Exact and heuristic algorithms for vehicle routing

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Vehicle routing problems consist of determining least-cost vehicle routes to perform a set of tasks while respecting operational constraints, such as vehicle capacity and service time windows at the customers. Several problem variants exist, arising from different applications in, e.g., freight transportation and humanitarian logistics. In this proposal, we develop mathematical optimization models and methods, called branch-price-and-cut methods, to help the planners determine the best possible vehicle routes. The optimization methods can be classified into two categories: an exact method seeks an optimal solution and can require substantial computational time; a heuristic method is much faster but provides a good-quality solution that may not be optimal. We explore four research directions for exact methods and one for heuristics. In particular, we aim at integrating machine learning algorithms developed in artificial intelligence into branch-price-and-cut algorithms that are widely used for vehicle routing. Furthermore, we develop optimization methods for two specific vehicle routing problems: 1) the simultaneous pickup and delivery problem with time windows and a load fragility constraint that forbids stacking heavy items over light ones and 2) the vehicle routing problem with a moving depot that arises in humanitarian logistics when drones are dispatched from a moving helicopter to assess the extent of damage in different zones of a devastated area. From a scientific point of view, the results of this research are methodological and will be applicable to a wide variety of vehicle routing problems in different modes of transportation and even to certain problems arising in other domains. From a commercial point of view, these results will help the freight companies and the humanitarian logistic providers to better manage the utilization of their vehicles and will therefore contribute to increase the productivity of Canadian companies and reduce greenhouse gas emissions. Finally, from an academic point of view, this research will provide financial support and training to three PhD, two MSc and one undergraduate students that will be in demand by the Canadian optimization software development companies after completing their studies.