Traveling Salesman Problem with a preprocessing method for classical and quantum optimization

TL;DR

This paper presents a preprocessing method for the Traveling Salesman Problem that reduces problem size and improves computational efficiency when using classical and quantum optimization methods.

Contribution

A novel preprocessing strategy that decreases the number of decision variables, enhancing scalability for classical and quantum TSP solvers.

Findings

Significant reduction in decision variables on benchmark instances.

Improved computational times for classical and quantum solvers.

Enhanced scalability of TSP formulations.

Abstract

The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search space and the large number of constraints required to eliminate subtours. This paper introduces a preprocessing strategy that significantly reduces the size of the optimization model by restricting the set of candidate arcs and retaining only the lowest-cost neighbors for each vertex. Computational experiments on TSPLIB benchmark instances demonstrate that the proposed approach substantially reduces the number of decision variables. The method is evaluated using both classical and quantum optimization techniques, showing improvements in computational time and reductions in optimality gaps. Overall, the results indicate that the proposed preprocessing enhances the scalability of the formulations and makes them more suitable for both classical solvers and emerging quantum optimization frameworks.