Improved Shuffled Frog Leaping Algorithm and its multi-phase model for multi-depot vehicle routing problem

In the present work, an improved Shuffled Frog Leaping Algorithm (SFLA) and its multi-phase model are presented to solve the multi-depots vehicle routing problems (MDVRPs). To further improve the local search ability of SFLA and speed up convergence, a Power Law Extremal Optimization Neighborhood Search (PLEONS) is introduced to SFLA. In the multi-phase model, firstly the proposed algorithm generates some clusters randomly to perform the clustering analyses considering the depots as the centroids of the clusters for all the customers of MDVRP. Afterward, it implements the local depth search using the SFLA for every cluster, and then globally re-adjusts the solutions, i.e., rectifies the positions of all frogs by PLEONS. In the next step, a new clustering analyses is performed to generate new clusters according to the best solution achieved by the preceding process. The improved path information is inherited to the new clusters, and the local search using SFLA for every cluster is used again. The processes continue until the convergence criterions are satisfied. The experiment results show that the proposed algorithm possesses outstanding performance to solve the MDVRP and the MDVRP with time windows.