Variable Metric Evolution Strategies for High-dimensional Multi-Objective Optimization

TL;DR

This paper introduces variable metric evolution strategies tailored for high-dimensional multi-objective optimization, combining efficient covariance matrix adaptation with multi-objective evolutionary techniques.

Contribution

It develops a novel class of algorithms that efficiently scale covariance matrix adaptation to high dimensions for multi-objective problems.

Findings

Outperforms full covariance matrix adaptation methods.

Effective in high-dimensional multi-objective optimization.

Combines covariance scaling with indicator-based selection.

Abstract

We design a class of variable metric evolution strategies well suited for high-dimensional problems. We target problems with many variables, not (necessarily) with many objectives. The construction combines two independent developments: efficient algorithms for scaling covariance matrix adaptation to high dimensions, and evolution strategies for multi-objective optimization. In order to design a specific instance of the class we first develop a (1+1) version of the limited memory matrix adaptation evolution strategy and then use an established standard construction to turn a population thereof into a state-of-the-art multi-objective optimizer with indicator-based selection. The method compares favorably to adaptation of the full covariance matrix.