Emergence of Structural Bias in Differential Evolution

TL;DR

This paper investigates how different configurations of Differential Evolution algorithms develop structural bias during optimization, affecting their exploration behavior, and provides recommendations to avoid biased configurations.

Contribution

It analyzes the emergence of structural bias in Differential Evolution based on mutation, crossover, and correction strategies, offering guidance to prevent bias.

Findings

Certain configurations lead to significant structural bias.

Bias emerges during the run-time of the algorithm.

Recommendations to avoid biased DE configurations.

Abstract

Heuristic optimisation algorithms are in high demand due to the overwhelming amount of complex optimisation problems that need to be solved. The complexity of these problems is well beyond the boundaries of applicability of exact optimisation algorithms and therefore require modern heuristics to find feasible solutions quickly. These heuristics and their effects are almost always evaluated and explained by particular problem instances. In previous works, it has been shown that many such algorithms show structural bias, by either being attracted to a certain region of the search space or by consistently avoiding regions of the search space, on a special test function designed to ensure uniform 'exploration' of the domain. In this paper, we analyse the emergence of such structural bias for Differential Evolution (DE) configurations and, specifically, the effect of different mutation, crossover and correction strategies. We also analyse the emergence of the structural bias during the run-time of each algorithm. We conclude with recommendations of which configurations should be avoided in order to run DE unbiased.