A Hybrid Shuffled Frog Leaping Algorithm and Its Performance Assessment in Multi-Dimensional Symmetric Function

Abstract

Ensemble learning of swarm intelligence evolutionary algorithm of artificial neural network (ANN) is one of the core research directions in the field of artificial intelligence (AI). As a representative member of swarm intelligence evolutionary algorithm, shuffled frog leaping algorithm (SFLA) has the advantages of simple structure, easy implementation, short operation time, and strong global optimization ability. However, SFLA is susceptible to fall into local optimas in the face of complex and multi-dimensional symmetric function optimization, which leads to the decline of convergence accuracy. This paper proposes an improved shuffled frog leaping algorithm of threshold oscillation based on simulated annealing (SA-TO-SFLA). In this algorithm, the threshold oscillation strategy and simulated annealing strategy are introduced into the SFLA, which makes the local search behavior more diversified and the ability to escape from the local optimas stronger. By using multi-dimensional symmetric function such as drop-wave function, Schaffer function N.2, Rastrigin function, and Griewank function, two groups (i: SFLA, SA-SFLA, TO-SFLA, and SA-TO-SFLA; ii: SFLA, ISFLA, MSFLA, DSFLA, and SA-TO-SFLA) of comparative experiments are designed to analyze the convergence accuracy and convergence time. The results show that the threshold oscillation strategy has strong robustness. Moreover, compared with SFLA, the convergence accuracy of SA-TO-SFLA algorithm is significantly improved, and the median of convergence time is greatly reduced as a whole. The convergence accuracy of SFLA algorithm on these four test functions are 90%, 100%, 78%, and 92.5%, respectively, and the median of convergence time is 63.67 s, 59.71 s, 12.93 s, and 8.74 s, respectively; The convergence accuracy of SA-TO-SFLA algorithm on these four test functions is 99%, 100%, 100%, and 97.5%, respectively, and the median of convergence time is 48.64 s, 32.07 s, 24.06 s, and 3.04 s, respectively.

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“…The Griewank function and the Rastrigin function are selected as fitness evaluation functions, 40,41 and the minimum values of the two functions are obtained at the origin and are 0. The function expression, search range, and functional image are presented in Table 1.…”