An enhanced whale migration algorithm for its application in engineering problems

In this paper, we proposed an enhanced whale migration algorithm (EWMA) that integrates two novel strategies: Normal cloud model mutation (NCMM) and Fast Random Opposition-Based Learning. NCMM enables adaptive uncertainty management through expectation-entropy-hyperentropy mechanisms to balance exploration and exploitation. FROBL improves population diversity and convergence speed via oscillatory perturbations and nonlinear scaling. EWMA outperformed eight competing algorithms when evaluated on 23 benchmark functions and the CEC 2019, achieving optimal results on 18 of the 23 benchmark functions and all 10 CEC 2019 functions. It ranked first overall, significantly surpassing the other algorithms. Statistical analysis confirmed notable improvements in solution accuracy, convergence speed, and stability, with standard deviations 2–4 orders of magnitude lower than those of competitors. Engineering applications, including pressure vessel design, cantilever beams, and reinforced concrete beams, further demonstrated EWMA's practical effectiveness, yielding optimal designs with improved constraint handling. EWMA offers a robust optimization tool for complex engineering problems requiring global search capability and precise local refinement.