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

TL;DR

This paper introduces a compact mixed integer linear programming approach to solve a variant of the Shortest Path Problem with conflicting arc pairs, demonstrating competitive performance and improvements over existing methods.

Contribution

The paper presents a novel compact MILP model for the conflicting arcs shortest path problem and shows its effectiveness using open-source solver CP-SAT.

Findings

Achieves results comparable to state-of-the-art solvers

Improves some best-known solutions

Closes some instances for the first time

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.