Genetic programming for the vehicle routing problem with zone-based pricing

The vehicle routing problem (VRP) is one of the most interesting NP-Hard problems due to the multitude of applications in the real world. This work tracks a VRP with zone-based prices in which each customer belongs to a particular zone, and the goal is to maximize the profit. The particularity of this VRP variant is that the provider needs to determine the prices for each zone and routes for all vehicles. However, depending on the selected zone prices, only a subset of customers will have to be visited. In this work, we propose a novel route generation scheme (RGS) that considers both decisions simultaneously. The RGS is guided by a priority function (PF), which determines the next customer to visit. Since designing efficient PFs manually is a difficult and time-consuming task, hyper-heuristic methods, specifically genetic programming (GP), have been used in this study to generate them automatically. Furthermore, to test the performance of the generated PFs, a genetic algorithm is also used to exploit the RGS to construct the solution. The experimental analysis shows that the evolved heuristics provide reasonable quality solutions quickly, in contrast with the current state-of-the-art. Furthermore, GP produces better results than GA for some problem instances.