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The aircraft routing problem with refueling

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Abstract

In this paper, we present, test, and compare two novel methods to solve the aircraft routing problem with aerial refueling with a multicriteria objective function. We present a mixed-integer linear program (MILP) that utilizes a combination of a network transformation and a formulation that creatively decouples refueling decisions from the nodes within the network. We also present a dynamic program (DP) that, when coupled with an alternative network transformation to account for the multiple criteria within the objective function, applies a node-labeling approach based on a modification of Dijkstra’s algorithm. We test and compare these alternative solution methods on a set of 264 synthetically-generated instances representing 66 combinations of network size and the frequency of aerial refueling point availability. Invoking CPLEX using the C++ callable library to solve the MILP and applying the DP in C++, we found that the application of the DP yields a 98.97 % reduction in the required computational effort, on average, relative to the MILP; the MILP fails to find an optimal solution within a 3,600-s time limit for selected instances of networks having at least 80 nodes and for all instances of networks having at least 350 nodes. In contrast, the DP is more robust than the MILP, as it only requires longer than 3,600 s to solve selected instances of networks having more than 3,000 nodes.

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Notes

  1. We use the attained optimality gap rather than the relative optimality gap reported directly by CPLEX, as the commercial solver computes its reported gap by dividing the the absolute optimality gap by the magnitude of the best integer-feasible objective function value [16] (i.e., the lowest feasible upper bound).

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Acknowledgments

The authors thank the Editor and two anonymous referees for their constructive comments and suggestions that have greatly helped improve the substance and presentation of this paper.

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Authors and Affiliations

  1. Department of Operational Sciences (ENS), Air Force Institute of Technology (AFIT), Bldg. 641, 2950 Hobson Way, Wright Patterson AFB, OH, 45433, USA

    Tanya E. Kannon, Sarah G. Nurre, Brian J. Lunday & Raymond R. Hill

  2. Department of Strategic Plans and Programs, Headquarters, United States Air Force, The Pentagon, Washington, DC, 20330, USA

    Tanya E. Kannon

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  1. Tanya E. Kannon
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  2. Sarah G. Nurre
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  3. Brian J. Lunday
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  4. Raymond R. Hill
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Correspondence to Brian J. Lunday.

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Kannon, T.E., Nurre, S.G., Lunday, B.J. et al. The aircraft routing problem with refueling. Optim Lett 9, 1609–1624 (2015). https://doi.org/10.1007/s11590-015-0849-8

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  • DOI: https://doi.org/10.1007/s11590-015-0849-8

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