Integer programming formulations for the elementary shortest path problem

Leonardo Taccari

European Journal of Operational Research, 2016, vol. 252, issue 1, 122-130

Abstract: Given a directed graph G=(V,A) with arbitrary arc costs, the Elementary Shortest Path Problem (ESPP) consists of finding a minimum-cost path between two nodes s and t such that each node of G is visited at most once. If negative costs are allowed, the problem is NP-hard. In this paper, several integer programming formulations for the ESPP are compared. We present analytical results based on a polyhedral study of the formulations, and computational experiments where we compare their linear programming relaxation bounds and their behavior within a branch-and-cut framework. The computational results show that a formulation with dynamically generated cutset inequalities is the most effective.

Keywords: Integer programming; Elementary shortest path; Branch-and-cut; Extended formulations; Subtour elimination constraints (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:252:y:2016:i:1:p:122-130

DOI: 10.1016/j.ejor.2016.01.003

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