Aims: To design a new variant of the Shuffled Frog Leaping Algorithm in which memeplexes formation is modified with a new strategy.
Background: Shuffled Frog Leaping (SFL) is a memetic meta-heuristic algorithm that inherits two other algorithms’ features. Its intensification component of search is similar to Particle Swarm Optimization, while the inspiration for diversification is inherited from the global exchange of information in Shuffled Complex Evolution. A basic variant has been applied to solve many optimisation problems. SFLA suffers from a slow acceleration rate.
Objective: To propose a robust hybrid SFLA that accelerates convergence.
Methods: Two modifications are proposed in the structure of basic SFLA. Firstly, memeplexes formation is modified to handle continuous optimization problems. Secondly, in the basic SFL algorithm, the position of the worst frog is improved by moving it towards the best frog in the respective memeplex. With the progress of execution, the difference between best and worst frog position reduces; there may be more chances to trap in local minima. To improve convergence and avoid trapping in local optima, a parent-centric operator is embedded in each memeplex while performing a local search. The proposed algorithm is named PC-SFLA (Parent Centric - Shuffled Frog Leaping Algorithm).
Results: The improved efficiency of PC-SFLA is validated on a robust and diverse set of standard test functions defined in CEC 2006 and 2010. Further, its efficacy is verified to optimize the total cost of supply chain management of a system. Non-parametric statistical result analysis demonstrates the efficiency of the proposal.
Conclusion: PC-SFLA performed better than PSO, DE, PESO+, Modified DE, ABC, and SFLA at 5% and 10% level of significance whereas at par with Shuffled-ABC for g01-g07 functions of CEC 2006 in terms of NFE’s. Similarly, PC-SFLA performed better than SaDE, SFLA, CMODE at both levels of significance (5% & 10%) and par with MPDE in terms of mean function value for 17 problems taken from CEC 2006. Further, PC-SFLA is investigated on 18 problems from CEC 2010, and Wilcoxon signed ranks test is performed at a 5% level of significance. PC-SFLA performed better than SFLA and CHDE and at par with PESO. The computational results present the competency of the proposed method to solve quadratic, nonlinear, polynomial, linear, and cubic functions efficiently. The simulated results show that the proposed algorithm can solve mix integer constrained continuous optimization problem efficiently.