Neuro-Ising: Accelerating Large-Scale Traveling Salesman Problems via Graph Neural Network Guided Localized Ising Solvers
One of the most extensively studied combinatorial optimization problems is the Travelling Salesman Problem (TSP). Considerable research efforts in the past have resulted in exact solvers. However, the runtime of such hand-crafted solutions increases exponentially with problem size. Ising model based...
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Veröffentlicht in: | IEEE transactions on computer-aided design of integrated circuits and systems 2022-12, Vol.41 (12), p.5408-5420 |
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Zusammenfassung: | One of the most extensively studied combinatorial optimization problems is the Travelling Salesman Problem (TSP). Considerable research efforts in the past have resulted in exact solvers. However, the runtime of such hand-crafted solutions increases exponentially with problem size. Ising model based solvers have also gained prominence due to their abilities to find fast and approximate solutions for combinatorial optimization problems. However, such Ising based heuristics also suffer from scalability as the solution quality becomes increasingly sub-optimal with increase in problem size. In this work, we propose Neuro-Ising - a machine learning framework which uses Ising models to find clusters of near-optimal partial solutions of large scale TSPs and combines those solutions by employing a supervised data driven mechanism, which we model as a Graph Neural Network (GNN). The GNN is trained from solution instances obtained through exact solvers and hence, the proposed approach generalizes to unseen problems while avoiding the run-time complexity otherwise required, if the solution is built from scratch. Using standard computing resources, our proposed framework rapidly converges to near-optimal solutions for 15 TSPs (upto \sim 5k cities) from the TSPLib benchmark suite. We report \sim 10.66\times speedup over Tabu Search for 8 problems. Furthermore, compared to two state-of-the-art clustering-based TSP solvers, Neuro-Ising achieves \sim 38 \times faster convergence along with \sim 8.9\% better quality of solution, on average. |
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ISSN: | 0278-0070 1937-4151 |
DOI: | 10.1109/TCAD.2022.3164330 |