Improved multi-objective grasshopper optimization algorithm and application in capacity configuration of urban rail hybrid energy storage systems

Aiming at addressing problems of poor diversity and ergodicity of initial population, slow convergence speed, and susceptibility to local optima in conventional multi-objective grasshopper optimization algorithm (MOGOA), an improved MOGOA is proposed in this paper. The proposed algorithm is based on Sobol sequence, adaptive social force, cosine parameter c, as well as Levy flight mechanism (SACLMOGOA), where Sobol sequence is adopted to initialize the population, thereby improving the diversity and ergodicity of the initial population. The adaptive social force is proposed to enhance the global exploration ability in the early stage of iteration and the local development ability in the late stage of iteration. A cosine type parameter c is used to ensure sufficient exploration time and rapid convergence of the algorithm during position update process and Levy flight is used to guide some grasshoppers to mutate, enhancing the ability to escape from the local optima and improving the performance and efficiency of the algorithm. The proposed algorithm is tested with ZDT and DTLZ series benchmark test functions to validate its effectiveness, and it is also compared with conventional MOGOA, multi-objective particle swarm optimization, multi-objective gray Wolf, and multi-objective jellyfish algorithms. The simulation results demonstrate that the proposed algorithm outperforms other algorithms in terms of inverse generational distance (IGD), spread (SP), maximum spread (MS), run time and Wilcoxon rank sum test. Furthermore, the proposed algorithm is successfully applied to the capacity configuration of the urban rail hybrid energy storage systems (HESS) of Changsha Metro Line 1 in China, reducing the traction network voltage fluctuations by 3.3 % and 2.2 % compared to no HESS capacity configuration optimization, and by 14 % and 5.7 % compared to no HESS during train starting and breaking, respectively. While achieving the goal of energy-saving and voltage stabilization, the cost of the hybrid energy storage systems is minimized as well. All of these have demonstrated SACLMOGOA is an effective tool for solving complex multi-objective optimization problems in engineering.