Black-box optimization benchmarking of IPOP-saACM-ES and BIPOP-saACM-ES on the BBOB-2012 noiseless testbed

TL;DR

This study evaluates the performance of surrogate-assisted CMA-ES algorithms, IPOP-saACM-ES and BIPOP-saACM-ES, on the BBOB-2012 noiseless testbed, demonstrating significant improvements over their non-surrogate counterparts on several benchmark problems.

Contribution

It introduces and benchmarks self-adaptive surrogate-assisted CMA-ES algorithms, showing their superior performance on noiseless optimization problems compared to traditional CMA-ES.

Findings

Surrogate-assisted algorithms outperform original CMA-ES by 2 to 4 times on 8 out of 24 problems.

They achieve the best results on several benchmark functions including Ellipsoid and Discus.

Surrogate methods show notable efficiency gains in noiseless black-box optimization.

Abstract

In this paper, we study the performance of IPOP-saACM-ES and BIPOP-saACM-ES, recently proposed self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategies. Both algorithms were tested using restarts till a total number of function evaluations of $10^6D$ was reached, where $D$ is the dimension of the function search space. We compared surrogate-assisted algorithms with their surrogate-less versions IPOP-saACM-ES and BIPOP-saACM-ES, two algorithms with one of the best overall performance observed during the BBOB-2009 and BBOB-2010. The comparison shows that the surrogate-assisted versions outperform the original CMA-ES algorithms by a factor from 2 to 4 on 8 out of 24 noiseless benchmark problems, showing the best results among all algorithms of the BBOB-2009 and BBOB-2010 on Ellipsoid, Discus, Bent Cigar, Sharp Ridge and Sum of different powers functions.