Real-Valued Evolutionary Multi-Modal Optimization driven by Hill-Valley Clustering

TL;DR

This paper introduces Hill-Valley Clustering, a simple adaptive niching method for evolutionary algorithms that effectively identifies multiple optima in multi-modal optimization problems, outperforming existing methods in long-term performance.

Contribution

The paper presents Hill-Valley Clustering, a novel adaptive niching technique that dynamically identifies problem modes, enhancing the capability of EAs to handle multi-modal landscapes.

Findings

HillVallEA detects multiple global optima effectively.

The method outperforms current niching algorithms over extended runs.

Hill-Valley Clustering is simple yet competitive in multi-modal optimization.

Abstract

Model-based evolutionary algorithms (EAs) adapt an underlying search model to features of the problem at hand, such as the linkage between problem variables. The performance of EAs often deteriorates as multiple modes in the fitness landscape are modelled with a unimodal search model. The number of modes is however often unknown a priori, especially in a black-box setting, which complicates adaptation of the search model. In this work, we focus on models that can adapt to the multi-modality of the fitness landscape. Specifically, we introduce Hill-Valley Clustering, a remarkably simple approach to adaptively cluster the search space in niches, such that a single mode resides in each niche. In each of the located niches, a core search algorithm is initialized to optimize that niche. Combined with an EA and a restart scheme, the resulting Hill-Valley EA (HillVallEA) is compared to current state-of-the-art niching methods on a standard benchmark suite for multi-modal optimization. Numerical results in terms of the detected number of global optima show that, in spite of its simplicity, HillVallEA is competitive within the limited budget of the benchmark suite, and shows superior performance in the long run.