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Close-enough general routing problem for multiple unmanned aerial vehicles in monitoring missions

Huan Liu, Michel Gendreau, Binjie Xu, Guohua Wu, Yi Gu

TL;DR

This work tackles coordinating multiple homogeneous UAVs to monitor nodes with disk neighborhoods and edges (CEMUAVGRP) by a nested, two-phase formulation: an outer phase selects representative points within disk neighborhoods and an inner phase solves a generalized routing problem on a graph to minimize total distance under UAV range constraints. The solution framework, AILS-VND-SOCP, alternates between a general routing phase using RI and VND and a close-enough routing phase using SOCP to refine representative points, within an adaptive iterated local search. Computational results on 150 benchmark instances show gaps no larger than 2.5% relative to best-known solutions, with disk neighborhoods significantly reducing flight distance and sometimes the number of UAVs, while maintaining favorable runtimes. These findings demonstrate practical gains for sensor-aware UAV monitoring and provide a scalable approach to integrate close-enough sensing with edge/node routing in multi-UAV missions.

Abstract

In this paper, we introduce a close-enough multi-UAV general routing problem (CEMUAVGRP) where a fleet of homogeneous UAVs conduct monitoring tasks containing nodes, each of which has its disk neighborhood, and edges, aiming to minimize the total distance. A two-phase iterative method is proposed, partitioning the CEMUAVGRP into a general routing phase where a satisfactory route including required nodes and edges for each UAV is obtained without considering the disk neighborhoods of required nodes, and a close-enough routing phase where representative points are optimized for each required node in the determined route. To be specific, a variable neighborhood descent (VND) heuristic is proposed for the general routing phase, while a second-order cone programming (SOCP) procedure is applied in the close-enough routing phase. These two phases are performed in an iterative fashion under the framework of an adaptive iterated local search (AILS) algorithm until the predefined termination criteria are satisfied. Extensive experiments and comparative studies are conducted, demonstrating the efficiency of the proposed AILS-VND-SOCP algorithm and the superiority of disk neighborhoods.

Close-enough general routing problem for multiple unmanned aerial vehicles in monitoring missions

TL;DR

This work tackles coordinating multiple homogeneous UAVs to monitor nodes with disk neighborhoods and edges (CEMUAVGRP) by a nested, two-phase formulation: an outer phase selects representative points within disk neighborhoods and an inner phase solves a generalized routing problem on a graph to minimize total distance under UAV range constraints. The solution framework, AILS-VND-SOCP, alternates between a general routing phase using RI and VND and a close-enough routing phase using SOCP to refine representative points, within an adaptive iterated local search. Computational results on 150 benchmark instances show gaps no larger than 2.5% relative to best-known solutions, with disk neighborhoods significantly reducing flight distance and sometimes the number of UAVs, while maintaining favorable runtimes. These findings demonstrate practical gains for sensor-aware UAV monitoring and provide a scalable approach to integrate close-enough sensing with edge/node routing in multi-UAV missions.

Abstract

In this paper, we introduce a close-enough multi-UAV general routing problem (CEMUAVGRP) where a fleet of homogeneous UAVs conduct monitoring tasks containing nodes, each of which has its disk neighborhood, and edges, aiming to minimize the total distance. A two-phase iterative method is proposed, partitioning the CEMUAVGRP into a general routing phase where a satisfactory route including required nodes and edges for each UAV is obtained without considering the disk neighborhoods of required nodes, and a close-enough routing phase where representative points are optimized for each required node in the determined route. To be specific, a variable neighborhood descent (VND) heuristic is proposed for the general routing phase, while a second-order cone programming (SOCP) procedure is applied in the close-enough routing phase. These two phases are performed in an iterative fashion under the framework of an adaptive iterated local search (AILS) algorithm until the predefined termination criteria are satisfied. Extensive experiments and comparative studies are conducted, demonstrating the efficiency of the proposed AILS-VND-SOCP algorithm and the superiority of disk neighborhoods.
Paper Structure (21 sections, 28 equations, 10 figures, 2 tables, 4 algorithms)

This paper contains 21 sections, 28 equations, 10 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Literature review
  3. Problem statement
  4. CEMUAVGRP
  5. Formulation
  6. Solution methodology
  7. Initial solution construction
  8. Local search
  9. Perturbation
  10. Acceptance criterion
  11. Representative point selection
  12. Computational results
  13. Comparison with best-known solutions
  14. Benchmark instances
  15. Parameter setting
  16. ...and 6 more sections

Figures (10)

  • Figure 1: CEMUAVGRP
  • Figure 2: The two-phase iterative optimization framework
  • Figure 3: The gap between the results obtained by the AILS-VND-SOCPI and the best-known solutions
  • Figure 4: The runtime of the AILS-VND-SOCPI
  • Figure 5: The saving rate of flight distance relative to the case without disk neighborhoods
  • ...and 5 more figures