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Title: A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption

Abstract

The past decade has seen a substantial increase in the use of small unmanned aerial vehicles (UAVs) in both civil and military applications. This article addresses an important aspect of refueling in the context of routing multiple small UAVs to complete a surveillance or data collection mission. Specifically, this article formulates a multiple-UAV routing problem with the refueling constraint of minimizing the overall fuel consumption for all the vehicles as a two-stage stochastic optimization problem with uncertainty associated with the fuel consumption of each vehicle. The two-stage model allows for the application of sample average approximation (SAA). Although the SAA solution asymptotically converges to the optimal solution for the two-stage model, the SAA run time can be prohibitive for medium- and large-scale test instances. Hence, we develop a tabu search-based heuristic that exploits the model structure while considering the uncertainty in fuel consumption. Extensive computational experiments corroborate the benefits of the two-stage model compared to a deterministic model and the effectiveness of the heuristic for obtaining high-quality solutions.

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. Wayne State Univ., Detroit, MI (United States). Dept. of Industrial and Systems Engineering
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Texas A & M Univ., College Station, TX (United States). Dept. of Mechanical Engineering
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE; LANL Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1483552
Report Number(s):
LA-UR-18-29794
Journal ID: ISSN 1424-8220
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Sensors
Additional Journal Information:
Journal Volume: 18; Journal Issue: 11; Journal ID: ISSN 1424-8220
Publisher:
MDPI AG
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; vehicle routing; unmanned aerial vehicles; fuel constraints; two-stage stochastic optimization; sample average approximation; tabu search

Citation Formats

Venkatachalam, Saravanan, Sundar, Kaarthik, and Rathinam, Sivakumar. A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption. United States: N. p., 2018. Web. doi:10.3390/s18113756.
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Venkatachalam, Saravanan, Sundar, Kaarthik, & Rathinam, Sivakumar. A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption. United States. https://doi.org/10.3390/s18113756
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Venkatachalam, Saravanan, Sundar, Kaarthik, and Rathinam, Sivakumar. Sat . "A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption". United States. https://doi.org/10.3390/s18113756. https://www.osti.gov/servlets/purl/1483552.
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@article{osti_1483552,
title = {A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption},
author = {Venkatachalam, Saravanan and Sundar, Kaarthik and Rathinam, Sivakumar},
abstractNote = {The past decade has seen a substantial increase in the use of small unmanned aerial vehicles (UAVs) in both civil and military applications. This article addresses an important aspect of refueling in the context of routing multiple small UAVs to complete a surveillance or data collection mission. Specifically, this article formulates a multiple-UAV routing problem with the refueling constraint of minimizing the overall fuel consumption for all the vehicles as a two-stage stochastic optimization problem with uncertainty associated with the fuel consumption of each vehicle. The two-stage model allows for the application of sample average approximation (SAA). Although the SAA solution asymptotically converges to the optimal solution for the two-stage model, the SAA run time can be prohibitive for medium- and large-scale test instances. Hence, we develop a tabu search-based heuristic that exploits the model structure while considering the uncertainty in fuel consumption. Extensive computational experiments corroborate the benefits of the two-stage model compared to a deterministic model and the effectiveness of the heuristic for obtaining high-quality solutions.},
doi = {10.3390/s18113756},
journal = {Sensors},
number = 11,
volume = 18,
place = {United States},
year = {Sat Nov 03 00:00:00 EDT 2018},
month = {Sat Nov 03 00:00:00 EDT 2018}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.3390/s18113756
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Cited by: 12 works
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Figures / Tables:

Figure 1 Figure 1: Illustration of a feasible first-stage solution and recourse action for a particular realization of the uncertainty. (a) A feasible first-stage solution to the two-stage FCMURP with two UAVs; the first-stage routes for the UAVs correspond to the ‘here-and-now’ decisions. (b) A feasible recourse action for the two-stage FCMURPmore » with two UAVs; for a given realization of the fuel consumed by any vehicle to traverse an edge, the refuel trips (colored in brown) are added to the first-stage solution.« less
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    Works referencing / citing this record:

    A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles
    journal, August 2019

    Heuristics for Two Depot Heterogeneous Unmanned Vehicle Path Planning to Minimize Maximum Travel Cost
    journal, May 2019

    Heuristics for Two Depot Heterogeneous Unmanned Vehicle Path Planning to Minimize Maximum Travel Cost
    journal, May 2019

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      Table 3 (p. 15)table
      Table 4 (p. 15)table
      Table 4: Cont'd (p. 16)table
      Table 5 (p. 16)table
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