8616 2022 eng article 0 -- -- -- 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. Optimization Methods and Software 10.1080/10556788.2022.2053972 yes 2022-02-24 publish urn:nbn:de:0297-zib-80489 Kai Hoppmann-Baum Kai Hoppmann-Baum Oleg Burdakov Gioni Mexi Carl Johan Casselgren Thorsten Koch Hoppmann, Kai Koch, Thorsten MODAL-GasLab MODAL-Gesamt Energy Network Optimization Mexi, Gioni Mathematical Algorithmic Intelligence Applied Algorithmic Intelligence Methods MODAL-EnergyLab Applied Optimization