Preference-Aware Constrained Multi-Objective Bayesian Optimization

Abstract

This paper addresses the problem of constrained multi-objective optimization over black-box objective functions with practitioner-specified preferences over the objectives when a large fraction of the input space is infeasible (i.e., violates constraints). This problem arises in many engineering design problems including analog circuits and electric power system design. Our overall goal is to approximate the optimal Pareto set over the small fraction of feasible input designs. The key challenges include the huge size of the design space, multiple objectives and large number of constraints, and the small fraction of feasible input designs which can be identified only after performing expensive simulations. We propose a novel and efficient preference-aware constrained multi-objective Bayesian optimization approach referred to as PAC-MOO to address these challenges. The key idea is to learn surrogate models for both output objectives and constraints, and select the candidate input for evaluation in each iteration that maximizes the information gained about the optimal constrained Pareto front while factoring in the preferences over objectives. Our experiments on two real-world analog circuit design optimization problems demonstrate the efficacy of PAC-MOO over prior methods.

Preference-Aware Constrained Multi-Objective Bayesian Optimization (Student Abstract)

“…A detailed explanation of the experimental setup, real-world problems, and the pseudo-code for PAC-MOO are included in (Ahmadianshalchi, Belakaria, and Doppa 2023). We utilize a modified version of the OSY problem (Osyczka and Kundu 1995) where each dimension of the input space is expanded to 1.5 times its original size; We include an additional constraint flagging any input outside the original input space as infeasible.…”

“…Where ϕ and Φ are the p.d.f and c.d.f of a standard normal distribution respectively. We provide The definition of γ and the complete derivation of this acquisition function in (Ahmadianshalchi, Belakaria, and Doppa 2023). The acquisition function proposed in Equation 1 resulted in a function in the form of a summation of an entropy term defined for each of the objective functions and constraints as AF (i, x).…”