Improved monarch butterfly optimization algorithm and its engineering application
[Objective]In recent years,a large number of nonconvex,highly nonlinear,multimodal,and multivariable complex optimization problems have emerged in scientific and engineering technology design due to the continuous development of science and technology.Owing to their advantages such as simple programming,flexible operation,and efficient optimization,intelligent optimization algorithms have become research hotspots to address diverse complex optimization problems in engineering applications.They have been successfully used to solve practical problems such as neural networks,resource allocation,and target tracking.In this research,multiple strategies were developed to improve the existing monarch optimization algorithm to address its shortcomings,such as slow convergence speed,low optimization accuracy,and ease of falling into local extremum.[Methods]First,the forward normal cloud generator is used to perform nonlinear cloud operation on the parent monarch butterfly,increasing the number of candidate solutions and improving the local development ability of the algorithm.Subsequently,an opposition-based learning strategy based on convex lens imaging is used to the current optimal individual which is generated by normal cloud generator to generate new individuals and improve the convergence accuracy and speed of the algorithm.Finally,adaptive strategies are incorporated into the adjustment operator to diversify the population.[Results]Several experiments were performed on benchmark functions to verify the performance of the algorithm:(1)Different strategies proposed were analyzed using ablation experiments to verify their effectiveness.The results revealed that the proposed strategies can effectively improve the algorithm's performance.(2)The improved algorithm was compared with other swarm intelligent optimization algorithms,and the results revealed that the improved algorithm can achieve the best results on most test functions.(3)The improved algorithm was also compared with other improved versions of monarch optimization algorithm,and the results revealed that the improved algorithm exhibited more advantages such as fast convergence speed and high convergence precision.(4)The Wilcoxon rank sum test and Friedman test were used to verify the performance of the proposed algorithm.The results revealed that the improved algorithm is superior to other algorithms.[Conclusions]The optimization and comparison results of the pressure vessel design and welded beam design in engineering applications further verified the superiority of the improved algorithm in addressing real-world engineering problems.