Length-Constrained Cycle Partition with an Application to UAV Routing
- This article discusses the Length-Constrained Cycle Partition Problem (LCCP), which constitutes a new generalization of the Travelling Salesperson Problem (TSP). Apart from nonnegative edge weights, the undirected graph in LCCP features a nonnegative critical length parameter for each vertex. A cycle partition, i.e., a vertex-disjoint cycle cover, is a feasible solution for LCCP if the length of each cycle is not greater than the critical length of each vertex contained in it. The goal is to find a feasible partition having a minimum number of cycles. Besides analyzing theoretical properties and developing preprocessing techniques, we propose an elaborate heuristic algorithm that produces solutions of good quality even for large-size instances. Moreover, we present two exact mixed-integer programming formulations (MIPs) for LCCP, which are inspired by well-known modeling approaches for TSP. Further, we introduce the concept of conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a discussion on computational experiments that we conducted using (A)TSPLIB-based problem instances. As a motivating example application, we describe a routing problem where a fleet of uncrewed aerial vehicles (UAVs) must patrol a given set of areas.
Author: | Kai Hoppmann-BaumORCiD, Oleg BurdakovORCiD, Gioni MexiORCiD, Carl Johan CasselgrenORCiD, Thorsten KochORCiD |
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Document Type: | Article |
Parent Title (English): | Optimization Methods and Software |
Year of first publication: | 2022 |
Preprint: | urn:nbn:de:0297-zib-80489 |
DOI: | https://doi.org/10.1080/10556788.2022.2053972 |