Abstract: A hybrid crossover variation beluga whale optimization (HCVBWO) is proposed to address the limitations of traditional methods in solving engineering optimization problems with complex constraints. Firstly, the algorithm utilizes an optimal point set mapping to initialize the population, thereby increasing the diversity of the population. Secondly, a cross-variation strategy is employed to enhance the algorithm’s mid-term development capability. Finally, an adaptive mixed perturbation strategy is used to balance the algorithm’s late-stage local and global search capabilities. The HCVBWO algorithm is compared with six other algorithms using simulations on the IEEE CEC2014 benchmark test set, and the results demonstrate the algorithm’s strong optimization capability and robustness. Furthermore, the application of the HCVBWO algorithm to two mechanical engineering design problems and a production scheduling problem verifies its superiority in engineering optimization.