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.
Journal reference
Proceedings - 2026 IEEE International Conference on Smart Computing Workshops and Other Affiliated Events, SMARTCOMP Companion 2026
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.
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.
We present novel path-slicing strategies integrated with quantum local search to optimize solutions for the Traveling Salesman Problem (TSP), addressing the limitations of current Noisy Intermediate-Scale Quantum (NISQ) technologies. Our hybrid quantum-classical approach leverages classical path initialization and quantum optimization to effectively manage the computational challenges posed by the TSP. We explore various path slicing methods, including k-means and anti-k-means clustering, to divide the TSP into manageable subproblems. These are then solved using quantum or classical solvers. Our analysis, performed on multiple TSP instances from the TSPlib, demonstrates the ability of our strategies to achieve near-optimal solutions efficiently, highlighting significant improvements in solving efficiency and resource utilization. This approach paves the way for future applications in larger combinatorial optimization scenarios, advancing the field of quantum optimization.
This paper studies quantum optimization baselines for the Generalized Traveling Salesman Problem (GTSP), a clustered routing problem that naturally models variant selection and sequencing problems under discrete alternatives. We propose a novel GTSP QUBO formulation focused on maintaining feasible solutions for quantum annealing, as well as a hardware-executable gate-based pipeline utilizing the Quantum Approximate Optimization Algorithm (QAOA). We implement a constrained QAOA variant using an XY-mixer, which preserves the stepwise Hamming weight in the ideal circuit model, while feasibility with respect to the full GTSP constraints is tracked explicitly during post-processing. We compare the two quantum optimization paradigms on problem instances from GTSPLIB, an established benchmark dataset, and validate against classical state-of-the-art solvers. To mitigate current quantum hardware size limitations, we further extend a preprocessing method to reduce the node count in instance clusters, constructing new NISQ-friendly instances from reduced subsets. Across all tested instances, quantum solvers often produce competitive solution quality when tested on smaller graphs, but exhibit higher runtimes and a sharp degradation in feasibility and scalability as instance size grows. Our evaluation highlights where quantum optimizers can already succeed and which algorithmic bottlenecks, like sampling rates, runtime issues, and other practical failure modes, remain as open problems.
The Steiner Traveling Salesman Problem (STSP) is a variant of the classical Traveling Salesman Problem. The STSP involves incorporating steiner nodes, which are extra nodes not originally part of the required visit set but that can be added to the route to enhance the overall solution and minimize the total travel cost. Given the NP-hard nature of the STSP, we propose a quantum approach to address it. Specifically, we employ quantum annealing using D-Wave's hardware to explore its potential for solving this problem. To enhance computational feasibility, we develop a preprocessing method that effectively reduces the network size. Our experimental results demonstrate that this reduction technique significantly decreases the problem complexity, making the Quadratic Unconstrained Binary Optimization formulation, the standard input for quantum annealers, better suited for existing quantum hardware. Furthermore, the results highlight the potential of quantum annealing as a promising and innovative approach for solving the STSP.
The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality solutions within reasonable timeframes. This study investigates the potential of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical method, to solve TSP under realistic constraints. We adopt a QUBO-based formulation of TSP that integrates real-world logistical constraints reflecting operational conditions, such as vehicle capacity, road accessibility, and time windows, while ensuring compatibility with the limitations of current quantum hardware. Our experiments are conducted in a simulated environment using high-performance computing (HPC) resources to assess QAOA's performance across different problem sizes and quantum circuit depths. In order to improve scalability, we propose clustering QAOA (Cl-QAOA), a hybrid approach combining classical machine learning with QAOA. This method decomposes large TSP instances into smaller sub-problems, making quantum optimization feasible even on devices with a limited number of qubits. The results offer a comprehensive evaluation of QAOA's strengths and limitations in solving constrained TSP scenarios. This study advances quantum optimization and lays groundwork for future large-scale applications.
This paper implements a new way of solving a problem called the traveling salesman problem (TSP) using quantum genetic algorithm (QGA). We compared how well this new approach works to the traditional method known as a classical genetic algorithm (CGA). The TSP is a well-established challenge in combinatorial optimization where the objective is to find the most efficient path to visit a series of cities, minimizing the total distance, and returning to the starting point. We chose the TSP to test the performance of both algorithms because of its computational complexity and importance in practical applications. We choose the dataset from the international standard library TSPLIB for our experiments. By designing and implementing both algorithms and conducting experiments on various sizes and types of TSP instances, we provide an in-depth analysis of the accuracy of the optimal solution, the number of iterations, the execution time, and the stability of the algorithms for both. The empirical findings indicate that the CGA outperforms the QGA in terms of finding superior solutions more quickly in most of the test instances, especially when the problem size is large. This suggests that although the principle of quantum computing provides a new way to solve complex combinatorial optimisation problems, the implementation of quantum phenomena and the setting of parameters such as the optimal angle for a quantum revolving gate is challenging and need further optimisation to achieve the desired results. Additionally, it is important to note that the QGA has not been tested on real quantum hardware, so its true performance remains unverified. These limitations provide rich opportunities for further research in the future.