White Whale Optimization Algorithm

Swarm intelligence optimization algorithms have been widely studied in continuous optimization, combinatorial optimization, and engineering applications due to their lack of gradient information requirements, simple structure, and wide applicability. However, most existing metaheuristic algorithms are highly similar in terms of information acquisition methods, swarm interaction structures, and search dynamics, mainly relying on individual optimality, global optimality, or simple neighborhood average information for updates. This leads to problems such as premature convergence, insufficient search diversity, and high parameter sensitivity in complex multimodal problems. To address this, this paper proposes a novel swarm intelligence optimization method—the multimodal resonance beluga optimization algorithm. Starting from the echolocation behavior of beluga whales, this method introduces the concept of acoustic resonance spectrum in the solution space, uses multi-frequency information to perceive the structure of the objective function landscape, and constructs a multimodal resonance migration mechanism based on this. Furthermore, this paper introduces a fitness-induced non-Euclidean search geometry, enabling the individual update direction to adaptively reflect the local structure of the objective function. Simultaneously, through self-evolutionary modeling of the swarm topology and a parameter-free control strategy based on information entropy, the self-organizing adjustment of the search process is achieved. The complete mathematical description of the algorithm is given, and the convergence properties of the algorithm are theoretically analyzed from the perspective of Markov processes and energy decay.