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

翻译：多模态优化旨在识别函数的多个全局与局部最优解，为搜索空间中多样化的最优解提供重要洞见。进化算法能够单次运行即发现多个解，相较于传统优化技术（通常需要多次重启且无法保证获得多样化解）具有显著优势。在众多进化算法中，差分进化算法因其在连续参数空间中的强大适应性与通用性而脱颖而出。该算法通过基于种群的搜索机制促进多个稳定子种群的形成，每个子种群针对不同最优解进行探索，在多模态优化领域取得了显著成功。近年来多模态差分进化算法的研究进展主要集中在小生境技术、参数自适应、与机器学习等其他算法的混合策略，以及跨领域应用等方面。鉴于这些发展，当前正是对最新文献进行批判性评述并明确未来关键研究方向的重要时机。本文系统综述了多模态优化中差分进化的最新进展，涵盖多最优解处理方法、与进化算法及机器学习的混合策略，并重点阐述了系列实际应用案例。此外，本文还从多维度提出了一系列具有挑战性的开放性问题与未来研究方向。