Study on Trajectory and Convergence Analysis of Shuffled Frog  Leaping Algorithm and Its Improved Algorithm

In order to understand the convergence characteristics of Shuffled Frog Leaping Algorithm (SFLA), the trajectories of frog of SFLA was analyzed by solving the differential equation. Further, the global convergence analysis was made using random search algorithm convergence criterion which was present by Solis and Wets, and the conclusion that SFLA is global convergent was drawn in this paper. A new optimization method, called hybrid extremal optimization and shuffled frog leaping algorithm(EO-SFLA), which introduces EO local search method to SFLA, was presented based on the convergence analysis of SFLA, and it was proved to be guaranteed to get the global optimization solution with probability one. EO-SFLA combines the merits of both SFLA and EO, improves local search ability while keeping the global convergence of SFLA. The mutation selection method of EO-SFLA referring to the Power-law expands the search space, gives the algorithm ability to jump out of local extreme points, and ensures the global convergence of the algorithm. The results of experiments carried out with four well-known benchmark functions had shown the proposed algorithm possesses outstanding performance in convergence speed and solution results. The simulation results matched the convergence analysis.