Complex design tasks require the support of efficient intelligent optimization algorithms, and the traditional beluga optimization algorithm is defective in convergence speed and optimization stability. In this study, we propose a multi-strategy hybrid improved beluga whale algorithm (MHIBWO) that integrates the MTent population initialization strategy, the step-size adjustment strategy, and the longitudinal and transversal crossover strategy to address the limitations of the traditional beluga optimization algorithms for complex design tasks. The MTent mapping enhances the diversity of the initial populations through the introduction of random numbers; the step-size adjustment strategy optimizes the weight allocation by using the sine-cosine model to improve the global optimization ability; the vertical and horizontal crossover strategy maintains the population diversity through horizontal crossover and vertical crossover operations to prevent premature convergence. Numerical experiments show that the MHIBWO algorithm has significant advantages in single-peak and multi-peak function tests, and the average optimization accuracy and standard deviation of the three test functions under 80-dimensional conditions are 0. Compared with the standard BWO and the other five swarm intelligence optimization algorithms, the MHIBWO algorithm has a faster convergence speed and higher solving accuracy. Among the 18 multitask optimization benchmark tasks, the MHIBWO algorithm has significantly better solution quality than the existing algorithms in 14 tasks, and achieves an accuracy of 2.21 × 10-² on task T2 of the CI+HS problem, which is close to the global optimum. The experimental results demonstrate that the MHIBWO algorithm has excellent global search capability, local development capability and stability in complex design tasks.
