Lévy Flight Shuffle Frog Leaping Algorithm Based on Differential Perturbation and Quasi-Newton Search

Abstract

Lévy flight Shuffle Frog Leaping Algorithm (LSFLA) is a SFLA variant and enhances the performance of SFLA largely, however, it still has some defects, such as poor convergence and low efficiency. So an improved LSFLA, namely, LSFLA based on Differential perturbation and Quasi-Newton search (DQLSFLA), is proposed in this paper. Firstly, the way of updating only one solution which is the worst one at every sub-iteration in LSFLA is replaced with an all-solution updating way in the subgroup to improve the probability of obtaining the best solution, to omit one sorting step at every sub-iteration and the sub-iteration number parameter setting, to reduce the computational complexity and to enhance the optimization efficiency. Secondly, a random differential perturbation approach and an improved Lévy flight updating one are created and used in the subgroup updating to form DLSFLA, that is, the first half frogs in the subgroup use the random differential perturbation updating approach to improve the global search ability, and the last half adopt the improved Lévy flight updating method to keep the advantage of the Lévy flight updating method and overcome its defects. Finally, quasi-Newton local search is integrated into DLSFLA near the end of the algorithm to improve the convergence speed. Experimental results on the complex functions from CEC-2014 show that DQLSFLA's convergence quality and optimization efficiency are much better than LSFLA's and that compared with quite a few other state-of-the-art algorithms, DQLSFLA has better performance. The results on medical image enhancement and Quadratic Assignment Problem (QAP) also show that DQLSFLA can solve the real word optimization problems better than LSFLA can.

Keywords

• Intelligent optimization algorithm
• shuffled frog leaping algorithm (SFLA)
• Lévy flight
• quasi-Newton search
• image enhancement
• quadratic assignment problem