The TSP with drones: The benefits of retraversing the arcs
Nicola Morandi, Roel Leus, Jannik Matuschke, Hande Yaman

TL;DR
This paper explores the Traveling Salesman Problem with Drones, highlighting the importance of arc retraversals in optimal solutions, and proves the computational difficulty of approximating this problem.
Contribution
It introduces arc-retraversing solutions into the TSP with drones, analyzes their necessity, and establishes the problem's inapproximability within a constant factor.
Findings
Optimal solutions may require arc retraversals.
Excluding arc-retraversing solutions can increase the optimal value.
The problem is NP-hard to approximate within a constant factor.
Abstract
In the Traveling Salesman Problem with Drones (TSP-mD), a truck and multiple drones cooperate to serve customers in the minimum amount of time. The drones are launched and retrieved by the truck at customer locations, and each of their flights must not consume more energy than allowed by their batteries. Most problem settings in the literature restrict the feasible truck routes to cycles, i.e., closed paths, which never visit a node more than once. Revisiting a node, however, may lower the time required to serve all the customers. Additionally, we observe that optimal solutions for the TSP-mD may retraverse arcs, i.e., optimal truck routes may contain the same arcs multiple times. We refer to such solutions as arc-retraversing, and include them in our solution space by modeling the truck route as a closed walk. We describe Euclidean instances where all the optimal solutions are…
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Taxonomy
TopicsVehicle Routing Optimization Methods · Optimization and Search Problems · Transportation and Mobility Innovations
