Length-constrained cycle partition with an application to UAV routing*. (2nd November 2022)

• Record Type: Journal Article
• Authors: Hoppmann-Baum, Kai; Burdakov, Oleg; Mexi, Gioni; Casselgren, Carl Johan; Koch, Thorsten
• Is Part Of: Optimization methods and software. Volume 37:Number 6(2022)
• Page Start: 2080
• Page End: 2116
• Publication Date: 2022-11-02
• Subjects: Combinatorial optimization -- mixed-integer programming -- uncrewed aerial vehicles -- travelling salesperson problem; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2022.2053972
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : 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.