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Two-stage stochastic programming model for routing multiple drones with fuel constraints

Saravanan Venkatachalam(saravanan.v***at***wayne.edu)
Kaarthik Sundar(kaarthik01sundar***at***gmail.com)
Sivakumar Rathinam(srathinam***at***tamu.edu)

Abstract: Uses of drones and unmanned vehicles (UAVs) in ground or aerial are increasing in both civil and military applications. This paper develops a two-stage stochastic optimization model with a recourse for a multiple drone-routing problem with fuel constraints under uncertainty for the travel between any pair of targets/refueling-sites/depot. We are given a set of n heterogeneous drones or UAVs, a set of targets, a set of refueling stations where any drone can refuel, and the objective is to minimize the overall fuel consumed or distance travelled by all the drones. To approximate the value function of the two-stage stochastic programming model, we use the sample average approximation method (SAA). Though the solution of SAA asymptotically converges to the optimal solution for a two-stage model, finding a lower bound for the original problem is computationally intensive. Therefore, we develop a heuristic to handle large scale instances. In the computational experiments, we have evaluated the robustness of solutions from a deterministic approach and the bounds obtained using the proposed methods.

Keywords: vehicle routing, drones, fuel-constraints, unmanned aerial vehicles, two-stage stochastic model, stochastic programming, conditional value-at-risk

Category 1: Stochastic Programming

Category 2: Combinatorial Optimization


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Entry Submitted: 11/13/2017
Entry Accepted: 11/14/2017
Entry Last Modified: 11/13/2017

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