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

2026-03-24

AI Summary

This work addresses the computational challenges of the Traveling Salesman Problem (TSP), which suffers from an exponentially growing search space and a large number of subtour elimination constraints, particularly hindering its integration into quantum optimization frameworks due to excessive model size. To mitigate this, the authors propose a lightweight graph pruning preprocessing strategy that retains only a small set of lowest-cost adjacent edges for each vertex, drastically reducing the candidate arc set and the number of decision variables. This approach is the first to be systematically applied in a hybrid classical–quantum optimization context. Evaluated on TSPLIB benchmark instances, it significantly shrinks problem scale, accelerates solution times, narrows optimality gaps, and thereby enhances both scalability and solution efficiency of TSP formulations on classical and quantum platforms, improving their compatibility with emerging quantum optimization architectures.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Traveling Salesman Problem
• combinatorial optimization
• subtour elimination
• computational complexity
• optimization scalability

Innovation

• preprocessing
• Traveling Salesman Problem
• quantum optimization
• model reduction
• neighborhood pruning