Coordinating drones with mothership vehicles: The mothership and drone routing problem with graphs

•Graphs arc routing problems with one drone and one mothership.•First mathematical formalization of the problem via MINLP formulations.•Matheuristic algorithm to deal with large instances.•Extensive experimental analysis on instances involving planar graphs. This paper addresses the optimization of...

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Veröffentlicht in:Computers & operations research Jg. 136; S. 105445
Hauptverfasser: Amorosi, Lavinia, Puerto, Justo, Valverde, Carlos
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Elsevier Ltd 01.12.2021
Pergamon Press Inc
Schlagworte:
Algorithms
Arc routing problems
Computing time
Conic programming
Drone vehicles
Drones
Euclidean geometry
Graphs
Mixed integer
Networks
Operations research
Optimization
Route planning
Networks
Arc routing problems
Conic programming
Drones
ISSN:0305-0548, 0305-0548
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Zusammenfassung:•Graphs arc routing problems with one drone and one mothership.•First mathematical formalization of the problem via MINLP formulations.•Matheuristic algorithm to deal with large instances.•Extensive experimental analysis on instances involving planar graphs. This paper addresses the optimization of routing problems with drones. It analyzes the coordination of one mothership with one drone to obtain optimal routes that have to visit some target objects modeled as general graphs. The goal is to minimize the overall weighted distance traveled by both vehicles while satisfying the requirements in terms of percentages of visits to targets. We discuss different approaches depending on the assumption made on the route followed by the mothership: i) the mothership can move on a continuous framework (the Euclidean plane), ii) on a connected piecewise linear polygonal chain or iii) on a general graph. In all cases, we develop exact formulations resorting to mixed integer second order cone programs that are compared on a testbed of instances to assess their performance. The high complexity of the exact methods makes it difficult to find optimal solutions in short computing time. For that reason, besides the exact formulations we also provide a tailored matheuristic algorithm that allows one to obtain high quality solutions in reasonable time. Computational experiments show the usefulness of our methods in different scenarios.
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ISSN:0305-0548
0305-0548
DOI:10.1016/j.cor.2021.105445