This paper presents an adaptive memetic algorithm\nto solve the vehicle routing problem with time windows\n(VRPTW). It is a well-known NP-hard discrete optimization\nproblem with two objectivesââ?¬â?to minimize the number\nof vehicles serving a set of geographically dispersed customers,\nand to minimize the total distance traveled in the\nrouting plan. Although memetic algorithms have been proven\nto be extremely efficient in solving the VRPTW, their main\ndrawback is an unclear tuning of their numerous parameters.\nHere, we introduce the adaptive memetic algorithm (AMAVRPTW)\nfor minimizing the total travel distance. In AMAVRPTW,\na population of solutions evolves with time. The\nparameters of the algorithm, including the selection scheme,\npopulation size and the number of child solutions generated\nfor each pair of parents, are adjusted dynamically during the\nsearch. We propose a new adaptive selection scheme to balance\nthe exploration and exploitation of the solution space.\nExtensive experimental study performed on the well-known\nSolomonââ?¬â?¢s and Gehring and Hombergerââ?¬â?¢s benchmark sets\nconfirms the efficacy and convergence capabilities of the proposed\nAMA-VRPTW. We show that it is very competitive\ncompared with other state-of-the-art techniques. Finally, the\ninfluence of the proposed adaptive schemes on the AMAVRPTW\nbehavior and performance is investigated in a thorough\nsensitivity analysis. This analysis is complemented with the two-tailed Wilcoxon test for verifying the statistical significance\nof the results.
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