Fitness Landscape Analysis for the Differential Evolution Algorithm

Differential evolution (DE) is a prominent evolutionary algorithm for solving continuous optimization problems. Despite its widespread adoption, DE exhibits a pronounced sensitivity to control parameter configurations and problem-specific landscape characteristics. This thesis undertakes a comprehensive investigation into three foundational aspects of DE design: the critical role and intricate interplay of its control parameters; the influence of fitness landscape characteristics (FLCs) on both algorithmic performance and search behavior; and the recurring failure patterns, which illuminate key vulnerabilities and inform the development of robust adaptive strategies. The first part of this thesis focuses on the control parameters, specifically the influence of population size and its interaction with other control parameters on the performance of DE across diverse problem modalities and dimensionalities. Moreover, the functional analysis of variance (fANOVA) is applied to quantify the relative importance and interaction effects of the DE parameters. The results reveal that the existing conventional one-size-fits-all guidelines for setting DE population size possess the possibility of overestimating initial population sizes. Further analysis indicates that the impact of varying population sizes on DE performance differs across various problem fitness landscapes, demonstrating that larger population sizes are more beneficial for complex composition problems. Additionally, the study highlights a critical interaction between population size and other DE control parameters, with larger population sizes found to be more advantageous at lower crossover rates. The second part explores the relationship between FLCs, DE performance, and algorithmic behavior. Two experiments assess how ruggedness, gradients, funnels, deception, and searchability relate to both performance metrics and behavioral patterns. The results revealed that DE reduced its diversity more slowly in landscapes with multiple funnels and resisted deception, but faced excessively slow convergence for high-dimensional problems. Overall, the results elucidate that the presence of multiple funnels and high deception levels are the FLCs most associated with DE performance and search behavior. The third part presents a landscape-aware failure analysis of the DE algorithm. A comprehensive analysis was conducted to understand the conditions under which DE fails, followed by a structured risk categorization of failure cases. A threshold-based failure prediction approach was also proposed. Based on these insights, an adaptive algorithm, called self-guided differential evolution (SGDE), is proposed. SGDE integrates six modular components, each of which is activated in response to diagnosed failure conditions. Comprehensive experimental evaluations show that SGDE improves performance for problems where traditional DE consistently fails. Overall, this work advances the understanding of DE parameterization, fitness landscape-aware behavior, and failure-resilient algorithm design, offering new tools and principles for adaptive optimization in complex problem domains.

Grantor dc:publisher

Stellenbosch : Stellenbosch University

Year dc:date.issued

2026

Author dc:creator

• Saad, Amani Dhumad

Advisors dc:contributor.advisor

• Engelbrecht, A. P.
• Khan, S. A.

Language dc:language.iso

en

Repository record dc:identifier.uri

https://scholar.sun.ac.za/handle/10019.1/135882

OAI identifier oai:identifier

oai:scholar.sun.ac.za:10019.1/135882