Dual Bounds from Decision Diagram-Based Route Relaxations: An Application to Truck-Drone Routing

Abstract

For vehicle routing problems, strong dual bounds on the optimal value are needed to develop scalable exact algorithms as well as to evaluate the performance of heuristics. In this work, we propose an iterative algorithm to compute dual bounds motivated by connections between decision diagrams and dynamic programming models used for pricing in branch-and-cut-and-price algorithms. We apply techniques from the decision diagram literature to generate and strengthen novel route relaxations for obtaining dual bounds without using column generation. Our approach is generic and can be applied to various vehicle routing problems in which corresponding dynamic programming models are available. We apply our framework to the traveling salesman with drone problem and show that it produces dual bounds competitive to those from the state of the art. Applied to larger problem instances in which the state-of-the-art approach does not scale, our method outperforms other bounding techniques from the literature. Funding: This work was supported by the National Science Foundation [Grant 1918102] and the Office of Naval Research [Grants N00014-18-1-2129 and N00014-21-1-2240]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2021.0170 .