Anytime Bi-Objective Optimization with a Hybrid Multi-Objective CMA-ES (HMO-CMA-ES)

TL;DR

This paper introduces HMO-CMA-ES, a hybrid multi-objective optimization algorithm designed for good anytime performance across diverse problems, evaluated using the hypervolume metric on a comprehensive benchmark suite.

Contribution

It presents a novel hybrid algorithm combining various CMA-ES variants and BOBYQA, optimized for bi-objective problems with broad applicability.

Findings

HMO-CMA-ES achieves competitive hypervolume performance.

The algorithm demonstrates robustness across 55 benchmark problems.

It outperforms some existing methods in early and overall convergence.

Abstract

We propose a multi-objective optimization algorithm aimed at achieving good anytime performance over a wide range of problems. Performance is assessed in terms of the hypervolume metric. The algorithm called HMO-CMA-ES represents a hybrid of several old and new variants of CMA-ES, complemented by BOBYQA as a warm start. We benchmark HMO-CMA-ES on the recently introduced bi-objective problem suite of the COCO framework (COmparing Continuous Optimizers), consisting of 55 scalable continuous optimization problems, which is used by the Black-Box Optimization Benchmarking (BBOB) Workshop 2016.