Adaptive memetic algorithm for minimizing distance in the vehicle routing problem with time windows

This paper presents an adaptive memetic algorithm to solve the vehicle routing problem with time windows (VRPTW). It is a well-known NP-hard discrete optimization problem with two objectives—to minimize the number of vehicles serving a set of geographically dispersed customers, and to minimize the total distance traveled in the routing plan. Although memetic algorithms have been proven to be extremely efficient in solving the VRPTW, their main drawback is an unclear tuning of their numerous parameters. Here, we introduce the adaptive memetic algorithm (AMA-VRPTW) for minimizing the total travel distance. In AMA-VRPTW, a population of solutions evolves with time. The parameters of the algorithm, including the selection scheme, population size and the number of child solutions generated for each pair of parents, are adjusted dynamically during the search. We propose a new adaptive selection scheme to balance the exploration and exploitation of the solution space. Extensive experimental study performed on the well-known Solomon’s and Gehring and Homberger’s benchmark sets confirms the efficacy and convergence capabilities of the proposed AMA-VRPTW. We show that it is very competitive compared with other state-of-the-art techniques. Finally, the influence of the proposed adaptive schemes on the AMA-VRPTW behavior and performance is investigated in a thorough sensitivity analysis. This analysis is complemented with the two-tailed Wilcoxon test for verifying the statistical significance of the results.