Improved particle swarm optimization for high-dimensional optimization problem

Abstract

Particle swarm optimization (PSO) has simple implementation and robust performance and is appreciated as a popular optimization algorithm among engineers and researchers. However, two of its issues have yet to be improved: PSO converges into the local optimum for the high-dimensional optimization problem, and it has slow convergence speed. This thesis aims to introduce a new variant of a particle swarm optimization algorithm (PSOLFS). PSOLFS is meant to acquire a global optimum solution and fast convergence speed for the high-dimensional optimization problem. It constitutes a combination of particle swarm optimization, Lévy flight-McCulloch and fast simulated annealing. We design PSOLFS based on a balance between exploration and exploitation. We implement Lévy flight-McCulloch in the PSO position to have the algorithm explore the large search space and to create diversity in the position. We implement Fast simulated annealing in the late iteration to make the algorithm select the most accurate solution. We evaluate the algorithm on 16 benchmark functions for 500 and 1,000 dimensions experiments. On 500 dimensions, the algorithm obtains the optimal value on 14 of the 16 functions. On 1,000 dimensions, the algorithm obtains the optimal value on eight benchmark functions and close to optimal on four functions. PSOLFS acquire 96% accuracy on 500 dimensions and 91% on 1000 dimensions. We also compare PSOLFS with other five PSO variants in terms of convergence accuracy and speed. The results demonstrate that it achieves a higher accuracy and faster convergence speed than other PSO variants. PSOLFS is an efficient and robust optimizer for optimizing high dimensional problems. In addition, the results of Wilcoxon test show a significant difference between PSOLFS and the other PSO variants. The results of all experiments have shown that the proposed method is useful for the PSO in terms not only avoiding the local optimum but also improving the convergence speed.