Many transit agencies operating paratransit and microtransit ser-vices have to respond to trip requests that arrive in real-time, which entails solving hard combinatorial and sequential decision-making problems under uncertainty. To avoid decisions that lead to signifi-cant inefficiency in the long term, vehicles should be allocated to requests by optimizing a non-myopic utility function or by batching requests together and optimizing a myopic utility function. While the former approach is typically offline, the latter can be performed online. We point out two major issues with such approaches when applied to paratransit services in practice. First, it is difficult to batch paratransit requests together as they are temporally sparse. Second, the environment in which transit agencies operate changes dynamically (e.g., traffic conditions can change over time), causing the estimates that are learned offline to become stale. To address these challenges, we propose a fully online approach to solve the dynamic vehicle routing problem (DVRP) with time windows and stochastic trip requests that is robust to changing environmental dynamics by construction. We focus on scenarios where requests are relatively sparse-our problem is motivated by applications to paratransit services. We formulate DVRP as a Markov decision process and use Monte Carlo tree search to evaluate actions for any given state. Accounting for stochastic requests while optimizing a non-myopic utility function is computationally challenging; indeed, the action space for such a problem is intractably large in practice. To tackle the large action space, we leverage the structure of the problem to design heuristics that can sample promising actions for the tree search. Our experiments using real-world data from our partner agency show that the proposed approach outperforms existing state-of-the-art approaches both in terms of performance and robustness.
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This content will become publicly available on December 20, 2024
Dual Bounds from Decision Diagram-Based Route Relaxations: An Application to Truck-Drone Routing
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 .
more » « less- Award ID(s):
- 1918102
- NSF-PAR ID:
- 10484633
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- Transportation Science
- ISSN:
- 0041-1655
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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