Abstract
The multiple traveling salespersons problem with moving targets is a generalization of the classical traveling salespersons problem, where the targets (nodes or objects) are moving over time. Additionally, for each target a visibility time window is given. The task is to find routes for several salespersons so that each target is reached exactly once within its visibility time window and the sum of all traveled distances of all salespersons is minimal. We present different modeling formulations for this TSP variant. The time requirements are modeled differently in each approach. Our goal is to examine what formulation is most suitable in terms of runtime to solve the multiple traveling salespersons problem with moving targets with exact methods. Computational experiments are carried out on randomly generated test instances to compare the different modeling approaches. The results for large-scale instances show, that the best way to model time requirements is to directly insert them into a formulation with discrete time steps.
Highlights
This research deals with a dynamic variant of the traveling salesperson problem (TSP), where the targets or nodes are not fixed
We addressed the multiple traveling salespersons problem with moving targets (MTSPMT), a dynamic variant of the TSP, where multiple salespersons are searching for their tours in a system with continuously moving targets
We presented four different model formulations, which can be separated by discrete and continuous time handling on one hand and on the other hand by the solution approach
Summary
This research deals with a dynamic variant of the traveling salesperson problem (TSP), where the targets or nodes are not fixed. If we restrict the number of salesman to one, fix the position of each target to a certain point in space and extend all visibility windows to the whole considered time horizon, we obtain the classical TSP, which is NP-hard, see Garey and Johnson (1979). Helvig et al (1998) addressed the Moving-Target TSP, which is the MTSPMT restricted to one salesperson. In the MTSPMT, there is no capacity restriction imposed and due to the moving targets, we have changing traveling times and distances between any pair of targets. 5. Computational experiments are carried out using randomly generated and feasible problem instances with a varying number of targets, salespersons, and time steps.
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