On Solving the Shortest Paths with Exclusive-Disjunction Arc Pairs Conflicts

Roberto Montemanni; Derek H. Smith

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arXiv · 2506.03326

On Solving the Shortest Paths with Exclusive-Disjunction Arc Pairs Conflicts

Roberto Montemanni·Derek H. Smith

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Abstract

A variant of the well-known Shortest Path Problem is studied in this paper, where pairs of conflicting arcs are provided, and for each conflicting pair a penalty is paid once neither or both of the arcs are selected. This configures a set of soft-constraints. The problem, which can be used to model real applications, looks for a path from a given origin to a given destination that minimizes the cost of the arcs traversed plus the penalties incurred. In this paper, we consider a compact mixed integer linear program representing the problem and we solve it with the open-source solver CP-SAT, part of the Google OR-Tools computational suite. An experimental campaign on the instances available from the literature indicates that the approach we propose achieves results comparable with those of state-of-the-art solvers, notwithstanding it is a compact model, while the other approaches require the generation of dynamic constraints in order for the models to be competitive. Some best-known results have been improved in this study, and some instances have been closed for the first time.

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BibTeX RIS

Roberto Montemanni, Derek H. Smith. 2025-06-03. On Solving the Shortest Paths with Exclusive-Disjunction Arc Pairs Conflicts. https://arxiv.org/abs/2506.03326

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