Preliminary study: Qualitative indicators in multi-objective DIRECT framework

Abstract

DIRECT is known for balancing the exploration and exploitation of a search space. This paper seeks to explore the improvement of diversity among solutions through the use of qualitative indicators in multi-objective DIRECT framework. Three different indicators - Hypervolume (HV), Epsilon (EPS), R2 indicators are used in this study. The three variants of indicators are tested on the Black-box Multi-objective Optimization Benchmarking (BMOB) Platform. The results are presented and some insights in the choice of selection operator are provided. Overall, HV indicator performs the best followed by R2, then EPS. EPS indicator performs worse than HV and R2 in unimodal problems. Also, HV indicator achieves notably better results at high dimensions. R2 performs better than EPS in non-separable problems.