Abstract：[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.
王振宇, 王磊. 多策略帝王蝶优化算法及其工程应用[J]. 清华大学学报（自然科学版）, 2024, 64(4): 668-678.
WANG Zhenyu, WANG Lei. Improved monarch butterfly optimization algorithm and its engineering application. Journal of Tsinghua University(Science and Technology), 2024, 64(4): 668-678.
[1] HAN M, GAO L, LI A, et al. An overview of high utility item sets mining methods based on intelligent optimization algorithms[J/OL]. Knowledge and Information Systems. https://doi.org/10.1007/s10115-022-01741-1. [2] ESSA F A, MOHAMED A E, AMMAR H E. An enhanced productivity prediction model of active solar still using artificial neural network and harris hawks optimizer[J]. Applied Thermal Engineering, 2020(170): 115020. [3] 向子权, 杨家其, 李慧琳, 等. 基于离散灰狼算法的资源分配问题求解[J]. 华中科技大学学报(自然科学版), 2021, 49(08): 81-85. XIANG Z Q, YANG J Q, LI H L, et al. Resource allocation problem solving based on discrete gray wolf algorithm[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2021, 49(08): 81-85.(in Chinese) [4] NENAVATH H, KUMAR JATOTH D R, et al. A synergy of the sine-cosine algorithm and particle swarm optimizer for improved global optimization and object tracking[J]. Swarm and Evolutionary Computation, 2018, 43: 1-30. [5] WANG G G, SUASH D, CUI Z H. Monarch butterfly optimization[J]. Neural Computing and Applications, 2019, 31(7): 1995-2014. [6] KAVIARASAN R, HARIKRISHNA P, ARULMURUGAN A. Load balancing in cloud environment using enhanced migration and adjustment operator based monarch butterfly optimization[J]. Advances in Engineering Software, 2022, 169: 1-11. [7] SUN L, SI S S, XU J C, et al. Feature selection using binary monarch butterfly optimization[J]. Applied Intelligence, 2023, 53: 706-727. [8] ABDELMONEM M, MOHAMED A T. A hybridization of differential evolution and monarch butterfly optimization for solving systems of nonlinear equations[J]. Journal of Computational Design and Engineering, 2019, 6: 354-367. [9] YAO X, LIU Y. Evolutionary programming made faster[J]. IEEE transactions on evolutionary computation, 1999, 3(2): 82-102. [10] DU N T, ZHOU Y Q, DENG W. Improved chimp optimization algorithm for three-dimensional path planning problem[J]. Multimedia Tools and Applications, 2022, (81): 27397-27422. [11] 刘志强, 何丽, 袁亮, 等. 采用改进灰狼算法的移动机器人路径规划[J]. 西安交通大学学报, 2022, 56(10): 49-60. LIU Z Q, HE L, YUAN L, et al. path planning of mobile robot based on TGWO Algorithm[J]. Journal of Xi'an Jiaotong University, 2022, 56(10): 49-60. (in Chinese) [12] DORIGO M, MANIEZZO V, COLORNI A. Ant system: Optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 1996, 26(1): 29-41. [13] Gaurav D, Vijay K. Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems[J]. Knowledge-Based Systems, 2019, 165(1): 169-196. [14] XU T P, ZHAO F Q, TANG J X, et al. A knowledge-driven monarch butterfly optimization algorithm with self-learning mechanism[J]. Applied Intelligence, 2023, (53): 12077-12097. [15] SAMANEH Y, ESMAEIL H, MOHAMMAD M. CCMBO: a covariance-based clustered monarch butterfly algorithm for optimization problems[J]. Memetic Computing, 2022, 14(3): 377-394. [16] Wilcoxon F. Individual comparisons by ranking methods[J]. Biometrics Bull, 1945, 1(6): 80-83. [17] 王宗山, 丁洪伟, 王杰, 等. 基于正交设计的折射反向学习樽海鞘群算法[J]. 哈尔滨工业大学学报, 2022, 54(11): 122-136. WANG Z S, DING H W, WANG J, et al. Salp swarmalgorithm based on orthogonalrefracted opposition-based learning[J]. Journal of Harbin Institute of Technology, 2022, 54(11): 122-136.(in Chinese) [18] Friedman M. The use of ranks to avoid the assumption of normality implicit in the analysis of variance[J]. Journal of the American Statistical Association, 1937, 32(200): 675-701.
2024, Vol. 64 
