An outer approximation algorithm for the robust shortest path problem

• Published in: Transportation research. Part E, Logistics and transportation review Vol. 58; pp. 52 - 66
• Main Authors: Shahabi, Mehrdad, Unnikrishnan, Avinash, Boyles, Stephen D.
• Format: Journal Article
• Language: English
• Published: Exeter Elsevier India Pvt Ltd 01.11.2013; Elsevier Sequoia S.A
• Subjects: Algorithms; Approximation; Costs; Integer programming; Mathematical problems; Mean – standard deviation objective; Outer approximation; Robust shortest path; Shortest path algorithms; Stochastic models; Studies; Mean – standard deviation objective; Robust shortest path; Outer approximation
• ISSN: 1366-5545; 1878-5794
• DOI: 10.1016/j.tre.2013.07.002

•We model the weighted mean standard deviation robust shortest path problem.•A conic integer programming formulation is provided.•Problem is solved using the outer approximation algorithm.•The algorithm delivers the optimal solution for four real world transportation networks.•The algorithm outperforms standard GAMS/CPLEX conic quadratic programming solver. This paper describes a new algorithm for the stochastic shortest path problem where path costs are a weighted sum of expected cost and cost standard deviation. We allow correlation between link costs, subject to a regularity condition excluding unbounded solutions. The chief complication in this variant is that path costs are not an additive sum of link costs. In this paper, we reformulate this problem as a conic quadratic program, and develop an outer-approximation algorithm based on this formulation. Numerical experiments show that the outer-approximation algorithm significantly outperforms standard integer programming algorithms implemented in solvers.