ASP: Learn a Universal Neural Solver

Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approac...

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Published in:	IEEE transactions on pattern analysis and machine intelligence Vol. 46; no. 6; pp. 4102 - 4114
Main Authors:	Wang, Chenguang, Yu, Zhouliang, McAleer, Stephen, Yu, Tianshu, Yang, Yaodong
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.06.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Adaptation models Combinatorial analysis Combinatorial optimization problems curriculum learning generalization ability and scalability Machine learning Optimization policy space response oracles Scalability Solvers Training Traveling salesman problem Traveling salesman problems Vehicle routing
ISSN:	0162-8828, 1939-3539, 2160-9292, 1939-3539
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Abstract	Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: A daptive S taircase P olicy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP.
AbstractList	Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: Adaptive Staircase Policy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP. Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: Adaptive Staircase Policy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP.Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: Adaptive Staircase Policy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP. Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: A daptive S taircase P olicy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP.
Author	Yu, Tianshu Yu, Zhouliang McAleer, Stephen Wang, Chenguang Yang, Yaodong
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SubjectTerms	Adaptation models Combinatorial analysis Combinatorial optimization problems curriculum learning generalization ability and scalability Machine learning Optimization policy space response oracles Scalability Solvers Training Traveling salesman problem Traveling salesman problems Vehicle routing
Title	ASP: Learn a Universal Neural Solver
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