Comparison of CLPSO, ECLPSO and ACLPSO on CEC2013 Multimodal Benchmark Functions

Particle swarm optimization (PSO) is a class of modern generalized intelligent optimization algorithms. Comprehensive learning PSO (CLPSO) is a powerful PSO variant that is good at exploration and works well on many multimodal problems. Enhanced CLPSO (ECLPSO) and adaptive CLPSO (ACLPSO) are improved versions of CLPSO that we have previously proposed. ECLPSO enhances the exploitation performance of CLPSO, and ACLPSO strengthens the exploration performance of ECLPSO. We have compared CLPSO, ECLPSO and ACLPSO on 16 benchmark functions in our previous study. To further understand the generalization performance of the three algorithms, this paper compares them on the well-known CEC2013 test set of multimodal benchmark functions. Compared with the benchmark functions employed in the previous study, though the number of dimensions for the CEC2013 benchmark functions are quite smaller, there are also a number of local optima in the search space. In addition, the CEC2013 test set contains composition functions that mix different characteristics of various basic functions, causing the search space to have a huge quantity of local optima and is very complex. Experimental results demonstrate that the accuracy of the solution obtained by ECLPSO is slightly better than that by CLPSO on just a few functions and is similar on all the other functions; both ECLPSO and CLPSO fail to derive the global optimum or a near-optimum on most of the composition functions; and ACLPSO is well balanced between exploration and exploitation, as it outperforms ECLPSO and CLPSO by being able to find the global optimum or a near-optimum with high accuracy on almost all the functions.