Two Evolutionary Metaheuristics for the Vehicle Routing Problem with Time Windows

The vehicle routing problem with time windows (VRPTW) is an extension of the well-known vehicle routing problem with a central depot. The objective is to design an optimal set of routes that services all customers and satisfies the given constraints, especially the time window constraints. The objective function considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance minimization (secondary criterion). In this paper, two evolution strategies for solving the VRPTW are proposed. The evolution strategies were tested on 58 problems from the literature with sizes varying from 100 to 417 customers and 2 to 54 vehicles. The generated new best known solutions indicate that evolution strategies are effective in reducing both the number of vehicles and the total travel distance.