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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Vydáno v:IEEE transactions on computer-aided design of integrated circuits and systems Ročník 41; číslo 12; s. 5408 - 5420
Hlavní autoři: Sanyal, Sourav, Roy, Kaushik
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.12.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Artificial intelligence
Clustering
Combinatorial analysis
Combinatorial mathematics
combinatorial optimization
Convergence
Graph neural networks
Ising model
ising optimization
Machine learning
Neural networks
NP-hard problem
NP-hard problems
Optimization
Solvers
Tabu search
Traveling salesman problem
Traveling salesman problems
travelling salesman problem
ISSN:0278-0070, 1937-4151
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Shrnutí: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 <inline-formula> <tex-math notation="LaTeX">\sim 5k </tex-math></inline-formula> cities) from the TSPLib benchmark suite. We report <inline-formula> <tex-math notation="LaTeX">\sim 10.66\times </tex-math></inline-formula> speedup over Tabu Search for 8 problems. Furthermore, compared to two state-of-the-art clustering-based TSP solvers, Neuro-Ising achieves <inline-formula> <tex-math notation="LaTeX">\sim 38 \times </tex-math></inline-formula> faster convergence along with <inline-formula> <tex-math notation="LaTeX">\sim 8.9\% </tex-math></inline-formula> better quality of solution, on average.
Bibliografie:ObjectType-Article-1
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ISSN:0278-0070
1937-4151
DOI:10.1109/TCAD.2022.3164330