Stagnation Detection in Highly Multimodal Fitness Landscapes

TL;DR

This paper introduces radius memory to enhance stagnation detection in evolutionary algorithms, improving search efficiency in complex multimodal landscapes without sacrificing performance on simpler functions.

Contribution

It proposes a new mechanism called radius memory for stagnation detection, implemented in SD-RLS^m, which better controls search radius based on past successes.

Findings

Speed-ups on linear functions and minimum spanning tree problems

Maintains performance on unimodal functions and Jump benchmark

Experimental validation shows improved efficiency

Abstract

Stagnation detection has been proposed as a mechanism for randomized search heuristics to escape from local optima by automatically increasing the size of the neighborhood to find the so-called gap size, i.e., the distance to the next improvement. Its usefulness has mostly been considered in simple multimodal landscapes with few local optima that could be crossed one after another. In multimodal landscapes with a more complex location of optima of similar gap size, stagnation detection suffers from the fact that the neighborhood size is frequently reset to $1$ without using gap sizes that were promising in the past. In this paper, we investigate a new mechanism called radius memory which can be added to stagnation detection to control the search radius more carefully by giving preference to values that were successful in the past. We implement this idea in an algorithm called SD-RLS$^{\text{m}}$ and show compared to previous variants of stagnation detection that it yields speed-ups for linear functions under uniform constraints and the minimum spanning tree problem. Moreover, its running time does not significantly deteriorate on unimodal functions and a generalization of the Jump benchmark. Finally, we present experimental results carried out to study SD-RLS$^{\text{m}}$ and compare it with other algorithms.