Pheromone-based Column Generation for the Vehicle Routing Problem with Black Box Feasibility

We propose an abstraction of emerging vehicle routing problems, the VRP with Black Box Feasibility. In this problem the routes of a basic VRP need to satisfy an unknown set of constraints. A black box function to test the feasibility of a route is provided. Practical examples of such problems are combinations of VRP with Loading or VRP with Scheduling. We propose a heuristic column generation-based approach to locally optimize this problem. We test the proposed approach on two applications from the literature, the Three-Dimensional Loading CVRP and the Multi-Pile VRP, showing the applicability of our approach and its good behavior compared to dedicated approaches.