A Bayesian approach to constrained single- and multi-objective optimization

Abstract

This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to evaluate. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited, as in complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle objectives and constraints in a unified way, and a corresponding expected hyper-volume improvement sampling criterion is proposed. This new criterion is naturally adapted to the search of a feasible point when none is available, and reduces to existing Bayesian sampling criteria---the classical Expected Improvement (EI) criterion and some of its constrained/multi-objective extensions---as soon as at least one feasible point is available. The calculation and optimization of the criterion are performed using Sequential Monte Carlo techniques. In particular, an algorithm similar to the subset simulation method, which is well known in the field of structural reliability, is used to estimate the criterion. The method, which we call BMOO (for Bayesian Multi-Objective Optimization), is compared to state-of-the-art algorithms for single- and multi-objective constrained optimization.

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Cited by in corpus (22)

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• Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization
• Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints
• Bayesian subset simulation
• Upper Trust Bound Feasibility Criterion for Mixed Constrained Bayesian Optimization with Application to Aircraft Design
• Revisiting Bayesian Optimization in the light of the COCO benchmark
• Sequential design of multi-fidelity computer experiments: maximizing the rate of stepwise uncertainty reduction
• Fast Exact Computation of Expected HyperVolume Improvement
• Bayesian optimization for stable properties amid processing fluctuations in sputter deposition
• Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization
• A hierarchical expected improvement method for Bayesian optimization
• Leveraging Trust for Joint Multi-Objective and Multi-Fidelity Optimization
• Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints
• Regularized infill criteria for multi-objective Bayesian optimization with application to aircraft design
• Parallel Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints
• Multi-objective Bayesian optimisation with preferences over objectives
• Uncertainty aware Search Framework for Multi-Objective Bayesian Optimization with Constraints
• A Batched Scalable Multi-Objective Bayesian Optimization Algorithm
• An Efficient Application of Goal Programming to Tackle Multiobjective Problems with Recurring Fitness Landscapes
• Surrogate-based Optimization using Mutual Information for Computer Experiments (optim-MICE)
• Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization
• Multi-Objective Bayesian Optimisation and Joint Inversion for Active Sensor Fusion