Enhancing neural combinatorial optimization by progressive training paradigm
Neural Combinatorial Optimization (NCO) methods have garnered considerable attention, due to their effectiveness in automatic algorithm design for solving combinatorial optimization problems. Current constructive NCO methods predominantly employ a one-stage training paradigm using either reinforceme...
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| Published in: | Neurocomputing (Amsterdam) Vol. 659; p. 131707 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.01.2026
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| ISSN: | 0925-2312 |
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| Abstract | Neural Combinatorial Optimization (NCO) methods have garnered considerable attention, due to their effectiveness in automatic algorithm design for solving combinatorial optimization problems. Current constructive NCO methods predominantly employ a one-stage training paradigm using either reinforcement learning (RL) or supervised learning (SL). The one-stage training inevitably entails the computation-intensive labeling (i.e., solving optimal solutions) in SL or less-informative sparse rewards in RL. In this work, we propose a progressive training paradigm that pre-trains a neural network on small-scale instances using SL and then fine-tunes it using RL. In the former stage, the optimal solutions as labels effectively guide the neural network training, thereby bypassing the sparse reward issue. In the latter, the neural network is trained using RL to solve large-scale problems, avoiding the labels of optimal solutions that are hard to obtain. Moreover, we propose a decomposition-based approach that enables RL training with larger problem scales, alleviating the issue of insufficient memory induced by the heavy neural network. The proposed paradigm advances existing NCO models to obtain near-optimal solutions for the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) with up to 10,000 nodes. Additionally, it enhances the generalization performance across instances of different sizes and distributions, as well as real-world TSPLib and CVRPLib instances. |
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| AbstractList | Neural Combinatorial Optimization (NCO) methods have garnered considerable attention, due to their effectiveness in automatic algorithm design for solving combinatorial optimization problems. Current constructive NCO methods predominantly employ a one-stage training paradigm using either reinforcement learning (RL) or supervised learning (SL). The one-stage training inevitably entails the computation-intensive labeling (i.e., solving optimal solutions) in SL or less-informative sparse rewards in RL. In this work, we propose a progressive training paradigm that pre-trains a neural network on small-scale instances using SL and then fine-tunes it using RL. In the former stage, the optimal solutions as labels effectively guide the neural network training, thereby bypassing the sparse reward issue. In the latter, the neural network is trained using RL to solve large-scale problems, avoiding the labels of optimal solutions that are hard to obtain. Moreover, we propose a decomposition-based approach that enables RL training with larger problem scales, alleviating the issue of insufficient memory induced by the heavy neural network. The proposed paradigm advances existing NCO models to obtain near-optimal solutions for the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) with up to 10,000 nodes. Additionally, it enhances the generalization performance across instances of different sizes and distributions, as well as real-world TSPLib and CVRPLib instances. |
| ArticleNumber | 131707 |
| Author | Ge, Hongwei Wu, Yaoxin Hou, Yaqing Cao, Zhi |
| Author_xml | – sequence: 1 givenname: Zhi surname: Cao fullname: Cao, Zhi organization: School of Computer Science and Technology, Dalian University of Technology, Dalian 116023, China – sequence: 2 givenname: Yaoxin surname: Wu fullname: Wu, Yaoxin organization: Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, 5600 MB Eindhoven, the Netherlands – sequence: 3 givenname: Yaqing surname: Hou fullname: Hou, Yaqing organization: School of Computer Science and Technology, Dalian University of Technology, Dalian 116023, China – sequence: 4 givenname: Hongwei orcidid: 0000-0002-8937-1515 surname: Ge fullname: Ge, Hongwei email: hwge@dlut.edu.cn organization: School of Computer Science and Technology, Dalian University of Technology, Dalian 116023, China |
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| Keywords | Attention model Neural combinatorial optimization Vehicle routing problem Reinforcement learning |
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