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Distributionally robust maximum probability shortest path problem

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Abstract

In this study, we discuss and develop a distributionally robust joint chance-constrained optimization model and apply it for the shortest path problem under resource uncertainty. In sch a case, robust chance constraints are approximated by constraints that can be reformulated using convex programming. Since the issue we are discussing here is of the multi-resource type, the resource related to cost is deterministic; however, we consider a robust set for other resources where covariance and mean are known. Thus, the chance-constrained problem can be expressed in terms of a cone constraint. In addition, since our problem is joint chance-constrained optimization, we can use Bonferroni approximation to divide the problem into L separate problems in order to build convex approximations of distributionally robust joint chance constraints. Finally, numerical results are presented to illustrate the rigidity of the bounds and the value of the distributionally robust approach.

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Acknowledgements

The first author is supported by grants from the University of Tabriz. P.M. Pardalos has been supported by the Paul and Heidi Brown Preeminent Professorship (ISE, University of Florida, USA) and a Humboldt Research Foundation Award (Germany).

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Authors and Affiliations

  1. School of Mathematics, University of Tabriz, Tabriz, Iran

    Rashed Khanjani-Shiraz, Ali Babapour-Azar & Zohreh Hosseini-Noudeh

  2. Center for Applied Optimization, Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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  1. Rashed Khanjani-Shiraz
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  2. Ali Babapour-Azar
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  3. Zohreh Hosseini-Noudeh
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  4. Panos M. Pardalos
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Correspondence to Rashed Khanjani-Shiraz.

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Khanjani-Shiraz, R., Babapour-Azar, A., Hosseini-Noudeh, Z. et al. Distributionally robust maximum probability shortest path problem. J Comb Optim 43, 140–167 (2022). https://doi.org/10.1007/s10878-021-00747-9

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  • DOI: https://doi.org/10.1007/s10878-021-00747-9

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