Efficient maximum iterations for swarm intelligence algorithms: a comparative study - Si-Ma, Shen; Liu, Han-Ming; Zhan, Hong-Xiang; Liu, Zhao-Fa; Guo, Gang; Yu, Cong; Hu, Peng-Cheng (The Artificial intelligence review, 2025)
A swarm intelligence algorithm usually iterates many times to approximate the optimum to obtain the solution of a problem. The maximum iteration is influenced by many factors such as the algorithm itself, problem types, as well as dimensions and search space sizes of decision variables. There are few existing studies on efficient maximum iterations, especially a large-scale study on comparison for different problem types. By dividing three CEC benchmark sets into several problem types, this study made a large-scale performance comparison of 123 common swarm intelligence algorithms from several views. The experimental results show that for low-dimensionality, wide search space, and/or simple- and medium-complex problems, about a quarter of the algorithms are concentrated in iterations of about 30 ~ 80, while most algorithms for other types of problems tend to have as many iterations as possible. By and large, for the Classical set, large iterations are beneficial for improving the performance of most algorithms, while less than half of the algorithms for CEC 2019 and CEC 2022 do so. And, the efficient iterations of excellent algorithms are about 300 on low dimensionality, wide search space and simple-complexity problems, while other types are as large as possible. In terms of algorithm speed, LSO, DE and RSA are the fastest on all the three benchmark sets, and the runtime of all algorithms is almost linearly related to the maximum iterations. Although the conclusions largely depend on the problem types, we believe that an efficient iteration is necessary to optimize algorithm performance.