n", + "def g3(x):\n", + " return 1.93 * x[3]**3 / (x[1] * x[2] * x[5]**4) - 1\n", + "\n", + "def g4(x):\n", + " return 1.93 * x[4]**3 / (x[1] * x[2] * x[6]**4) - 1\n", + "\n", + "def g5(x):\n", + " return (1 / (0.1 * x[5]**3)) * np.sqrt((745 * x[3] / (x[1] * x[2]))**2 + 16.9e6) - 1100\n", + "\n", + "def g6(x):\n", + " return (1 / (0.1 * x[6]**3)) * np.sqrt((745 * x[4] / (x[1] * x[2]))**2 + 157.5e6) - 850\n", + "\n", + "def g7(x):\n", + " return x[1] * x[2] - 40\n", + "\n", + "def g8(x):\n", + " return 5 - x[0] / x[1]\n", + "\n", + "def g9(x):\n", + " return x[0] / x[1] - 12\n", + "\n", + "def g10(x):\n", + " return (1.5 * x[5] + 1.9) / x[3] - 1\n", + "\n", + "def g11(x):\n", + " return (1.1 * x[6] + 1.9) / x[4] - 1 \n", + "\n", + "# Handles to evaluate constraints\n", + "def eval_g1(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g1\"\"\"\n", + " return g1(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g2(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g2\"\"\"\n", + " return g2(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g3(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g3\"\"\"\n", + " return g3(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g4(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g4\"\"\"\n", + " return g4(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g5(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g5\"\"\"\n", + " return g5(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g6(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g6\"\"\"\n", + " return g6(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g7(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g7\"\"\"\n", + " return g7(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g8(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g8\"\"\"\n", + " return g8(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g9(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g9\"\"\"\n", + " return g9(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g10(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g10\"\"\"\n", + " return g10(unnormalize(x, funS.bounds)) \n", + "\n", + "def eval_g11(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g11\"\"\"\n", + " return g11(unnormalize(x, funS.bounds)) " + ] + }, + { + "cell_type": "markdown", + "id": "e7668384", + "metadata": {}, + "source": [ + "#### Evaluate algorithms" ] }, { "cell_type": "code", - "execution_count": 189, - "id": "671ec5e5", + "execution_count": 19, + "id": "ea71286a", "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FuRBO on speed reducer problem\n", + "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 2.38e-01, MND radius: 1.0\n", + "Samples evaluated: 17 | Best value: -4.93e+03, MND radius: 1.0\n", + "Samples evaluated: 24 | Best value: -3.88e+03, MND radius: 1.0\n", + "Samples evaluated: 31 | Best value: -3.13e+03, MND radius: 1.0\n", + "Samples evaluated: 38 | Best value: -3.09e+03, MND radius: 1.0\n", + "Samples evaluated: 45 | Best value: -3.09e+03, MND radius: 1.0\n", + "Samples evaluated: 52 | Best value: -3.09e+03, MND radius: 1.0\n", + "Samples evaluated: 59 | Best value: -3.09e+03, MND radius: 1.0\n", + "Samples evaluated: 66 | Best value: -3.04e+03, MND radius: 0.5\n", + "Samples evaluated: 73 | Best value: -3.04e+03, MND radius: 0.5\n", + "Samples evaluated: 80 | Best value: -3.04e+03, MND radius: 0.5\n", + "Samples evaluated: 87 | Best value: -3.04e+03, MND radius: 0.5\n", + "Samples evaluated: 94 | Best value: -3.04e+03, MND radius: 0.25\n", + "Samples evaluated: 101 | Best value: -3.03e+03, MND radius: 0.25\n", + "Samples evaluated: 108 | Best value: -3.03e+03, MND radius: 0.25\n", + "Samples evaluated: 115 | Best value: -3.03e+03, MND radius: 0.25\n", + "Samples evaluated: 122 | Best value: -3.03e+03, MND radius: 0.25\n", + "Samples evaluated: 129 | Best value: -3.03e+03, MND radius: 0.125\n", + "Samples evaluated: 136 | Best value: -3.03e+03, MND radius: 0.125\n", + "Samples evaluated: 143 | Best value: -3.03e+03, MND radius: 0.125\n", + "Samples evaluated: 150 | Best value: -3.03e+03, MND radius: 0.125\n", + "Samples evaluated: 157 | Best value: -3.01e+03, MND radius: 0.0625\n", + "Samples evaluated: 164 | Best value: -3.01e+03, MND radius: 0.0625\n", + "Samples evaluated: 171 | Best value: -3.01e+03, MND radius: 0.0625\n", + "Samples evaluated: 178 | Best value: -3.01e+03, MND radius: 0.0625\n", + "Samples evaluated: 185 | Best value: -3.01e+03, MND radius: 0.03125\n", + "Samples evaluated: 192 | Best value: -3.01e+03, MND radius: 0.03125\n", + "Samples evaluated: 199 | Best value: -3.01e+03, MND radius: 0.03125\n", + "Samples evaluated: 206 | Best value: -3.01e+03, MND radius: 0.03125\n", + "Samples evaluated: 213 | Best value: -3.00e+03, MND radius: 0.015625\n", + "Optimization finished \n", + "\t Optimum: -3.00e+03, \n", + "\t X: [[9.02528720e-01 1.17360979e-03 9.05342813e-05 2.10989121e-01\n", + " 5.95593310e-01 4.58617181e-01 3.86871766e-01]]\n", + "\n", + " SCBO on speed reducer problem\n", + "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 2.38e-01, TR volume: 0.2097152000000001\n", + "Samples evaluated: 17 | No feasible point yet! Smallest total violation: 4.13e-02, TR volume: 0.03737699729156021\n", + "Samples evaluated: 24 | No feasible point yet! Smallest total violation: 9.70e-04, TR volume: 0.02103152421386524\n", + "Samples evaluated: 31 | Best value: -3.43e+03, TR volume: 0.04873321441954075\n", + "Samples evaluated: 38 | Best value: -3.22e+03, TR volume: 0.028856063920429414\n", + "Samples evaluated: 45 | Best value: -3.21e+03, TR volume: 0.024116579298590846\n", + "Samples evaluated: 52 | Best value: -3.13e+03, TR volume: 0.02118393716356287\n", + "Samples evaluated: 59 | Best value: -3.13e+03, TR volume: 0.014900499128629683\n", + "Samples evaluated: 66 | Best value: -3.12e+03, TR volume: 0.014900499128629683\n", + "Samples evaluated: 73 | Best value: -3.12e+03, TR volume: 0.011343326759723086\n", + "Samples evaluated: 80 | Best value: -3.12e+03, TR volume: 0.011343326759723086\n", + "Samples evaluated: 87 | Best value: -3.12e+03, TR volume: 0.011343326759723086\n", + "Samples evaluated: 94 | Best value: -3.07e+03, TR volume: 0.00014358101224495537\n", + "Samples evaluated: 101 | Best value: -3.07e+03, TR volume: 0.00029068378750287505\n", + "Samples evaluated: 108 | Best value: -3.07e+03, TR volume: 0.00029068378750287505\n", + "Samples evaluated: 115 | Best value: -3.07e+03, TR volume: 0.00029068378750287505\n", + "Samples evaluated: 122 | Best value: -3.05e+03, TR volume: 3.2199173185070756e-06\n", + "Samples evaluated: 129 | Best value: -3.05e+03, TR volume: 2.520842270461592e-06\n", + "Samples evaluated: 136 | Best value: -3.05e+03, TR volume: 2.520842270461592e-06\n", + "Samples evaluated: 143 | Best value: -3.05e+03, TR volume: 2.520842270461592e-06\n", + "Samples evaluated: 150 | Best value: -3.03e+03, TR volume: 2.7034417934772597e-08\n", + "Samples evaluated: 157 | Best value: -3.03e+03, TR volume: 3.00388114029285e-08\n", + "Samples evaluated: 164 | Best value: -3.03e+03, TR volume: 3.1578071834415887e-06\n", + "Samples evaluated: 171 | Best value: -3.03e+03, TR volume: 3.1578071834415887e-06\n", + "Samples evaluated: 178 | Best value: -3.03e+03, TR volume: 3.1578071834415887e-06\n", + "Samples evaluated: 185 | Best value: -3.03e+03, TR volume: 2.810991202840537e-08\n", + "Samples evaluated: 192 | Best value: -3.03e+03, TR volume: 2.810991202840537e-08\n", + "Samples evaluated: 199 | Best value: -3.03e+03, TR volume: 2.810991202840537e-08\n", + "Samples evaluated: 206 | Best value: -3.02e+03, TR volume: 2.451099170436267e-10\n", + "Samples evaluated: 213 | Best value: -3.02e+03, TR volume: 2.7067026843538696e-10\n", + "Optimization finished \n", + "\t Optimum: -3.02e+03, \n", + "\t X: [[9.17650597e-01 9.43228246e-03 1.55023053e-04 3.73859052e-01\n", + " 7.72787844e-01 4.56641981e-01 3.88081869e-01]]\n" + ] + }, { "data": { - "image/png": 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", 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" ] @@ -946,41 +1808,67 @@ } ], "source": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "from matplotlib import rc\n", - "\n", - "def ensure_tensor(x, tkwargs, dim=0):\n", - " \"\"\"Helper function to concatenate or convert to tensor to handle potential multiple restarts.\"\"\"\n", - " if isinstance(x, (list, tuple)):\n", - " # flatten if there's only one element\n", - " if len(x) == 1:\n", - " x = x[0]\n", - " else:\n", - " x = torch.cat([xi if torch.is_tensor(xi) else torch.as_tensor(xi) for xi in x], dim=dim)\n", - " # ensure final type is tensor\n", - " if not torch.is_tensor(x):\n", - " x = torch.as_tensor(x)\n", - " return x.to(**tkwargs)\n", + "from matplotlib import patches\n", "\n", - "Y_all = ensure_tensor(Y_all, tkwargs)\n", - "C_all = ensure_tensor(C_all, tkwargs)\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", + "# Defining settings\n", + "batch_size = funS.dim\n", + "n_init = int(10)\n", + "max_budget = 210\n", + "N_CANDIDATES = 2000\n", "\n", - "fig, ax = plt.subplots(figsize=(8, 6))\n", + "# Generate initial DoE\n", + "X_ini = SobolEngine(dimension=funS.dim, scramble=True, seed=1).draw(n=n_init).to(**tkwargs)\n", "\n", - "score = Y_all.clone()\n", - "# Set infeasible to -inf\n", - "score[~(C_all <= 0).all(dim=-1)] = float(\"-inf\")\n", - "fx = np.maximum.accumulate(score.cpu())\n", - "plt.plot(fx, marker=\"\", lw=3)\n", + "# Evaluate FuRBO optimization \n", + "print(\"FuRBO on speed reducer problem\")\n", + "X_all, Y_all, C_all = furbo_optimize(funS,\n", + " eval_objective, \n", + " [eval_g1, eval_g2, eval_g3,\n", + " eval_g4, eval_g5, eval_g6,\n", + " eval_g7, eval_g8, eval_g9,\n", + " eval_g10, eval_g11],\n", + " X_ini,\n", + " batch_size = batch_size,\n", + " n_init = n_init,\n", + " max_budget = max_budget,\n", + " N_CANDIDATES = N_CANDIDATES) \n", + "\n", + "# Print optimization result\n", + "print_results(X_all, Y_all, C_all)\n", + "\n", + "# Plot FuRBO convergence curve\n", + "plot_results(ax, \"darkgreen\", Y_all, C_all)\n", + "\n", + "# Evaluate SCBO optimization \n", + "print(\"\\n SCBO on speed reducer problem\")\n", + "X_all, Y_all, C_all = scbo_optimize(funS,\n", + " eval_objective, \n", + " [eval_g1, eval_g2, eval_g3,\n", + " eval_g4, eval_g5, eval_g6,\n", + " eval_g7, eval_g8, eval_g9,\n", + " eval_g10, eval_g11],\n", + " X_ini,\n", + " batch_size = batch_size,\n", + " n_init = n_init,\n", + " max_budget = max_budget,\n", + " N_CANDIDATES = N_CANDIDATES) \n", + "\n", + "# Print optimization result\n", + "print_results(X_all, Y_all, C_all)\n", + "\n", + "# Plot SCBO convergence curve\n", + "plot_results(ax, \"darkorange\", Y_all, C_all)\n", "\n", - "plt.plot([0, len(Y_all)], [obj.fun.optimal_value, obj.fun.optimal_value], \"k--\", lw=3)\n", - "plt.ylabel(\"Function value\", fontsize=18)\n", - "plt.xlabel(\"Number of evaluations\", fontsize=18)\n", - "plt.title(\"10D Ackley with 2 outcome constraints\", fontsize=20)\n", "plt.xlim([0, len(Y_all)])\n", - "plt.ylim([np.floor(min(fx[(C_all <= 0).all(dim=-1)])), 1]) \n", + "\n", + "patchList = []\n", + "patchList.append(patches.Patch(color='darkgreen', label='FuRBO'))\n", + "patchList.append(patches.Patch(color='darkorange', label='SCBO'))\n", + "ax.legend(handles=patchList, loc='lower right')\n", + "\n", + "ax.set_title(\"7D Speed Reducer Weight Minimization with 11 constraints (Batch 1D)\")\n", "\n", "plt.grid(True)\n", "plt.show()" @@ -989,7 +1877,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "COCOTeemo", "language": "python", "name": "python3" }, @@ -1003,7 +1891,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.15" + "version": "3.12.9" } }, "nbformat": 4, From d2291548861feb43b1a9159fcade40129c38b4f9 Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Thu, 4 Dec 2025 13:58:43 +0100 Subject: [PATCH 6/9] Add files via upload --- 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zn#BHoR>RHh4Hmp7R3Mx-23^{9h=cLA`-voiGs*hOywl$v9C{xdnEgRdH2=#}|6{Fn z#lS`*+MhnW?K@4s{qw`Ugp<7``dePD&}oA#nfQUz&vbr&|GK;2aG7{V)8qee$N%y%_pmWDfFm{oyz_tmLjSWrRgea+ ztwp8tZ$1WC$@7fmUtLek|7XAU?+EkHpY&%Xhwg*#in*cwZ$4)KIf%qqt0n($m+wDz z?f>{|%E5Q#Ec`|MZ$3s)1}rmGk4^;6pHTn5fA~LglKJb|5gwKKI2I3TkjjVR&PdV^e0~b&t3d~jR9eB zaA1zb@8JBKKCk;4`24eO-mf6e|IfVpzkg>DXK-*Co3>E=uP^$qL&g90Fh@oZJ8C%R zK5_q>A2xRDjZ`=sV*BrW6nMM7OzfF45cFvL-~2FR`ggSA|CvVrOV9on?<^9FJ$s}% mLd-y3`0u<@82tOijhH2wYwvqaUR(nIyb_mti4cAB{{I6;+a*c> literal 0 HcmV?d00001 From c7aa7b040e24ffc880aa64732a43d6927ea96a61 Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Thu, 4 Dec 2025 14:05:17 +0100 Subject: [PATCH 7/9] Update FuRBO.ipynb Added graphical abstract --- notebooks_community/FuRBO/FuRBO.ipynb | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/notebooks_community/FuRBO/FuRBO.ipynb b/notebooks_community/FuRBO/FuRBO.ipynb index 1c13811606..e2a7ced17f 100644 --- a/notebooks_community/FuRBO/FuRBO.ipynb +++ b/notebooks_community/FuRBO/FuRBO.ipynb @@ -27,6 +27,14 @@ "[2] [David Eriksson and Matthias Poloczek. Scalable constrained Bayesian optimization. In International Conference on Artificial Intelligence and Statistics, pages 730–738. PMLR, 2021.](https://doi.org/10.48550/arxiv.2002.08526)\n" ] }, + { + "cell_type": "markdown", + "id": "07b7f421", + "metadata": {}, + "source": [ + "![title](graphical_abstract_furbo.png)" + ] + }, { "cell_type": "markdown", "id": "ba4aa821", From 3f343e0af3d683327640c405669aa9ffb4f4a3a6 Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Fri, 19 Dec 2025 10:20:01 +0100 Subject: [PATCH 8/9] Update FuRBO with BoTorch test case --- notebooks_community/FuRBO/FuRBO.ipynb | 629 +++++++++++--------------- 1 file changed, 254 insertions(+), 375 deletions(-) diff --git a/notebooks_community/FuRBO/FuRBO.ipynb b/notebooks_community/FuRBO/FuRBO.ipynb index e2a7ced17f..a30ce36589 100644 --- a/notebooks_community/FuRBO/FuRBO.ipynb +++ b/notebooks_community/FuRBO/FuRBO.ipynb @@ -32,7 +32,7 @@ "id": "07b7f421", "metadata": {}, "source": [ - "![title](graphical_abstract_furbo.png)" + "![Graphical abstract](graphical_abstract_furbo.png)" ] }, { @@ -57,7 +57,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "id": "890f1a54-b6cf-4af4-9bfb-1835b2f737a6", "metadata": {}, "outputs": [], @@ -82,7 +82,7 @@ "\n", "def eval_objective(x):\n", " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", - " return fun(unnormalize(x - 0.3, fun.bounds))\n" + " return fun(unnormalize(x, fun.bounds))\n" ] }, { @@ -106,17 +106,13 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "id": "228d816a-6452-4078-b3fd-6a42569237c3", "metadata": {}, "outputs": [], "source": [ "def c1(x):\n", - " return x.sum()\n", - " \n", - "def eval_c1(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint c1\"\"\"\n", - " return c1(unnormalize(x, fun.bounds))" + " return x.sum()" ] }, { @@ -129,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "id": "1e0f4e8d-657f-49d8-bb59-eb8c2ff4a9f5", "metadata": {}, "outputs": [], @@ -137,9 +133,9 @@ "def c2(x):\n", " return torch.norm(x, p=2) - 5\n", " \n", - "def eval_c2(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint c2\"\"\"\n", - " return c2(unnormalize(x, fun.bounds))" + "def eval_constraints(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on the constraints\"\"\"\n", + " return Tensor([c1(unnormalize(x - 0.3, fun.bounds)), c2(unnormalize(x - 0.3, fun.bounds))])" ] }, { @@ -159,7 +155,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "id": "020338e2-9eaf-49cf-9e5c-fd00e1a46835", "metadata": {}, "outputs": [], @@ -170,6 +166,7 @@ "\n", "from botorch.models import SingleTaskGP\n", "from botorch.models.transforms.outcome import Standardize\n", + "from botorch.models.transforms import Normalize\n", "from botorch.models.model_list_gp_regression import ModelListGP\n", "\n", "from gpytorch.constraints import Interval\n", @@ -203,7 +200,7 @@ " Y,\n", " covar_module=covar_module,\n", " likelihood=likelihood,\n", - " outcome_transform=Standardize(m=1),\n", + " outcome_transform=Standardize(m=1)\n", " )\n", " mll = ExactMarginalLogLikelihood(model.likelihood, model)\n", "\n", @@ -227,6 +224,7 @@ " \n", " # Domain bounds\n", " self.lb, self.ub = fcn.bounds\n", + " self.bounds = fcn.bounds\n", " \n", " # Problem dimensions\n", " self.batch_size: int = batch_size # Dimension of the batch at each iteration\n", @@ -400,7 +398,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "id": "3d36cf01-c5be-44ee-96bb-12564225bd7b", "metadata": {}, "outputs": [], @@ -545,7 +543,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "id": "0116ca79-7555-4da3-bfd4-69941926eb11", "metadata": {}, "outputs": [], @@ -566,7 +564,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 9, "id": "2d969ea7-2f1e-4433-b3b4-53413546c2f2", "metadata": {}, "outputs": [], @@ -631,7 +629,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 10, "id": "189aae72-f033-49db-bcc8-0e791774bd76", "metadata": {}, "outputs": [], @@ -659,7 +657,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 11, "id": "81f9bd26", "metadata": {}, "outputs": [], @@ -681,7 +679,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 12, "id": "b9d52417-aaa5-40b6-bf07-12c074460283", "metadata": {}, "outputs": [], @@ -733,11 +731,11 @@ " # Evaluate batch on obj ...\n", " Y_next.append(objective(x))\n", " # ... and constraints\n", - " C_next.append([c(x) for c in constraints])\n", + " C_next.append(constraints(x))\n", " \n", " # process vector for PyTorch\n", - " Y_next = torch.tensor(Y_next).unsqueeze(-1).to(**tkwargs)\n", - " C_next = torch.tensor(C_next).to(**tkwargs)\n", + " Y_next = torch.stack(Y_next).unsqueeze(-1).to(**tkwargs)\n", + " C_next = torch.stack(C_next).to(**tkwargs)\n", " \n", " # Update FuRBO status with newly evaluated batch\n", " state.update(X_next, Y_next, C_next, **tkwargs) \n", @@ -792,7 +790,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 13, "id": "17675f23", "metadata": {}, "outputs": [], @@ -846,7 +844,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 14, "id": "027a9ec9-930a-48d0-b481-ffe9e9ca0d90", "metadata": {}, "outputs": [ @@ -854,66 +852,66 @@ "name": "stdout", "output_type": "stream", "text": [ - "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 1.01e+01, MND radius: 1.0\n", - "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 1.90e+00, MND radius: 1.0\n", - "Samples evaluated: 30 | No feasible point yet! Smallest total violation: 1.90e+00, MND radius: 1.0\n", - "Samples evaluated: 40 | Best value: -1.46e+01, MND radius: 1.0\n", - "Samples evaluated: 50 | Best value: -1.41e+01, MND radius: 1.0\n", - "Samples evaluated: 60 | Best value: -1.37e+01, MND radius: 1.0\n", - "Samples evaluated: 70 | Best value: -1.35e+01, MND radius: 1.0\n", - "Samples evaluated: 80 | Best value: -1.35e+01, MND radius: 1.0\n", - "Samples evaluated: 90 | Best value: -1.35e+01, MND radius: 1.0\n", - "Samples evaluated: 100 | Best value: -1.35e+01, MND radius: 1.0\n", - "Samples evaluated: 110 | Best value: -1.30e+01, MND radius: 0.5\n", - "Samples evaluated: 120 | Best value: -1.30e+01, MND radius: 0.5\n", - "Samples evaluated: 130 | Best value: -1.30e+01, MND radius: 0.5\n", - "Samples evaluated: 140 | Best value: -1.30e+01, MND radius: 0.5\n", - "Samples evaluated: 150 | Best value: -1.30e+01, MND radius: 0.25\n", - "Samples evaluated: 160 | Best value: -1.30e+01, MND radius: 0.25\n", - "Samples evaluated: 170 | Best value: -1.30e+01, MND radius: 0.25\n", - "Samples evaluated: 180 | Best value: -1.30e+01, MND radius: 0.125\n", - "Samples evaluated: 190 | Best value: -1.30e+01, MND radius: 0.125\n", - "Samples evaluated: 200 | Best value: -1.27e+01, MND radius: 0.125\n", - "Samples evaluated: 210 | Best value: -1.27e+01, MND radius: 0.125\n", - "Samples evaluated: 220 | Best value: -1.27e+01, MND radius: 0.125\n", - "Samples evaluated: 230 | Best value: -1.25e+01, MND radius: 0.125\n", - "Samples evaluated: 240 | Best value: -1.25e+01, MND radius: 0.125\n", - "Samples evaluated: 250 | Best value: -1.25e+01, MND radius: 0.125\n", - "Samples evaluated: 260 | Best value: -1.23e+01, MND radius: 0.125\n", - "Samples evaluated: 270 | Best value: -1.23e+01, MND radius: 0.125\n", - "Samples evaluated: 280 | Best value: -1.23e+01, MND radius: 0.25\n", - "Samples evaluated: 290 | Best value: -1.23e+01, MND radius: 0.25\n", - "Samples evaluated: 300 | Best value: -1.23e+01, MND radius: 0.25\n", - "Samples evaluated: 310 | Best value: -1.23e+01, MND radius: 0.125\n", - "Samples evaluated: 320 | Best value: -1.22e+01, MND radius: 0.125\n", - "Samples evaluated: 330 | Best value: -1.22e+01, MND radius: 0.125\n", - "Samples evaluated: 340 | Best value: -1.21e+01, MND radius: 0.125\n", - "Samples evaluated: 350 | Best value: -1.21e+01, MND radius: 0.125\n", - "Samples evaluated: 360 | Best value: -1.21e+01, MND radius: 0.125\n", - "Samples evaluated: 370 | Best value: -1.21e+01, MND radius: 0.125\n", - "Samples evaluated: 380 | Best value: -1.21e+01, MND radius: 0.0625\n", - "Samples evaluated: 390 | Best value: -1.21e+01, MND radius: 0.0625\n", - "Samples evaluated: 400 | Best value: -1.21e+01, MND radius: 0.125\n", - "Samples evaluated: 410 | Best value: -1.21e+01, MND radius: 0.125\n", - "Samples evaluated: 420 | Best value: -1.21e+01, MND radius: 0.125\n", - "Samples evaluated: 430 | Best value: -1.21e+01, MND radius: 0.0625\n", - "Samples evaluated: 440 | Best value: -1.21e+01, MND radius: 0.0625\n", - "Samples evaluated: 450 | Best value: -1.21e+01, MND radius: 0.0625\n", - "Samples evaluated: 460 | Best value: -1.21e+01, MND radius: 0.03125\n", - "Samples evaluated: 470 | Best value: -1.21e+01, MND radius: 0.03125\n", - "Samples evaluated: 480 | Best value: -1.21e+01, MND radius: 0.03125\n", - "Samples evaluated: 490 | Best value: -1.21e+01, MND radius: 0.015625\n", - "Samples evaluated: 500 | Best value: -1.21e+01, MND radius: 0.015625\n", - "Samples evaluated: 510 | Best value: -1.21e+01, MND radius: 0.03125\n", + "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 5.98e+00, MND radius: 1.0\n", + "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 5.98e+00, MND radius: 1.0\n", + "Samples evaluated: 30 | No feasible point yet! Smallest total violation: 5.24e+00, MND radius: 1.0\n", + "Samples evaluated: 40 | No feasible point yet! Smallest total violation: 2.28e+00, MND radius: 1.0\n", + "Samples evaluated: 50 | Best value: -1.38e+01, MND radius: 1.0\n", + "Samples evaluated: 60 | Best value: -1.18e+01, MND radius: 1.0\n", + "Samples evaluated: 70 | Best value: -1.18e+01, MND radius: 1.0\n", + "Samples evaluated: 80 | Best value: -1.10e+01, MND radius: 1.0\n", + "Samples evaluated: 90 | Best value: -1.10e+01, MND radius: 1.0\n", + "Samples evaluated: 100 | Best value: -1.10e+01, MND radius: 1.0\n", + "Samples evaluated: 110 | Best value: -1.10e+01, MND radius: 1.0\n", + "Samples evaluated: 120 | Best value: -1.10e+01, MND radius: 1.0\n", + "Samples evaluated: 130 | Best value: -1.08e+01, MND radius: 0.5\n", + "Samples evaluated: 140 | Best value: -1.05e+01, MND radius: 0.5\n", + "Samples evaluated: 150 | Best value: -1.05e+01, MND radius: 1.0\n", + "Samples evaluated: 160 | Best value: -1.05e+01, MND radius: 1.0\n", + "Samples evaluated: 170 | Best value: -1.05e+01, MND radius: 1.0\n", + "Samples evaluated: 180 | Best value: -1.05e+01, MND radius: 0.5\n", + "Samples evaluated: 190 | Best value: -1.05e+01, MND radius: 0.5\n", + "Samples evaluated: 200 | Best value: -1.02e+01, MND radius: 0.5\n", + "Samples evaluated: 210 | Best value: -1.02e+01, MND radius: 0.5\n", + "Samples evaluated: 220 | Best value: -1.02e+01, MND radius: 0.5\n", + "Samples evaluated: 230 | Best value: -1.02e+01, MND radius: 0.5\n", + "Samples evaluated: 240 | Best value: -1.00e+01, MND radius: 0.25\n", + "Samples evaluated: 250 | Best value: -1.00e+01, MND radius: 0.25\n", + "Samples evaluated: 260 | Best value: -9.94e+00, MND radius: 0.25\n", + "Samples evaluated: 270 | Best value: -9.94e+00, MND radius: 0.25\n", + "Samples evaluated: 280 | Best value: -9.79e+00, MND radius: 0.25\n", + "Samples evaluated: 290 | Best value: -9.79e+00, MND radius: 0.25\n", + "Samples evaluated: 300 | Best value: -9.79e+00, MND radius: 0.25\n", + "Samples evaluated: 310 | Best value: -9.79e+00, MND radius: 0.25\n", + "Samples evaluated: 320 | Best value: -9.29e+00, MND radius: 0.125\n", + "Samples evaluated: 330 | Best value: -9.29e+00, MND radius: 0.125\n", + "Samples evaluated: 340 | Best value: -9.23e+00, MND radius: 0.125\n", + "Samples evaluated: 350 | Best value: -9.23e+00, MND radius: 0.125\n", + "Samples evaluated: 360 | Best value: -9.23e+00, MND radius: 0.125\n", + "Samples evaluated: 370 | Best value: -9.23e+00, MND radius: 0.125\n", + "Samples evaluated: 380 | Best value: -9.18e+00, MND radius: 0.0625\n", + "Samples evaluated: 390 | Best value: -9.18e+00, MND radius: 0.0625\n", + "Samples evaluated: 400 | Best value: -9.18e+00, MND radius: 0.0625\n", + "Samples evaluated: 410 | Best value: -9.17e+00, MND radius: 0.0625\n", + "Samples evaluated: 420 | Best value: -9.12e+00, MND radius: 0.0625\n", + "Samples evaluated: 430 | Best value: -9.12e+00, MND radius: 0.125\n", + "Samples evaluated: 440 | Best value: -9.12e+00, MND radius: 0.125\n", + "Samples evaluated: 450 | Best value: -9.12e+00, MND radius: 0.125\n", + "Samples evaluated: 460 | Best value: -9.12e+00, MND radius: 0.0625\n", + "Samples evaluated: 470 | Best value: -9.12e+00, MND radius: 0.0625\n", + "Samples evaluated: 480 | Best value: -9.11e+00, MND radius: 0.0625\n", + "Samples evaluated: 490 | Best value: -9.11e+00, MND radius: 0.125\n", + "Samples evaluated: 500 | Best value: -9.11e+00, MND radius: 0.125\n", + "Samples evaluated: 510 | Best value: -9.11e+00, MND radius: 0.125\n", "Optimization finished \n", - "\t Optimum: -1.21e+01, \n", - "\t X: [[0.30068576 0.36640939 0.2989651 0.23413855 0.30010012 0.43401068\n", - " 0.36672435 0.3660089 0.23313606 0.43276746]]\n" + "\t Optimum: -9.11e+00, \n", + "\t X: [[0.47302596 0.5352108 0.53682257 0.53979566 0.53497679 0.53344312\n", + " 0.53510397 0.53976004 0.53606554 0.53302409]]\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -937,7 +935,7 @@ "# Run optimization loop \n", "X_all, Y_all, C_all = furbo_optimize(fun,\n", " eval_objective, \n", - " [eval_c1, eval_c2],\n", + " eval_constraints,\n", " X_ini,\n", " batch_size = batch_size,\n", " n_init = n_init,\n", @@ -991,7 +989,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 15, "id": "faf1d844", "metadata": {}, "outputs": [], @@ -1012,6 +1010,7 @@ " \n", " # Domain bounds\n", " self.lb, self.ub = fcn.bounds\n", + " self.bounds = fcn.bounds\n", " \n", " # Problem dimensions\n", " self.batch_size: int = batch_size # Dimension of the batch at each iteration\n", @@ -1264,11 +1263,11 @@ " # Evaluate batch on obj ...\n", " Y_next.append(objective(x))\n", " # ... and constraints\n", - " C_next.append([c(x) for c in constraints])\n", + " C_next.append(constraints(x))\n", " \n", " # process vector for PyTorch\n", - " Y_next = torch.tensor(Y_next).unsqueeze(-1).to(**tkwargs)\n", - " C_next = torch.tensor(C_next).to(**tkwargs)\n", + " Y_next = torch.stack(Y_next).unsqueeze(-1).to(**tkwargs)\n", + " C_next = torch.stack(C_next).to(**tkwargs)\n", " \n", " # Update SCBO status with newly evaluated batch\n", " state.update(X_next, Y_next, C_next, **tkwargs) \n", @@ -1323,7 +1322,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 16, "id": "05045730", "metadata": {}, "outputs": [], @@ -1334,7 +1333,7 @@ "\n", "def eval_objective(x):\n", " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", - " return fun20(unnormalize(x - 0.3, fun20.bounds))" + " return fun20(unnormalize(x, fun20.bounds))" ] }, { @@ -1351,7 +1350,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 17, "id": "3abb68dd", "metadata": {}, "outputs": [], @@ -1362,13 +1361,9 @@ "def c2(x):\n", " return torch.norm(x, p=2) - 5\n", " \n", - "def eval_c1(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint c1\"\"\"\n", - " return c1(unnormalize(x, fun20.bounds))\n", - "\n", - "def eval_c2(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint c2\"\"\"\n", - " return c2(unnormalize(x, fun20.bounds))" + "def eval_constraints(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point on the constraints\"\"\"\n", + " return Tensor([c1(unnormalize(x - 0.3, fun20.bounds)), c2(unnormalize(x - 0.3, fun20.bounds))])" ] }, { @@ -1381,7 +1376,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 18, "id": "63e1529c", "metadata": {}, "outputs": [ @@ -1390,95 +1385,95 @@ "output_type": "stream", "text": [ "FuRBO on 20D Ackley function\n", - "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 1.24e+01, MND radius: 1.0\n", - "Samples evaluated: 80 | No feasible point yet! Smallest total violation: 8.11e+00, MND radius: 1.0\n", - "Samples evaluated: 140 | No feasible point yet! Smallest total violation: 4.24e+00, MND radius: 1.0\n", - "Samples evaluated: 200 | No feasible point yet! Smallest total violation: 1.52e+00, MND radius: 1.0\n", - "Samples evaluated: 260 | Best value: -1.37e+01, MND radius: 1.0\n", - "Samples evaluated: 320 | Best value: -1.35e+01, MND radius: 1.0\n", - "Samples evaluated: 380 | Best value: -1.35e+01, MND radius: 1.0\n", - "Samples evaluated: 440 | Best value: -1.35e+01, MND radius: 1.0\n", - "Samples evaluated: 500 | Best value: -1.34e+01, MND radius: 1.0\n", - "Samples evaluated: 560 | Best value: -1.34e+01, MND radius: 1.0\n", - "Samples evaluated: 620 | Best value: -1.34e+01, MND radius: 1.0\n", - "Samples evaluated: 680 | Best value: -1.34e+01, MND radius: 1.0\n", - "Samples evaluated: 740 | Best value: -1.34e+01, MND radius: 1.0\n", - "Samples evaluated: 800 | Best value: -1.34e+01, MND radius: 1.0\n", - "Samples evaluated: 860 | Best value: -1.34e+01, MND radius: 0.5\n", - "Samples evaluated: 920 | Best value: -1.34e+01, MND radius: 0.5\n", - "Samples evaluated: 980 | Best value: -1.33e+01, MND radius: 0.5\n", - "Samples evaluated: 1040 | Best value: -1.33e+01, MND radius: 0.5\n", - "Samples evaluated: 1100 | Best value: -1.33e+01, MND radius: 0.5\n", - "Samples evaluated: 1160 | Best value: -1.33e+01, MND radius: 0.5\n", - "Samples evaluated: 1220 | Best value: -1.33e+01, MND radius: 0.25\n", - "Samples evaluated: 1280 | Best value: -1.30e+01, MND radius: 0.25\n", - "Samples evaluated: 1340 | Best value: -1.30e+01, MND radius: 0.25\n", - "Samples evaluated: 1400 | Best value: -1.30e+01, MND radius: 0.25\n", - "Samples evaluated: 1460 | Best value: -1.30e+01, MND radius: 0.25\n", - "Samples evaluated: 1520 | Best value: -1.27e+01, MND radius: 0.25\n", - "Samples evaluated: 1580 | Best value: -1.27e+01, MND radius: 0.5\n", - "Samples evaluated: 1640 | Best value: -1.27e+01, MND radius: 0.5\n", - "Samples evaluated: 1700 | Best value: -1.27e+01, MND radius: 0.5\n", - "Samples evaluated: 1760 | Best value: -1.27e+01, MND radius: 0.25\n", - "Samples evaluated: 1820 | Best value: -1.27e+01, MND radius: 0.25\n", - "Samples evaluated: 1880 | Best value: -1.27e+01, MND radius: 0.25\n", - "Samples evaluated: 1940 | Best value: -1.25e+01, MND radius: 0.125\n", - "Samples evaluated: 2000 | Best value: -1.24e+01, MND radius: 0.125\n", - "Samples evaluated: 2060 | Best value: -1.24e+01, MND radius: 0.25\n", + "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 1.28e+01, MND radius: 1.0\n", + "Samples evaluated: 80 | No feasible point yet! Smallest total violation: 4.99e+00, MND radius: 1.0\n", + "Samples evaluated: 140 | No feasible point yet! Smallest total violation: 2.91e+00, MND radius: 1.0\n", + "Samples evaluated: 200 | No feasible point yet! Smallest total violation: 2.97e-01, MND radius: 1.0\n", + "Samples evaluated: 260 | Best value: -1.32e+01, MND radius: 1.0\n", + "Samples evaluated: 320 | Best value: -1.23e+01, MND radius: 1.0\n", + "Samples evaluated: 380 | Best value: -1.18e+01, MND radius: 1.0\n", + "Samples evaluated: 440 | Best value: -1.16e+01, MND radius: 1.0\n", + "Samples evaluated: 500 | Best value: -1.15e+01, MND radius: 1.0\n", + "Samples evaluated: 560 | Best value: -1.15e+01, MND radius: 1.0\n", + "Samples evaluated: 620 | Best value: -1.15e+01, MND radius: 1.0\n", + "Samples evaluated: 680 | Best value: -1.15e+01, MND radius: 1.0\n", + "Samples evaluated: 740 | Best value: -1.15e+01, MND radius: 0.5\n", + "Samples evaluated: 800 | Best value: -1.15e+01, MND radius: 0.5\n", + "Samples evaluated: 860 | Best value: -1.15e+01, MND radius: 0.5\n", + "Samples evaluated: 920 | Best value: -1.15e+01, MND radius: 0.5\n", + "Samples evaluated: 980 | Best value: -1.15e+01, MND radius: 0.5\n", + "Samples evaluated: 1040 | Best value: -1.13e+01, MND radius: 0.25\n", + "Samples evaluated: 1100 | Best value: -1.13e+01, MND radius: 0.25\n", + "Samples evaluated: 1160 | Best value: -1.08e+01, MND radius: 0.25\n", + "Samples evaluated: 1220 | Best value: -1.08e+01, MND radius: 0.25\n", + "Samples evaluated: 1280 | Best value: -1.08e+01, MND radius: 0.5\n", + "Samples evaluated: 1340 | Best value: -1.08e+01, MND radius: 0.5\n", + "Samples evaluated: 1400 | Best value: -1.08e+01, MND radius: 0.5\n", + "Samples evaluated: 1460 | Best value: -1.07e+01, MND radius: 0.25\n", + "Samples evaluated: 1520 | Best value: -1.07e+01, MND radius: 0.25\n", + "Samples evaluated: 1580 | Best value: -1.07e+01, MND radius: 0.25\n", + "Samples evaluated: 1640 | Best value: -1.07e+01, MND radius: 0.25\n", + "Samples evaluated: 1700 | Best value: -1.04e+01, MND radius: 0.125\n", + "Samples evaluated: 1760 | Best value: -1.04e+01, MND radius: 0.125\n", + "Samples evaluated: 1820 | Best value: -1.04e+01, MND radius: 0.25\n", + "Samples evaluated: 1880 | Best value: -1.04e+01, MND radius: 0.25\n", + "Samples evaluated: 1940 | Best value: -1.04e+01, MND radius: 0.25\n", + "Samples evaluated: 2000 | Best value: -1.03e+01, MND radius: 0.125\n", + "Samples evaluated: 2060 | Best value: -1.03e+01, MND radius: 0.125\n", "Optimization finished \n", - "\t Optimum: -1.24e+01, \n", - "\t X: [[0.29986496 0.22883195 0.36632051 0.36075071 0.29621583 0.3632648\n", - " 0.29325852 0.2913269 0.36938339 0.29182121 0.22704174 0.29191579\n", - " 0.50050442 0.30535068 0.36156627 0.30391326 0.36148896 0.42429123\n", - " 0.42693231 0.297737 ]]\n", + "\t Optimum: -1.03e+01, \n", + "\t X: [[0.60256461 0.60120611 0.53488419 0.52727941 0.59689253 0.59943624\n", + " 0.53083688 0.53199396 0.59954937 0.53219281 0.53400376 0.59956843\n", + " 0.59933336 0.52968873 0.53267404 0.59606141 0.59290767 0.60142492\n", + " 0.60550072 0.53692576]]\n", "\n", " SCBO on 20D Ackley function\n", - "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 1.24e+01, TR volume: 0.011529215046068493\n", - "Samples evaluated: 80 | No feasible point yet! Smallest total violation: 8.80e+00, TR volume: 4.448000994609387e-05\n", - "Samples evaluated: 140 | No feasible point yet! Smallest total violation: 5.27e+00, TR volume: 0.00012368295952370722\n", - "Samples evaluated: 200 | No feasible point yet! Smallest total violation: 3.98e+00, TR volume: 0.0005001296693795576\n", - "Samples evaluated: 260 | No feasible point yet! Smallest total violation: 3.98e+00, TR volume: 0.0005404477468218018\n", - "Samples evaluated: 320 | No feasible point yet! Smallest total violation: 3.79e+00, TR volume: 0.0005404477468218018\n", - "Samples evaluated: 380 | No feasible point yet! Smallest total violation: 3.79e+00, TR volume: 0.0006255176611259401\n", - "Samples evaluated: 440 | No feasible point yet! Smallest total violation: 3.79e+00, TR volume: 0.0006255176611259401\n", - "Samples evaluated: 500 | No feasible point yet! Smallest total violation: 3.79e+00, TR volume: 0.0006255176611259401\n", - "Samples evaluated: 560 | No feasible point yet! Smallest total violation: 6.08e-01, TR volume: 6.171161145432459e-09\n", - "Samples evaluated: 620 | No feasible point yet! Smallest total violation: 2.51e-01, TR volume: 9.820559727080237e-09\n", - "Samples evaluated: 680 | No feasible point yet! Smallest total violation: 2.51e-01, TR volume: 0.00065009265457945\n", - "Samples evaluated: 740 | No feasible point yet! Smallest total violation: 2.51e-01, TR volume: 0.00065009265457945\n", - "Samples evaluated: 800 | No feasible point yet! Smallest total violation: 2.51e-01, TR volume: 0.00065009265457945\n", - "Samples evaluated: 860 | Best value: -1.40e+01, TR volume: 9.989878884692766e-09\n", - "Samples evaluated: 920 | Best value: -1.40e+01, TR volume: 1.0995116277760021e-08\n", - "Samples evaluated: 980 | Best value: -1.40e+01, TR volume: 1.0995116277760021e-08\n", - "Samples evaluated: 1040 | Best value: -1.40e+01, TR volume: 1.0995116277760021e-08\n", - "Samples evaluated: 1100 | Best value: -1.33e+01, TR volume: 1.0485760000000007e-14\n", - "Samples evaluated: 1160 | Best value: -1.33e+01, TR volume: 1.048575999999999e-14\n", - "Samples evaluated: 1220 | Best value: -1.33e+01, TR volume: 1.048575999999999e-14\n", - "Samples evaluated: 1280 | Best value: -1.33e+01, TR volume: 1.048575999999999e-14\n", - "Samples evaluated: 1340 | Best value: -1.33e+01, TR volume: 9.999999999999956e-21\n", - "Samples evaluated: 1400 | Best value: -1.33e+01, TR volume: 9.999999999999956e-21\n", - "Samples evaluated: 1460 | Best value: -1.33e+01, TR volume: 9.999999999999956e-21\n", - "Samples evaluated: 1520 | Best value: -1.32e+01, TR volume: 9.53674316406265e-27\n", - "Samples evaluated: 1580 | Best value: -1.31e+01, TR volume: 9.536743164062644e-27\n", - "Samples evaluated: 1640 | Best value: -1.31e+01, TR volume: 9.999999999999956e-21\n", - "Samples evaluated: 1700 | Best value: -1.31e+01, TR volume: 9.999999999999956e-21\n", - "Samples evaluated: 1760 | Best value: -1.31e+01, TR volume: 9.999999999999956e-21\n", - "Samples evaluated: 1820 | Best value: -1.29e+01, TR volume: 9.536743164062637e-27\n", - "Samples evaluated: 1880 | Best value: -1.29e+01, TR volume: 9.536743164062644e-27\n", - "Samples evaluated: 1940 | Best value: -1.29e+01, TR volume: 9.999999999999963e-21\n", - "Samples evaluated: 2000 | Best value: -1.29e+01, TR volume: 9.999999999999963e-21\n", - "Samples evaluated: 2060 | Best value: -1.29e+01, TR volume: 9.999999999999963e-21\n", + "Samples evaluated: 20 | No feasible point yet! Smallest total violation: 1.28e+01, TR volume: 0.011529215046068493\n", + "Samples evaluated: 80 | No feasible point yet! Smallest total violation: 7.55e+00, TR volume: 9.493838712662034e-05\n", + "Samples evaluated: 140 | No feasible point yet! Smallest total violation: 3.62e+00, TR volume: 0.0007152000816873457\n", + "Samples evaluated: 200 | No feasible point yet! Smallest total violation: 2.60e+00, TR volume: 0.0018178914917088116\n", + "Samples evaluated: 260 | No feasible point yet! Smallest total violation: 2.60e+00, TR volume: 0.0019607148503827557\n", + "Samples evaluated: 320 | No feasible point yet! Smallest total violation: 2.60e+00, TR volume: 0.0019607148503827557\n", + "Samples evaluated: 380 | No feasible point yet! Smallest total violation: 2.60e+00, TR volume: 0.0019607148503827557\n", + "Samples evaluated: 440 | No feasible point yet! Smallest total violation: 7.24e-01, TR volume: 9.01920780049975e-09\n", + "Samples evaluated: 500 | No feasible point yet! Smallest total violation: 3.13e-01, TR volume: 1.0995116277760001e-08\n", + "Samples evaluated: 560 | No feasible point yet! Smallest total violation: 3.13e-01, TR volume: 0.003105585761579358\n", + "Samples evaluated: 620 | No feasible point yet! Smallest total violation: 3.13e-01, TR volume: 0.003105585761579358\n", + "Samples evaluated: 680 | No feasible point yet! Smallest total violation: 3.13e-01, TR volume: 0.003105585761579358\n", + "Samples evaluated: 740 | No feasible point yet! Smallest total violation: 3.13e-01, TR volume: 1.0510773194237722e-08\n", + "Samples evaluated: 800 | No feasible point yet! Smallest total violation: 3.13e-01, TR volume: 1.0510773194237722e-08\n", + "Samples evaluated: 860 | No feasible point yet! Smallest total violation: 3.13e-01, TR volume: 1.0510773194237722e-08\n", + "Samples evaluated: 920 | Best value: -1.33e+01, TR volume: 1.0485759999999946e-14\n", + "Samples evaluated: 980 | Best value: -1.28e+01, TR volume: 1.0485759999999946e-14\n", + "Samples evaluated: 1040 | Best value: -1.28e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1100 | Best value: -1.28e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1160 | Best value: -1.28e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1220 | Best value: -1.28e+01, TR volume: 1.0485759999999955e-14\n", + "Samples evaluated: 1280 | Best value: -1.22e+01, TR volume: 1.0485759999999962e-14\n", + "Samples evaluated: 1340 | Best value: -1.22e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1400 | Best value: -1.22e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1460 | Best value: -1.22e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1520 | Best value: -1.19e+01, TR volume: 1.0485759999999946e-14\n", + "Samples evaluated: 1580 | Best value: -1.16e+01, TR volume: 1.0485759999999954e-14\n", + "Samples evaluated: 1640 | Best value: -1.16e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1700 | Best value: -1.16e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1760 | Best value: -1.16e+01, TR volume: 1.0995116277760013e-08\n", + "Samples evaluated: 1820 | Best value: -1.16e+01, TR volume: 1.0485759999999946e-14\n", + "Samples evaluated: 1880 | Best value: -1.16e+01, TR volume: 1.0485759999999946e-14\n", + "Samples evaluated: 1940 | Best value: -1.16e+01, TR volume: 1.0485759999999946e-14\n", + "Samples evaluated: 2000 | Best value: -1.16e+01, TR volume: 1.0000000000000144e-20\n", + "Samples evaluated: 2060 | Best value: -1.16e+01, TR volume: 1.0000000000000144e-20\n", "Optimization finished \n", - "\t Optimum: -1.29e+01, \n", - "\t X: [[0.30035487 0.31809956 0.30696511 0.23543128 0.30153329 0.42668045\n", - " 0.43635181 0.41619196 0.28313953 0.29624711 0.2341553 0.37516172\n", - " 0.25547553 0.30038809 0.29715446 0.31140388 0.36711527 0.43834427\n", - " 0.31500617 0.44621602]]\n" + "\t Optimum: -1.16e+01, \n", + "\t X: [[0.60107475 0.6496233 0.67631394 0.60271574 0.60526597 0.46455616\n", + " 0.53615492 0.65658673 0.50182849 0.59929085 0.58332372 0.53025066\n", + " 0.65932202 0.60278264 0.53806963 0.59039729 0.5222196 0.59601261\n", + " 0.55778584 0.59322277]]\n" ] }, { "data": { - "image/png": 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", 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"text/plain": [ "
" ] @@ -1505,7 +1500,7 @@ "print(\"FuRBO on 20D Ackley function\")\n", "X_all, Y_all, C_all = furbo_optimize(fun20,\n", " eval_objective, \n", - " [eval_c1, eval_c2],\n", + " eval_constraints,\n", " X_ini,\n", " batch_size = batch_size,\n", " n_init = n_init,\n", @@ -1522,7 +1517,7 @@ "print(\"\\n SCBO on 20D Ackley function\")\n", "X_all, Y_all, C_all = scbo_optimize(fun20,\n", " eval_objective, \n", - " [eval_c1, eval_c2],\n", + " eval_constraints,\n", " X_ini,\n", " batch_size = batch_size,\n", " n_init = n_init,\n", @@ -1557,52 +1552,9 @@ "\n", "The problem minimizes the weight $W$ of a speed reducer:\n", "\n", - "$W = 0.7854x_1x_2^2(3.3333x_e^2+14.9334x_3-43.0934)-1.508x_1(x_6^2+x_7^2)+7.4777(x_6^3+x_7^3)+0.7854(x_4x_6^2+x_5x_7^2)$" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "5a56a1e4", - "metadata": {}, - "outputs": [], - "source": [ - "class speedReducer():\n", - "\n", - " def __init__(self):\n", - " self.lower_bounds = torch.Tensor([2.6, 0.7, 17., 7.3, 7.3, 2.9, 4.9])\n", - " self.upper_bounds = torch.Tensor([3.6, 0.8, 28., 8.3, 8.3, 3.9, 5.9])\n", - " self.bounds = [self.lower_bounds, self.upper_bounds]\n", + "$W = 0.7854x_1x_2^2(3.3333x_e^2+14.9334x_3-43.0934)-1.508x_1(x_6^2+x_7^2)+7.4777(x_6^3+x_7^3)+0.7854(x_4x_6^2+x_5x_7^2)$\n", "\n", - " self.dim: int = 7\n", - "\n", - " return\n", - " \n", - " def __call__(self, x):\n", - " x1, x2, x3, x4, x5, x6, x7 = x\n", - " \n", - " term1 = 0.7854 * x1 * x2**2 * (3.3333 * x3**2 + 14.9334 * x3 - 43.0934)\n", - " term2 = 1.508 * x1 * (x6**2 + x7**2)\n", - " term3 = 7.4777 * (x6**3 + x7**3)\n", - " term4 = 0.7854 * (x4 * x6**2 + x5 * x7**2)\n", - " \n", - " return term1 - term2 + term3 + term4 \n", - " \n", - "funS = speedReducer()\n", - "\n", - "def eval_objective(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", - " return -1 * funS(unnormalize(x, funS.bounds))" - ] - }, - { - "cell_type": "markdown", - "id": "8634f6c8", - "metadata": {}, - "source": [ - "#### Speed Reducer Constraint functions\n", - "\n", - "The problem is constrained by 11 functions.\n", + "Under the following constraints:\n", "\n", "$g_1(x) = 27x^{−1}_1 x^{−2}_2 x^{−1}_3 \\leq 1$\n", "\n", @@ -1629,88 +1581,21 @@ }, { "cell_type": "code", - "execution_count": 18, - "id": "695f8690", + "execution_count": 19, + "id": "5a56a1e4", "metadata": {}, "outputs": [], "source": [ - "def g1(x):\n", - " return 27.0 / (x[0] * x[1]**2 * x[2]) - 1\n", - "\n", - "def g2(x):\n", - " return 397.5 / (x[0] * x[1]**2 * x[2]**2) - 1\n", + "from botorch.test_functions.synthetic import SpeedReducer \n", "\n", - "def g3(x):\n", - " return 1.93 * x[3]**3 / (x[1] * x[2] * x[5]**4) - 1\n", + "funS = SpeedReducer()\n", "\n", - "def g4(x):\n", - " return 1.93 * x[4]**3 / (x[1] * x[2] * x[6]**4) - 1\n", - "\n", - "def g5(x):\n", - " return (1 / (0.1 * x[5]**3)) * np.sqrt((745 * x[3] / (x[1] * x[2]))**2 + 16.9e6) - 1100\n", - "\n", - "def g6(x):\n", - " return (1 / (0.1 * x[6]**3)) * np.sqrt((745 * x[4] / (x[1] * x[2]))**2 + 157.5e6) - 850\n", - "\n", - "def g7(x):\n", - " return x[1] * x[2] - 40\n", - "\n", - "def g8(x):\n", - " return 5 - x[0] / x[1]\n", - "\n", - "def g9(x):\n", - " return x[0] / x[1] - 12\n", - "\n", - "def g10(x):\n", - " return (1.5 * x[5] + 1.9) / x[3] - 1\n", - "\n", - "def g11(x):\n", - " return (1.1 * x[6] + 1.9) / x[4] - 1 \n", - "\n", - "# Handles to evaluate constraints\n", - "def eval_g1(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g1\"\"\"\n", - " return g1(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g2(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g2\"\"\"\n", - " return g2(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g3(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g3\"\"\"\n", - " return g3(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g4(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g4\"\"\"\n", - " return g4(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g5(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g5\"\"\"\n", - " return g5(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g6(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g6\"\"\"\n", - " return g6(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g7(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g7\"\"\"\n", - " return g7(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g8(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g8\"\"\"\n", - " return g8(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g9(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g9\"\"\"\n", - " return g9(unnormalize(x, funS.bounds)) \n", - "\n", - "def eval_g10(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g10\"\"\"\n", - " return g10(unnormalize(x, funS.bounds)) \n", + "def eval_objective(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", + " return -1 * funS.evaluate_true(unnormalize(x, funS.bounds))\n", "\n", - "def eval_g11(x):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point on constraint g11\"\"\"\n", - " return g11(unnormalize(x, funS.bounds)) " + "def eval_constraints(x):\n", + " return -1 * funS.evaluate_slack_true(unnormalize(x, funS.bounds))" ] }, { @@ -1723,7 +1608,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 21, "id": "ea71286a", "metadata": {}, "outputs": [ @@ -1732,81 +1617,81 @@ "output_type": "stream", "text": [ "FuRBO on speed reducer problem\n", - "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 2.38e-01, MND radius: 1.0\n", - "Samples evaluated: 17 | Best value: -4.93e+03, MND radius: 1.0\n", - "Samples evaluated: 24 | Best value: -3.88e+03, MND radius: 1.0\n", - "Samples evaluated: 31 | Best value: -3.13e+03, MND radius: 1.0\n", - "Samples evaluated: 38 | Best value: -3.09e+03, MND radius: 1.0\n", - "Samples evaluated: 45 | Best value: -3.09e+03, MND radius: 1.0\n", - "Samples evaluated: 52 | Best value: -3.09e+03, MND radius: 1.0\n", - "Samples evaluated: 59 | Best value: -3.09e+03, MND radius: 1.0\n", - "Samples evaluated: 66 | Best value: -3.04e+03, MND radius: 0.5\n", + "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 1.47e-01, MND radius: 1.0\n", + "Samples evaluated: 17 | Best value: -3.63e+03, MND radius: 1.0\n", + "Samples evaluated: 24 | Best value: -3.11e+03, MND radius: 1.0\n", + "Samples evaluated: 31 | Best value: -3.11e+03, MND radius: 1.0\n", + "Samples evaluated: 38 | Best value: -3.11e+03, MND radius: 1.0\n", + "Samples evaluated: 45 | Best value: -3.11e+03, MND radius: 1.0\n", + "Samples evaluated: 52 | Best value: -3.06e+03, MND radius: 0.5\n", + "Samples evaluated: 59 | Best value: -3.06e+03, MND radius: 0.5\n", + "Samples evaluated: 66 | Best value: -3.06e+03, MND radius: 0.5\n", "Samples evaluated: 73 | Best value: -3.04e+03, MND radius: 0.5\n", "Samples evaluated: 80 | Best value: -3.04e+03, MND radius: 0.5\n", "Samples evaluated: 87 | Best value: -3.04e+03, MND radius: 0.5\n", - "Samples evaluated: 94 | Best value: -3.04e+03, MND radius: 0.25\n", - "Samples evaluated: 101 | Best value: -3.03e+03, MND radius: 0.25\n", - "Samples evaluated: 108 | Best value: -3.03e+03, MND radius: 0.25\n", - "Samples evaluated: 115 | Best value: -3.03e+03, MND radius: 0.25\n", + "Samples evaluated: 94 | Best value: -3.04e+03, MND radius: 0.5\n", + "Samples evaluated: 101 | Best value: -3.04e+03, MND radius: 0.25\n", + "Samples evaluated: 108 | Best value: -3.04e+03, MND radius: 0.25\n", + "Samples evaluated: 115 | Best value: -3.04e+03, MND radius: 0.25\n", "Samples evaluated: 122 | Best value: -3.03e+03, MND radius: 0.25\n", - "Samples evaluated: 129 | Best value: -3.03e+03, MND radius: 0.125\n", - "Samples evaluated: 136 | Best value: -3.03e+03, MND radius: 0.125\n", - "Samples evaluated: 143 | Best value: -3.03e+03, MND radius: 0.125\n", - "Samples evaluated: 150 | Best value: -3.03e+03, MND radius: 0.125\n", - "Samples evaluated: 157 | Best value: -3.01e+03, MND radius: 0.0625\n", - "Samples evaluated: 164 | Best value: -3.01e+03, MND radius: 0.0625\n", - "Samples evaluated: 171 | Best value: -3.01e+03, MND radius: 0.0625\n", - "Samples evaluated: 178 | Best value: -3.01e+03, MND radius: 0.0625\n", - "Samples evaluated: 185 | Best value: -3.01e+03, MND radius: 0.03125\n", - "Samples evaluated: 192 | Best value: -3.01e+03, MND radius: 0.03125\n", - "Samples evaluated: 199 | Best value: -3.01e+03, MND radius: 0.03125\n", - "Samples evaluated: 206 | Best value: -3.01e+03, MND radius: 0.03125\n", - "Samples evaluated: 213 | Best value: -3.00e+03, MND radius: 0.015625\n", + "Samples evaluated: 129 | Best value: -3.03e+03, MND radius: 0.5\n", + "Samples evaluated: 136 | Best value: -3.03e+03, MND radius: 0.5\n", + "Samples evaluated: 143 | Best value: -3.03e+03, MND radius: 0.5\n", + "Samples evaluated: 150 | Best value: -3.03e+03, MND radius: 0.25\n", + "Samples evaluated: 157 | Best value: -3.03e+03, MND radius: 0.25\n", + "Samples evaluated: 164 | Best value: -3.03e+03, MND radius: 0.25\n", + "Samples evaluated: 171 | Best value: -3.02e+03, MND radius: 0.125\n", + "Samples evaluated: 178 | Best value: -3.02e+03, MND radius: 0.125\n", + "Samples evaluated: 185 | Best value: -3.02e+03, MND radius: 0.125\n", + "Samples evaluated: 192 | Best value: -3.02e+03, MND radius: 0.125\n", + "Samples evaluated: 199 | Best value: -3.01e+03, MND radius: 0.0625\n", + "Samples evaluated: 206 | Best value: -3.01e+03, MND radius: 0.0625\n", + "Samples evaluated: 213 | Best value: -3.01e+03, MND radius: 0.0625\n", "Optimization finished \n", - "\t Optimum: -3.00e+03, \n", - "\t X: [[9.02528720e-01 1.17360979e-03 9.05342813e-05 2.10989121e-01\n", - " 5.95593310e-01 4.58617181e-01 3.86871766e-01]]\n", + "\t Optimum: -3.01e+03, \n", + "\t X: [[9.02336695e-01 3.16653570e-04 2.27025084e-04 5.73721960e-01\n", + " 3.57072089e-01 4.53617526e-01 5.73731164e-01]]\n", "\n", " SCBO on speed reducer problem\n", - "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 2.38e-01, TR volume: 0.2097152000000001\n", - "Samples evaluated: 17 | No feasible point yet! Smallest total violation: 4.13e-02, TR volume: 0.03737699729156021\n", - "Samples evaluated: 24 | No feasible point yet! Smallest total violation: 9.70e-04, TR volume: 0.02103152421386524\n", - "Samples evaluated: 31 | Best value: -3.43e+03, TR volume: 0.04873321441954075\n", - "Samples evaluated: 38 | Best value: -3.22e+03, TR volume: 0.028856063920429414\n", - "Samples evaluated: 45 | Best value: -3.21e+03, TR volume: 0.024116579298590846\n", - "Samples evaluated: 52 | Best value: -3.13e+03, TR volume: 0.02118393716356287\n", - "Samples evaluated: 59 | Best value: -3.13e+03, TR volume: 0.014900499128629683\n", - "Samples evaluated: 66 | Best value: -3.12e+03, TR volume: 0.014900499128629683\n", - "Samples evaluated: 73 | Best value: -3.12e+03, TR volume: 0.011343326759723086\n", - "Samples evaluated: 80 | Best value: -3.12e+03, TR volume: 0.011343326759723086\n", - "Samples evaluated: 87 | Best value: -3.12e+03, TR volume: 0.011343326759723086\n", - "Samples evaluated: 94 | Best value: -3.07e+03, TR volume: 0.00014358101224495537\n", - "Samples evaluated: 101 | Best value: -3.07e+03, TR volume: 0.00029068378750287505\n", - "Samples evaluated: 108 | Best value: -3.07e+03, TR volume: 0.00029068378750287505\n", - "Samples evaluated: 115 | Best value: -3.07e+03, TR volume: 0.00029068378750287505\n", - "Samples evaluated: 122 | Best value: -3.05e+03, TR volume: 3.2199173185070756e-06\n", - "Samples evaluated: 129 | Best value: -3.05e+03, TR volume: 2.520842270461592e-06\n", - "Samples evaluated: 136 | Best value: -3.05e+03, TR volume: 2.520842270461592e-06\n", - "Samples evaluated: 143 | Best value: -3.05e+03, TR volume: 2.520842270461592e-06\n", - "Samples evaluated: 150 | Best value: -3.03e+03, TR volume: 2.7034417934772597e-08\n", - "Samples evaluated: 157 | Best value: -3.03e+03, TR volume: 3.00388114029285e-08\n", - "Samples evaluated: 164 | Best value: -3.03e+03, TR volume: 3.1578071834415887e-06\n", - "Samples evaluated: 171 | Best value: -3.03e+03, TR volume: 3.1578071834415887e-06\n", - "Samples evaluated: 178 | Best value: -3.03e+03, TR volume: 3.1578071834415887e-06\n", - "Samples evaluated: 185 | Best value: -3.03e+03, TR volume: 2.810991202840537e-08\n", - "Samples evaluated: 192 | Best value: -3.03e+03, TR volume: 2.810991202840537e-08\n", - "Samples evaluated: 199 | Best value: -3.03e+03, TR volume: 2.810991202840537e-08\n", - "Samples evaluated: 206 | Best value: -3.02e+03, TR volume: 2.451099170436267e-10\n", - "Samples evaluated: 213 | Best value: -3.02e+03, TR volume: 2.7067026843538696e-10\n", + "Samples evaluated: 10 | No feasible point yet! Smallest total violation: 1.47e-01, TR volume: 0.2097152000000001\n", + "Samples evaluated: 17 | Best value: -3.94e+03, TR volume: 0.03737699729156021\n", + "Samples evaluated: 24 | Best value: -3.17e+03, TR volume: 0.03373239388744261\n", + "Samples evaluated: 31 | Best value: -3.17e+03, TR volume: 0.020444206473667594\n", + "Samples evaluated: 38 | Best value: -3.17e+03, TR volume: 0.020444206473667594\n", + "Samples evaluated: 45 | Best value: -3.17e+03, TR volume: 0.020444206473667594\n", + "Samples evaluated: 52 | Best value: -3.08e+03, TR volume: 0.00027066473891622817\n", + "Samples evaluated: 59 | Best value: -3.07e+03, TR volume: 0.00019705197652677295\n", + "Samples evaluated: 66 | Best value: -3.07e+03, TR volume: 0.015282894754867538\n", + "Samples evaluated: 73 | Best value: -3.07e+03, TR volume: 0.015282894754867538\n", + "Samples evaluated: 80 | Best value: -3.07e+03, TR volume: 0.015282894754867538\n", + "Samples evaluated: 87 | Best value: -3.07e+03, TR volume: 0.0002285679021852515\n", + "Samples evaluated: 94 | Best value: -3.07e+03, TR volume: 0.0002285679021852515\n", + "Samples evaluated: 101 | Best value: -3.07e+03, TR volume: 0.0002285679021852515\n", + "Samples evaluated: 108 | Best value: -3.05e+03, TR volume: 3.3678680097487228e-06\n", + "Samples evaluated: 115 | Best value: -3.05e+03, TR volume: 2.249204192881997e-06\n", + "Samples evaluated: 122 | Best value: -3.04e+03, TR volume: 2.249204192881997e-06\n", + "Samples evaluated: 129 | Best value: -3.04e+03, TR volume: 2.279091575415814e-06\n", + "Samples evaluated: 136 | Best value: -3.04e+03, TR volume: 2.279091575415814e-06\n", + "Samples evaluated: 143 | Best value: -3.04e+03, TR volume: 2.279091575415814e-06\n", + "Samples evaluated: 150 | Best value: -3.02e+03, TR volume: 2.7096532197889234e-08\n", + "Samples evaluated: 157 | Best value: -3.02e+03, TR volume: 2.597092345178189e-08\n", + "Samples evaluated: 164 | Best value: -3.02e+03, TR volume: 2.597092345178189e-08\n", + "Samples evaluated: 171 | Best value: -3.02e+03, TR volume: 2.597092345178189e-08\n", + "Samples evaluated: 178 | Best value: -3.02e+03, TR volume: 2.3164793875383555e-10\n", + "Samples evaluated: 185 | Best value: -3.02e+03, TR volume: 2.3164793875383555e-10\n", + "Samples evaluated: 192 | Best value: -3.02e+03, TR volume: 2.3164793875383555e-10\n", + "Samples evaluated: 199 | Best value: -3.01e+03, TR volume: 2.0939318604694748e-12\n", + "Samples evaluated: 206 | Best value: -3.01e+03, TR volume: 1.6188776032377124e-12\n", + "Samples evaluated: 213 | Best value: -3.01e+03, TR volume: 2.184814696346965e-10\n", "Optimization finished \n", - "\t Optimum: -3.02e+03, \n", - "\t X: [[9.17650597e-01 9.43228246e-03 1.55023053e-04 3.73859052e-01\n", - " 7.72787844e-01 4.56641981e-01 3.88081869e-01]]\n" + "\t Optimum: -3.01e+03, \n", + "\t X: [[9.02411601e-01 2.88696295e-03 7.05214473e-05 2.30094595e-01\n", + " 9.59491912e-01 4.51435260e-01 5.76963988e-01]]\n" ] }, { "data": { - "image/png": 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", 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", 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" ] @@ -1833,10 +1718,7 @@ "print(\"FuRBO on speed reducer problem\")\n", "X_all, Y_all, C_all = furbo_optimize(funS,\n", " eval_objective, \n", - " [eval_g1, eval_g2, eval_g3,\n", - " eval_g4, eval_g5, eval_g6,\n", - " eval_g7, eval_g8, eval_g9,\n", - " eval_g10, eval_g11],\n", + " eval_constraints,\n", " X_ini,\n", " batch_size = batch_size,\n", " n_init = n_init,\n", @@ -1853,10 +1735,7 @@ "print(\"\\n SCBO on speed reducer problem\")\n", "X_all, Y_all, C_all = scbo_optimize(funS,\n", " eval_objective, \n", - " [eval_g1, eval_g2, eval_g3,\n", - " eval_g4, eval_g5, eval_g6,\n", - " eval_g7, eval_g8, eval_g9,\n", - " eval_g10, eval_g11],\n", + " eval_constraints,\n", " X_ini,\n", " batch_size = batch_size,\n", " n_init = n_init,\n", @@ -1885,7 +1764,7 @@ ], "metadata": { "kernelspec": { - "display_name": "COCOTeemo", + "display_name": "LastBoTorch", "language": "python", "name": "python3" }, @@ -1899,7 +1778,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.9" + "version": "3.13.10" } }, "nbformat": 4, From 026fa32cb27a78aa1b1e6fcd21e4158ff79465d0 Mon Sep 17 00:00:00 2001 From: paoloascia <157011383+paoloascia@users.noreply.github.com> Date: Fri, 19 Dec 2025 10:23:07 +0100 Subject: [PATCH 9/9] Update FuRBO.ipynb --- notebooks_community/FuRBO/FuRBO.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/notebooks_community/FuRBO/FuRBO.ipynb b/notebooks_community/FuRBO/FuRBO.ipynb index a30ce36589..c8362d42e3 100644 --- a/notebooks_community/FuRBO/FuRBO.ipynb +++ b/notebooks_community/FuRBO/FuRBO.ipynb @@ -8,8 +8,8 @@ "# Feasibility-driven trust Region Bayesian Optimization (FuRBO)\n", "\n", "- Contributors: paoloascia, elenaraponi\n", - "- Last update 04 December 2025\n", - "- BoTorch version: 0.12.0\n", + "- Last update 19 December 2025\n", + "- BoTorch version: 0.16.1\n", "\n", "In this tutorial, we show how to implement the Feasibility-driven trust Region Bayesian Optimization (FuRBO) [1] algorithm in a closed loop, with restarts. This is a Bayesian optimization (BO) algorithm developed specifically to handle severely constrained problems, while still performing well in simpler settings. \n", "\n",