An improved whale algorithm for real-time boundary processing and its convergence analysis

Abstract To tackle the deficiencies in the whale algorithm, including its weak stability, sluggish convergence rate, and tendency to get trapped in local optima, an adapted whale optimization algorithm has been created, which introduces quasi-opposition learning and a real-time boundary processing mechanism. In the enhanced algorithm, a quasi-opposition learning mechanism is implemented to broaden the search scope and augment the variety of the population during the initial phases of iteration. This approach also helps to guarantee the convergence of the algorithm in the later phases of iteration. The unified boundary processing method of delay concentration is improved to solve the problem that a large amount of convergence damages diversity if a large number of transgressive individuals are unified and centralized. The algorithm flow is given and the asymptotic fitness and the asymptotic global optimal solution are proved. The time complexity is analyzed theoretically. Ultimately, six recognized algorithms were utilized to simulate the CEC 2017 function set across different scales. Findings indicate that the enhanced algorithm significantly boosts convergence rate, optimization precision, and solution robustness, demonstrating strong convergence characteristics.