BiGNN: Bipartite graph neural network with attention mechanism for solving multiple traveling salesman problems in urban logistics
•Learn to Branch: A new approach is proposed to optimize the branch strategy in Branch-and-bound.•Deep Learning Model: The new model Bipartite Graph Neural Network with Attention Mechanism is proposed to learn the branch strategies.•Comparative Analysis: The models outperform other machine learning...
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| Published in: | International journal of applied earth observation and geoinformation Vol. 129; p. 103863 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.05.2024
Elsevier |
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| ISSN: | 1569-8432, 1872-826X |
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| Abstract | •Learn to Branch: A new approach is proposed to optimize the branch strategy in Branch-and-bound.•Deep Learning Model: The new model Bipartite Graph Neural Network with Attention Mechanism is proposed to learn the branch strategies.•Comparative Analysis: The models outperform other machine learning algorithms.•Real-World Application: The method is used to solve the Surat Road network data.
The multiple traveling salesman problems (MTSP), which arise from real world problems, are essential in urban logistics. Variations such as MinMax-MTSP and Bounded-MTSP aim to distribute workload evenly among salesmen and impose constraints on visited cities, respectively. Branch-and-bound (B&B) provides an exact algorithm solution for these problems. The Learn to Branch (L2B) approach guides branch node selection through deep learning. In this study, we utilize mathematical modeling of Bipartite Graph Neural Network (BiGNN) and an attention mechanism to support B&B in exploring solution spaces through imitation learning. The problems are framed to formulate mixed integer linear programming, which is different from conventional algorithms. It is proposed that a bipartite graph network approach makes a feature representation by setting a structure of constraints and variables. Experimental results showed that our model can generate more accurate solutions than three benchmark models. The BiGNN model can effectively learn the strong branch strategy, which reduces solution time by replacing complex calculations with fast approximations. Additionally, the small-scale instances model can be applied to larger-scale ones. |
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| AbstractList | •Learn to Branch: A new approach is proposed to optimize the branch strategy in Branch-and-bound.•Deep Learning Model: The new model Bipartite Graph Neural Network with Attention Mechanism is proposed to learn the branch strategies.•Comparative Analysis: The models outperform other machine learning algorithms.•Real-World Application: The method is used to solve the Surat Road network data.
The multiple traveling salesman problems (MTSP), which arise from real world problems, are essential in urban logistics. Variations such as MinMax-MTSP and Bounded-MTSP aim to distribute workload evenly among salesmen and impose constraints on visited cities, respectively. Branch-and-bound (B&B) provides an exact algorithm solution for these problems. The Learn to Branch (L2B) approach guides branch node selection through deep learning. In this study, we utilize mathematical modeling of Bipartite Graph Neural Network (BiGNN) and an attention mechanism to support B&B in exploring solution spaces through imitation learning. The problems are framed to formulate mixed integer linear programming, which is different from conventional algorithms. It is proposed that a bipartite graph network approach makes a feature representation by setting a structure of constraints and variables. Experimental results showed that our model can generate more accurate solutions than three benchmark models. The BiGNN model can effectively learn the strong branch strategy, which reduces solution time by replacing complex calculations with fast approximations. Additionally, the small-scale instances model can be applied to larger-scale ones. The multiple traveling salesman problems (MTSP), which arise from real world problems, are essential in urban logistics. Variations such as MinMax-MTSP and Bounded-MTSP aim to distribute workload evenly among salesmen and impose constraints on visited cities, respectively. Branch-and-bound (B&B) provides an exact algorithm solution for these problems. The Learn to Branch (L2B) approach guides branch node selection through deep learning. In this study, we utilize mathematical modeling of Bipartite Graph Neural Network (BiGNN) and an attention mechanism to support B&B in exploring solution spaces through imitation learning. The problems are framed to formulate mixed integer linear programming, which is different from conventional algorithms. It is proposed that a bipartite graph network approach makes a feature representation by setting a structure of constraints and variables. Experimental results showed that our model can generate more accurate solutions than three benchmark models. The BiGNN model can effectively learn the strong branch strategy, which reduces solution time by replacing complex calculations with fast approximations. Additionally, the small-scale instances model can be applied to larger-scale ones. |
| ArticleNumber | 103863 |
| Author | Li, Huilai Liang, Haojian Zhou, Liang Wang, Shaohua Zhang, Xueyan Wang, Shaowen |
| Author_xml | – sequence: 1 givenname: Haojian surname: Liang fullname: Liang, Haojian organization: Key Laboratory of Remote Sensing and Digital Earth Chinese Academy of Sciences, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China – sequence: 2 givenname: Shaohua orcidid: 0000-0001-8651-9505 surname: Wang fullname: Wang, Shaohua email: wangshaohua@aircas.ac.cn organization: Key Laboratory of Remote Sensing and Digital Earth Chinese Academy of Sciences, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China – sequence: 3 givenname: Huilai surname: Li fullname: Li, Huilai organization: School of Artificial Intelligence, Jilin University, Changchun 130012, China – sequence: 4 givenname: Liang surname: Zhou fullname: Zhou, Liang organization: Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China – sequence: 5 givenname: Xueyan surname: Zhang fullname: Zhang, Xueyan organization: Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089, USA – sequence: 6 givenname: Shaowen surname: Wang fullname: Wang, Shaowen email: shaowen@illinois.edu organization: CyberGIS Center for Advanced Digital and Spatial Studies, University of Illinois Urbana-Champaign, 1301 W Green St, Urbana, IL, 61801, USA |
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| Keywords | Attention mechanism Branch-and-bound Bipartite graph Multiple traveling salesman problem Graph neural network |
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| Title | BiGNN: Bipartite graph neural network with attention mechanism for solving multiple traveling salesman problems in urban logistics |
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