TY - GEN A1 - Hoppmann-Baum, Kai A1 - Mexi, Gioni A1 - Burdakov, Oleg A1 - Casselgren, Carl Johan A1 - Koch, Thorsten T1 - Length-Constrained Cycle Partition with an Application to UAV Routing N2 - In this article, we discuss the Length-Constrained Cycle Partition Problem (LCCP). Besides edge weights, the undirected graph in LCCP features an individual critical weight value for each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is a feasible solution if the length of each cycle is not greater than the critical weight of each of the vertices in the cycle. The goal is to find a feasible partition with the minimum number of cycles. In this article, we discuss theoretical properties, preprocessing techniques, and two mixed-integer programming models (MIP) for LCCP both inspired by formulations for the closely related Travelling Salesperson Problem (TSP). Further, we introduce conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a report on computational experiments conducted on (A)TSPLIB-based instances. As an example, we use a routing problem in which a fleet of uncrewed aerial vehicles (UAVs) patrols a set of areas. T3 - ZIB-Report - 20-30 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-80489 SN - 1438-0064 ER - TY - CHAP A1 - Hoppmann-Baum, Kai A1 - Mexi, Gioni A1 - Burdakov, Oleg A1 - Casselgren, Carl Johan A1 - Koch, Thorsten ED - Hebrard, Emmanuel ED - Musliu, Nysret T1 - Minimum Cycle Partition with Length Requirements T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research N2 - 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. Y1 - 2020 SN - 978-3-030-58941-7 U6 - https://doi.org/10.1007/978-3-030-58942-4_18 VL - 12296 SP - 273 EP - 282 PB - Springer International Publishing CY - Cham ER - TY - THES A1 - Mexi, Gioni T1 - Node Partitioning and Subtours Creation Problem (NPSC) Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77094 ER -