A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows

• The Pareto optimal set is sought for the vehicle routing problem with time windows.
• The number of vehicles and total distance are minimized simultaneously.
• Problem-specific knowledge makes the genetic operators effective.
• Ten benchmark algorithms and 99 problem instances are included in the experiments.
• We update more than 1/3 of the best known non-dominated solutions.

This paper addresses the multiobjective vehicle routing problem with time windows (MOVRPTW). The objectives are to minimize the number of vehicles and the total distance simultaneously. Our approach is based on an evolutionary algorithm and aims to find the set of Pareto optimal solutions. We incorporate problem-specific knowledge into the genetic operators. The crossover operator exchanges one of the best routes, which has the shortest average distance, the relocation mutation operator relocates a large number of customers in non-decreasing order of the length of the time window, and the split mutation operator breaks the longest-distance link in the routes. Our algorithm is compared with 10 existing algorithms by standard 100-customer and 200-customer problem instances. It shows competitive performance and updates more than 1/3 of the net set of the non-dominated solutions.