Surrogate-Assisted Reference Vector Adaptation to Various Pareto Front Shapes for Many-Objective Bayesian Optimization

TL;DR

This paper introduces SRVA, a surrogate-assisted method that adaptively generates reference vectors to effectively optimize multi- and many-objective problems with diverse Pareto front shapes using Bayesian optimization.

Contribution

The paper presents a novel SRVA method that adapts reference vectors based on Pareto front estimation, improving diversity and early-stage solutions in Bayesian optimization.

Findings

SRVA outperforms other MBO algorithms on various Pareto front shapes.

It enhances solution diversity for continuous, discontinuous, and degenerated fronts.

The method achieves better solutions early in the optimization process, especially in many-objective problems.

Abstract

We propose a surrogate-assisted reference vector adaptation (SRVA) method to solve expensive multi- and many-objective optimization problems with various Pareto front shapes. SRVA is coupled with a multi-objective Bayesian optimization (MBO) algorithm using reference vectors for scalarization of objective functions. The Kriging surrogate models for MBO is used to estimate the Pareto front shape and generate adaptive reference vectors uniformly distributed on the estimated Pareto front. We combine SRVA with expected improvement of penalty-based boundary intersection as an infill criterion for MBO. The proposed algorithm is compared with two other MBO algorithms by applying them to benchmark problems with various Pareto front shapes. Experimental results show that the proposed algorithm outperforms the other two in the problems whose objective functions are reasonably approximated by the Kriging models. SRVA improves diversity of non-dominated solutions for these problems with continuous, discontinuous, and degenerated Pareto fronts. Besides, the proposed algorithm obtains much better solutions from early stages of optimization especially in many-objective problems.