Automatic Configuration of Bi-Objective Optimisation Algorithms: Impact of Correlation Between Objectives

Abstract

Multi-objective optimisation algorithms expose various parameters that have to be tuned in order to be efficient. Moreover, in multi-objective optimisation, the correlation between objective functions is known to affect search space structure and algorithm performance. Considering the recent success of automatic algorithm configuration (AAC) techniques for the design of multi-objective optimisation algorithms, this raises two interesting questions: what is the impact of correlation between optimisation objectives on (1) the efficacy of different AAC approaches and (2) on the optimised algorithm designs obtained from these automated approaches? In this work, we study these questions for multi-objective local search algorithms (MOLS) for three well-known bi-objective permutation problems, using two single-objective AAC approaches and one multi-objective approach. Our empirical results clearly show that overall, multi-objective AAC is the most effective approach for the automatic configuration of the highly parametric MOLS framework, and that there is no systematic impact of the degree of correlation on the relative performance of the three AAC approaches. We also find that the best-performing configurations differ, depending on the correlation between objectives and the size of the problem instances to be solved, providing further evidence for the usefulness of automatic configuration of multi-objective optimisation algorithms.