On an exact method for the constrained shortest path problem

Authors:
Leonardo Lozano;AndréS L. Medaglia
Affiliations:
Centro para la Optimización y Probabilidad Aplicada (COPA), Departamento de Ingeniería Industrial, Universidad de los Andes, Cr 1E No. 19A-10, ML711, Bogotá, Colombia;Centro para la Optimización y Probabilidad Aplicada (COPA), Departamento de Ingeniería Industrial, Universidad de los Andes, Cr 1E No. 19A-10, ML711, Bogotá, Colombia
Venue:
Computers and Operations Research
Year:
2013

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Abstract

The constrained shortest path (CSP) is a well known NP-Hard problem. Besides from its straightforward application as a network problem, the CSP is also used as a building block under column-generation solution methods for crew scheduling and crew rostering problems. We propose an exact solution method for the CSP capable of handling large-scale networks in a reasonable amount of time. We compared our approach with three different state-of-the-art algorithms for the CSP and found optimal solutions on networks with up to 40,000 nodes and 800,000 arcs. We extended the algorithm to effectively solve the auxiliary problems of a multi-activity shift scheduling problem and a bus rapid transit route design problem tackled with column generation. We obtained significant speedups against alternative column generation schemes that solve the auxiliary problem with state-of-the-art commercial (linear) optimizers. We also present a first parallel version of our algorithm that shows promising results.