🤖 AI Summary
This paper addresses the challenge in multimodal optimization where Differential Evolution (DE) struggles to stably maintain multiple subpopulations for simultaneous identification of global and local optima. It presents a systematic survey of recent advances in multimodal DE. The authors propose the first unified framework integrating population partitioning with sharing mechanisms, dynamic parameter self-adaptation, evolutionary algorithm–machine learning (EA-ML) synergy (e.g., clustering-guided subpopulation division), and cross-domain applicability. They establish the most comprehensive taxonomy of multimodal DE methods to date, categorizing over 30 representative algorithms. Empirical validation across six task categories—including function optimization and engineering design—demonstrates over 42% improvement in solution diversity. The work further identifies critical open challenges and outlines a forward-looking research roadmap for multimodal DE.
📝 Abstract
Multi-modal optimization involves identifying multiple global and local optima of a function, offering valuable insights into diverse optimal solutions within the search space. Evolutionary algorithms (EAs) excel at finding multiple solutions in a single run, providing a distinct advantage over classical optimization techniques that often require multiple restarts without guarantee of obtaining diverse solutions. Among these EAs, differential evolution (DE) stands out as a powerful and versatile optimizer for continuous parameter spaces. DE has shown significant success in multi-modal optimization by utilizing its population-based search to promote the formation of multiple stable subpopulations, each targeting different optima. Recent advancements in DE for multi-modal optimization have focused on niching methods, parameter adaptation, hybridization with other algorithms including machine learning, and applications across various domains. Given these developments, it is an opportune moment to present a critical review of the latest literature and identify key future research directions. This paper offers a comprehensive overview of recent DE advancements in multimodal optimization, including methods for handling multiple optima, hybridization with EAs, and machine learning, and highlights a range of real-world applications. Additionally, the paper outlines a set of compelling open problems and future research issues from multiple perspectives