Cutting-plane methodology via quantum optimization for solving the Traveling Salesman Problem

TL;DR

This paper explores a novel framework combining classical and quantum optimization techniques, including quantum annealing, to efficiently solve the NP-hard Traveling Salesman Problem by reducing model complexity and improving computational performance.

Contribution

It introduces a dynamic subtour elimination approach integrated with quantum annealing methods, advancing the application of quantum computing in combinatorial optimization.

Findings

Significant reduction in model size using the proposed framework

Positive performance improvements with classical, quantum, and hybrid methods

Quantum annealing approaches show promising results for TSP solutions

Abstract

The Traveling Salesman Problem is a classical NP-hard combinatorial optimization problem that has been extensively studied in operations research. A major challenge in Traveling Salesman Problem formulations is the large number of subtour elimination constraints required to ensure a valid tour. To address this issue, we adopt an iterative approach grounded in well-established operations research techniques, in which subtour elimination constraints are generated dynamically. In addition, we integrate a preprocessing phase to reduce the number of candidate arcs. In this work, we investigate both classical and quantum optimization approaches for solving the problem using the proposed framework. In particular, for quantum optimization we analyze quantum annealing techniques within the D-Wave framework, considering both direct quantum execution on the QPU and hybrid quantum classical solvers. Computational experiments show that the proposed strategies significantly reduce the model size and lead to positive improvements in computational performance across classical, direct quantum, and hybrid optimization approaches.