Diversity Enhancement for Micro-Differential Evolution

TL;DR

This paper introduces a novel micro-differential evolution algorithm with vectorized random mutation factors, enhancing exploration and preventing premature convergence in small populations, validated through extensive benchmark testing.

Contribution

It proposes the MDEVM algorithm with vectorized random mutation factors and new mutation schemes for very small populations, improving exploration and convergence speed.

Findings

MDEVM outperforms traditional micro-DE algorithms in convergence speed.

The proposed mutation schemes enhance exploration in small populations.

Experimental results on benchmark functions confirm high performance.

Abstract

The differential evolution (DE) algorithm suffers from high computational time due to slow nature of evaluation. In contrast, micro-DE (MDE) algorithms employ a very small population size, which can converge faster to a reasonable solution. However, these algorithms are vulnerable to a premature convergence as well as to high risk of stagnation. In this paper, MDE algorithm with vectorized random mutation factor (MDEVM) is proposed, which utilizes the small size population benefit while empowers the exploration ability of mutation factor through randomizing it in the decision variable level. The idea is supported by analyzing mutation factor using Monte-Carlo based simulations. To facilitate the usage of MDE algorithms with very-small population sizes, new mutation schemes for population sizes less than four are also proposed. Furthermore, comprehensive comparative simulations and analysis on performance of the MDE algorithms over various mutation schemes, population sizes, problem types (i.e. uni-modal, multi-modal, and composite), problem dimensionalities, and mutation factor ranges are conducted by considering population diversity analysis for stagnation and trapping in local optimum situations. The studies are conducted on 28 benchmark functions provided for the IEEE CEC-2013 competition. Experimental results demonstrate high performance and convergence speed of the proposed MDEVM algorithm.