Adaptive Evolutionary and Information-Theoretic Frameworks for Multimodal and Multiobjective Optimization: Integrative Advances, Applications, and Theoretical Implications
Keywords:
Evolutionary optimization, multimodal optimization, multiobjective algorithms, swarm intelligenceAbstract
Optimization problems characterized by multimodality, multiple conflicting objectives, large-scale decision spaces, uncertainty, and dynamic constraints have become increasingly prevalent across engineering, finance, logistics, and complex adaptive systems. Traditional deterministic optimization approaches struggle to address such complexity due to their reliance on convexity assumptions, gradient availability, and single-solution convergence. As a result, evolutionary computation and swarm intelligence have emerged as dominant paradigms for addressing these challenges. This article presents a comprehensive, theory-driven synthesis of adaptive evolutionary and information-theoretic optimization frameworks, grounded strictly in established scholarly works on differential evolution, particle swarm optimization, coevolutionary multiobjective systems, hyper-heuristics, evolutionary multitasking, memetic algorithms, and portfolio optimization under uncertainty and transaction costs. By deeply elaborating the algorithmic philosophies, learning mechanisms, population interaction strategies, and theoretical trade-offs inherent in these methods, this study articulates how modern optimization research has evolved toward adaptive, distributed, and knowledge-driven paradigms. Particular emphasis is placed on multimodal optimization, where multiple global and local optima coexist, and multiobjective optimization, where solution sets must be evaluated in terms of trade-offs rather than scalar dominance. Furthermore, the integration of information theory, online learning, and decision-theoretic perspectives is examined as a unifying lens for understanding algorithmic behavior, convergence dynamics, and robustness. Through extensive conceptual analysis, this article identifies key methodological synergies, unresolved theoretical tensions, and future research trajectories, offering a publication-ready contribution to the ongoing discourse on advanced optimization systems.
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