Survey on whale optimization algorithm: from fundamental principles to modern adaptations and applications

The Whale Optimization Algorithm (WOA), inspired by the bubble-net hunting behavior of humpback whales, has emerged as one of the most influential swarm intelligence algorithms for solving complex optimization problems. Since its introduction, WOA has attracted substantial research attention due to its balance between exploration and exploitation, simplicity of implementation, and competitive performance across diverse problem domains. This survey provides a comprehensive analysis of WOA, encompassing its fundamental principles, mathematical formulation, variants, hybridizations, and extensive real-world applications. A systematic taxonomy is presented to classify WOA modifications into adaptive, chaotic, hybrid, discrete, multi-objective, and intelligent-learning-based frameworks. The review also highlights WOA’s successful integration into fields such as structural engineering, energy systems, machine learning, bioinformatics, and emerging intelligent technologies including IoT and cloud computing. Comparative benchmarking and statistical analyses demonstrate the superiority of enhanced WOA variants over traditional metaheuristics in terms of convergence rate, stability, and accuracy. Finally, the paper identifies existing challenges and outlines promising research directions, including theoretical convergence proofs, parameter self-adaptation, large-scale optimization, and hybridization with deep learning and quantum paradigms. This work provides a consolidated and critical overview of WOA’s evolution, serving as a valuable reference for researchers and practitioners in the field of metaheuristic optimization.