Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and … Read more
We present a new solution approach for the Time Dependent Traveling Salesman Prob- lem with Time Windows. This problem considers a salesman who departs from his home, has to visit a number of cities within a pre-determined period of time, and then returns home. The problem allows for travel times that can depend on the … Read more
The Traveling Salesman Problem with Pickup and Delivery (TSPPD) describes the problem of finding a minimum cost path in which pickups precede their associated deliveries. The TSPPD is particularly important in the growing field of Dynamic Pickup and Delivery Problems (DPDP). These include the many-to-many Dial-A-Ride Problems (DARP) of companies such as Uber and Lyft, … Read more
We study the traveling salesperson problem with forbidden neighborhoods (TSPFN) on regular three-dimensional grids. The TSPFN asks for a shortest tour over all grid points such that successive points along a tour have at least some given distance. We present optimal solutions and explicit construction schemes for the Euclidean TSP and the TSPFN where edges … Read more
Let a (generalized) chessboard in two or three dimensions be given. A closed knight’s tour is defined as a Hamiltonian cycle over all cells of the chessboard where all moves are knight’s moves, i.,e. have length 5^0.5. It is well-characterized for which chessboard sizes it is not possible to construct a closed knight’s tour. On … Read more
We introduce the Traveling Salesman Problem with forbidden neighborhoods (TSPFN). This is an extension of the Euclidean TSP in the plane where direct connections between points that are too close are forbidden. The TSPFN is motivated by an application in laser beam melting. In the production of a workpiece in several layers using this method … Read more
The traveling salesman problem (TSP) asks for a shortest tour through all vertices of a graph with respect to the weights of the edges. The symmetric quadratic traveling salesman problem (SQTSP) associates a weight with every three vertices traversed in succession. If these weights correspond to the turning angles of the tour, we speak of … Read more
A variety of formulations for the Travelling Salesman Problem as Mixed Integer Program have been proposed. They contain either non-binary variables or the number of constraints and variables is large. We want to give a new formulation that consists solely of binary variables; the number of variables and the number of constraints are of order … Read more
The integration of Unmanned Aircraft Systems (UAS) into civil airspace is one of the most challenging problems for the automation of the Controlled Airspace, and the optimization of the UAS route is a key step for this process. In this paper, we optimize the planning phase of a UAS mission that consists of departing from … Read more
The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph G = (V, E) and nonnegative real edge distances d, the TSP asks for a shortest tour through all vertices with respect to the distances d. The method of choice for solving the TSP to optimality is … Read more