Convergence Analysis of Differential Evolution Variants on Unconstrained Global Optimization Functions

TL;DR

This study empirically evaluates the convergence behavior of fourteen Differential Evolution variants on fourteen diverse benchmark functions for unconstrained global optimization, analyzing their competitiveness and convergence characteristics.

Contribution

It provides a comparative analysis of DE variants' convergence properties and performance on various benchmark functions, highlighting their strengths and weaknesses.

Findings

Best variants achieved lower mean objective function values.

Convergence speed varied significantly among variants.

Some variants showed consistent performance across different problem types.

Abstract

In this paper, we present an empirical study on convergence nature of Differential Evolution (DE) variants to solve unconstrained global optimization problems. The aim is to identify the competitive nature of DE variants in solving the problem at their hand and compare. We have chosen fourteen benchmark functions grouped by feature: unimodal and separable, unimodal and nonseparable, multimodal and separable, and multimodal and nonseparable. Fourteen variants of DE were implemented and tested on fourteen benchmark problems for dimensions of 30. The competitiveness of the variants are identified by the Mean Objective Function value, they achieved in 100 runs. The convergence nature of the best and worst performing variants are analyzed by measuring their Convergence Speed (Cs) and Quality Measure (Qm).