[Paper Review] Coordinating drones with mothership vehicles: The mothership and multiple drones routing problem with Graphs

Lavinia Amorosi, Justo Puerto+1 more|arXiv (Cornell University)|Sep 3, 2021

Vehicle Routing Optimization Methods4 citations

TL;DR

This paper proposes a novel coordination model for a mothership vehicle and multiple drones to minimize the mothership's total travel distance while ensuring all target graphs are fully inspected. It introduces exact mixed-integer second-order cone programming formulations and a matheuristic algorithm, demonstrating effectiveness on small-to-medium instances and a real-world case study in Cordoba during COVID-19 restrictions, achieving a 11.27 km mothership tour with 83% optimality gap within 2 hours.

ABSTRACT

This paper considers the optimization problems that arise to coordinate a tandem between a mothership vehicle and a fleet of drones. %more than one drone. Each drone can be launched from the mothership to perform an operation. After completing the operations the drones return to the mothership to recharge batteries and to be ready for a new operation. Operations consist on (partially) visiting graphs with given lengths to deliver some service or to perform some surveillance/inspection activity. The goal is to minimize the overall weighted distance traveled by the mothership while satisfying some requirements in terms of percentages of visits to the target graphs. 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. We also develop a matheuristic algorithm that provides reasonable solutions. Computational experiments show the usefulness of our methods in different scenarios.

Motivation & Objective

• To address the gap in literature on multi-drone coordination with motherships for graph-visit operations rather than point-to-point delivery.
• To model the mothership and fleet of drones as a synchronized system where all drones are launched and retrieved in the same mission stage.
• To minimize the total distance traveled by the mothership while ensuring full coverage of specified target graphs.
• To develop exact formulations and a matheuristic for solving large-scale instances efficiently.
• To validate the approach through computational experiments and a real-world case study in Cordoba, Spain, during pandemic-related restrictions.

Proposed method

• Formulates the problem as a mixed-integer nonlinear program using second-order cone constraints to model drone and mothership trajectories.
• Develops exact formulations for both synchronized and non-synchronized versions of the mothership and multiple drones routing problem.
• Incorporates valid inequalities to strengthen the formulations and improve solution convergence.
• Proposes a matheuristic algorithm that combines exact optimization with heuristic initialization to generate high-quality feasible solutions quickly.
• Uses a decomposition-based approach where the mothership's route is optimized in coordination with drone missions, ensuring rendezvous points are properly scheduled.
• Employs a graph-based representation of target operations, modeling inspections as full traversals of line segments or polygonal chains.

Experimental results

Research questions

• RQ1 How can a mothership efficiently coordinate multiple drones to minimize its own travel distance while ensuring full inspection of target graphs?
• RQ2 What exact mathematical formulations can model the synchronized routing of a mothership and multiple drones for graph-visit operations?
• RQ3 How effective are valid inequalities in improving the solution quality and convergence speed of the proposed formulations?
• RQ4 Can a matheuristic algorithm provide high-quality feasible solutions for large-scale instances within practical computation time?
• RQ5 How does the proposed model perform in real-world scenarios involving complex urban or historical networks under operational constraints?

Key findings

• The proposed exact formulations are effective for small-to-medium instances but become computationally challenging as problem size increases.
• The matheuristic algorithm produces feasible solutions with a gap of 83% from the optimal solution within a 2-hour time limit, demonstrating practical utility.
• In the Cordoba case study, the mothership traveled a total of 11.27 km to coordinate three drones over six target graphs, achieving full inspection coverage.
• The synchronized model ensures all drones are launched and retrieved in the same mission stage, simplifying coordination and reducing operational complexity.
• Computational experiments show that the problem is highly challenging even for small instances, justifying the need for heuristic approaches.
• The integration of graph-based operations (e.g., full path inspection) extends prior work focused on point visits, enabling new applications in surveillance and infrastructure inspection.