Monarch butterfly optimization-based genetic algorithm operators for nonlinear constrained optimization and design of engineering problems

This paper aims to present a hybrid method to solve nonlinear constrained optimization problems and engineering design problems (EDPs). The hybrid method is a combination of monarch butterfly optimization (MBO) with the cross-over and mutation operators of the genetic algorithm (GA). It is called a hybrid monarch butterfly optimization with genetic algorithm operators (MBO-GAO). Combining MBO and GA operators is meant to overcome the drawbacks of both algorithms while merging their advantages. The self-adaptive cross-over and the real-valued mutation are the GA operators that are used in MBO-GAO. These operators are merged in a distinctive way within MBO processes to improve the variety of solutions in the later stages of the search process, speed up the convergence process, keep the search from getting stuck in local optima, and achieve a balance between the tendencies of exploration and exploitation. In addition, the greedy approach is presented in both the migration operator and the butterfly adjusting operator, which can only accept offspring of the monarch butterfly groups who are fitter than their parents. Finally, popular test problems, including a set of 19 benchmark problems, are used to test the proposed hybrid algorithm, MBO-GAO. The findings obtained provide evidence supporting the higher performance of MBO-GAO compared with other search techniques. Additionally, the performance of the MBO-GAO is examined for several EDPs. The computational results show that the MBO-GAO method exhibits competitiveness and superiority over other optimization algorithms employed for the resolution of EDPs.