An effective theoretical and experimental analysis method for the improved slime mould algorithm

Metaheuristic intelligent optimization algorithms are effective methods for solving high-dimensional nonlinear complex optimization problems. The slime mould algorithm is a novel intelligent optimization algorithm proposed in 2020. However, the basic slime mould algorithm still has some shortcomings, such as slow convergence rate, easy to fall into local extremum, and unbalanced exploration and development capability. To further improve and expand the optimization ability and application scope of the slime mould algorithm, and enhance its performance in solving large-scale complex optimization problems, this paper proposes a slime mould algorithm (PPMSMA) based on Gaussian perturbation and phased position update, positive variation, and multi-strategy greedy selection. Firstly, Gaussian perturbation and phased position update mechanism are introduced to avoid the difficulty of the algorithm to jump out of the local extrema and also to speed up the convergence of the algorithm. Then, a positive variation strategy based on the sine cosine mechanism is introduced to move the variation of the population towards a better direction. Finally, a multi-strategy greedy selection mechanism is introduced, which effectively improves the search ability of the algorithm. The analysis and research on the optimization ability and performance of metaheuristic algorithms mainly include two aspects: theoretical analysis and experimental testing. Theoretical analysis has always been a relatively weak link in the research of metaheuristic algorithms, and there is currently no clear and effective method formed. For experimental testing, although there are more methods, they often lack systematization and adequacy. In this paper, a more complete, fine-grained and systematic approach to theoretical and experimental analysis is proposed. In the theoretical analysis part, the time complexity and spatial complexity of the PPMSMA algorithm are analytically proved to be the same as the basic slime mould algorithm, and the probability measure method is used to prove that PPMSMA algorithm can converge to the global optimal solution. In the simulation experiment section, the PPMSMA algorithm is compared with multiple sets of 10 representative comparison algorithms on the CEC2017 complex test function set suite for optimization accuracy analysis, Friedman comprehensive ranking analysis, average optimization rate analysis of PPMSMA relative to other algorithms, convergence curve analysis, and Wilcoxon rank-sum test analysis. To further examine the scalability of the improved algorithm in solving large-scale optimization problems, PPMSMA is compared with the above 10 comparative algorithms under 1000 dimensional conditions in the large-scale global optimization test set CEC2010, and the solution stability of each algorithm is analyzed through violin plots. The results show that the PPMSMA algorithm has significantly improved convergence performance, optimization accuracy, and solution stability in both high-dimensional and large-scale complex problems, and has significant advantages compared to multiple sets of 10 representative comparative algorithms. Finally, PPMSMA and 10 other comparative algorithms are used to solve engineering design optimization problems with different complexities. The experimental results validate the universality, reliability, and superiority of PPMSMA in handling engineering design constraint optimization problems.