We examine an extension of the Traveling Salesperson Problem (TSP), the so called TSP with Forbidden Neighborhoods (TSPFN). The TSPFN is asking for a shortest Hamiltonian cycle of a given graph, where vertices traversed successively have a distance larger than a given radius. This problem is motivated by an application in mechanical engineering, more precisely in laser beam melting. This paper discusses a heuristic for solving the TSPFN when there don't exist closed-form solutions and exact approaches fail. The underlying concept is based on Warnsdorff's Rule but allows arbitrary step sizes and produces a Hamiltonian cycle instead of a Hamiltonian path. We implemented the heuristic and conducted a computational study for various neighborhoods. In particular the heuristic is able to find high quality TSPFN tours on 2D and 3D grids, i.e., it produces optimum and near-optimum solutions and shows a very good scalability also for large instances.

## Citation

TR-AAUK-M-O-18-09-10, Alpen-Adria-UniversitĂ¤t Klagenfurt, Mathematics, Optimization Group, September 2018