@incollection{HoppmannBaumMexiBurdakovetal., author = {Hoppmann-Baum, Kai and Mexi, Gioni and Burdakov, Oleg and Casselgren, Carl Johan and Koch, Thorsten}, title = {Minimum Cycle Partition with Length Requirements}, series = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research}, volume = {12296}, booktitle = {Integration of Constraint Programming, Artificial Intelligence, and Operations Research}, editor = {Hebrard, Emmanuel and Musliu, Nysret}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-58941-7}, doi = {10.1007/978-3-030-58942-4_18}, pages = {273 -- 282}, abstract = {In this article we introduce a Minimum Cycle Partition Problem with Length Requirements (CPLR). This generalization of the Travelling Salesman Problem (TSP) originates from routing Unmanned Aerial Vehicles (UAVs). Apart from nonnegative edge weights, CPLR has an individual critical weight value associated with each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is regarded as a feasible solution if the length of each cycle, which is the sum of the weights of its edges, is not greater than the critical weight of each of its vertices. The goal is to find a feasible partition, which minimizes the number of cycles. In this article, a heuristic algorithm is presented together with a Mixed Integer Programming (MIP) formulation of CPLR. We furthermore introduce a conflict graph, whose cliques yield valid constraints for the MIP model. Finally, we report on computational experiments conducted on TSPLIB-based test instances.}, language = {en} } @article{HoppmannBaumBurdakovMexietal., author = {Hoppmann-Baum, Kai and Burdakov, Oleg and Mexi, Gioni and Casselgren, Carl Johan and Koch, Thorsten}, title = {Length-Constrained Cycle Partition with an Application to UAV Routing}, series = {Optimization Methods and Software}, journal = {Optimization Methods and Software}, doi = {10.1080/10556788.2022.2053972}, 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.}, language = {en} }