The vehicle routing problem
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
A Savings Based Ant System For The Vehicle Routing Problem
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
D-Ants: savings based ants divide and conquer the vehicle routing problem
Computers and Operations Research
A Tabu Search Algorithm for a Routing and Container Loading Problem
Transportation Science
IEEE Transactions on Intelligent Transportation Systems
European Driver Rules in Vehicle Routing with Time Windows
Transportation Science
HM'10 Proceedings of the 7th international conference on Hybrid metaheuristics
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This paper proposes an abstraction of emerging vehicle routing problems, the Vehicle Routing Problem 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. This function is considered of non-linear complexity (in the length of the route). Practical examples of such problems are combinations of VRP with Loading problems or VRP with Scheduling problems. The difficulty in addressing the VRP with Black Box Feasibility lies in the unknown problem structure and the costly feasibility check. We propose a column generation-based approach to locally optimize this problem. Columns are heuristically generated by so-called Collector ants, executing a construction heuristic while guided by pheromones. To find an integer solution we solve an integer Set Partitioning Problem defined on the set of columns generated by the ants. We test the proposed approach on two applications from the literature, the Three-Dimensional Loading Capacitated Vehicle Routing Problem and the Multi-Pile Vehicle Routing Problem, showing the applicability of our approach and its good behavior compared to dedicated approaches.