{"type":"ScholarlyArticle","title":"Cross-Problem Learning for Solving Vehicle Routing Problems","authors":[{"name":"Zhuoyi Lin","slug":"zhuoyi-lin","given":"Zhuoyi","family":"Lin","affiliation":"Institute for Infocomm Research , Agency for Science, Technology and Research (A * STAR)"},{"name":"Yaoxin Wu","slug":"yaoxin-wu","given":"Yaoxin","family":"Wu","affiliation":"Eindhoven University of Technology"},{"name":"Bangjian Zhou","slug":"bangjian-zhou","given":"Bangjian","family":"Zhou","affiliation":"Unidt"},{"name":"Zhiguang Cao","slug":"zhiguang-cao","given":"Zhiguang","family":"Cao","affiliation":"Singapore Management University"},{"name":"Wen Song","slug":"wen-song","given":"Wen","family":"Song","affiliation":"Shandong University"},{"name":"Yingqian Zhang","slug":"yingqian-zhang","given":"Yingqian","family":"Zhang","affiliation":"Eindhoven University of Technology"},{"name":"Senthilnath Jayavelu","slug":"senthilnath-jayavelu","given":"Senthilnath","family":"Jayavelu","affiliation":"Institute for Infocomm Research , Agency for Science, Technology and Research (A * STAR)"}],"abstract":"Existing neural heuristics often train a deep architecture from scratch for each specific vehicle routing problem (VRP), ignoring the transferable knowledge across different VRP variants. This paper proposes the cross-problem learning to assist heuristics training for different downstream VRP variants. Particularly, we modularize neural architectures for complex VRPs into 1) the backbone Transformer for tackling the travelling salesman problem (TSP), and 2) the additional lightweight modules for processing problem-specific features in complex VRPs. Accordingly, we propose to pre-train the backbone Transformer for TSP, and then apply it in the process of fine-tuning the Transformer models for each target VRP variant. On the one hand, we fully fine-tune the trained backbone Transformer and problem-specific modules simultaneously. On the other hand, we only fine-tune small adapter networks along with the modules, keeping the backbone Transformer still. Extensive experiments on typical VRPs substantiate that 1) the full fine-tuning achieves significantly better performance than the one trained from scratch, and 2) the adapter-based fine-tuning also delivers comparable performance while being notably parameter-efficient. Furthermore, we empirically demonstrate the favorable effect of our method in terms of cross-distribution application and versatility.","doi":"10.24963/ijcai.2024/769","url":"https://ijcai.org/proceedings/2024/769","pdf":"https://ijcai.org/proceedings/2024/0769.pdf","markdown":"https://ijcai.org/proceedings/2024/769.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/769","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Search","track":"Main Track","number":769,"pages":{"first":6958,"last":6966},"keywords":["Search: S: Search and machine learning","Search: S: Combinatorial search and optimisation","Machine Learning: ML: Applications"],"videos":[],"references":[{"position":1,"raw":"[Bao et al., 2022] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. Beit: Bert pre-training of image transformers. In ICLR, 2022.","title":"Beit: Bert pre-training of image transformers","authors":"Bao","year":"2022","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bello et al., 2017] Irwan Bello, Hieu Pham, Quoc V. Le, Mohammad Norouzi, and Samy Bengio. Neural combina- torial optimization with reinforcement learning. In ICLR, 2017.","title":"Neural combinatorial optimization with reinforcement learning","authors":"Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, Samy Bengio","year":"2017","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bengio et al., 2021] Yoshua Bengio, Andrea Lodi, and An- toine Prouvost. Machine learning for combinatorial op- timization: a methodological tour d'horizon. European Journal of Operational Research, 290(2):405-421, 2021.","title":"Machine learning for combinatorial optimization: a methodological tour d'horizon","authors":"Yoshua Bengio, Andrea Lodi","year":"2021","venue":"European Journal of Operational Research","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bi et al., 2022] Jieyi Bi, Yining Ma, Jiahai Wang, Zhiguang Cao, Jinbiao Chen, Yuan Sun, and Yeow Meng Chee. Learning generalizable models for vehicle routing prob- lems via knowledge distillation. In NeurIPS, 2022.","title":"Learning generalizable models for vehicle routing problems via knowledge distillation","authors":"Jieyi Bi, Yining Ma, Jiahai Wang, Zhiguang Cao, Jinbiao Chen, Yuan Sun, Yeow Meng Chee","year":"2022","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Chen et al., 2020] Ting Chen, Simon Kornblith, Moham- mad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In ICML, pages 1597-1607, 2020.","title":"A simple framework for contrastive learning of visual representations","authors":"Ting Chen, Simon Kornblith, Mohammad Norouzi, Geoffrey Hinton","year":"2020","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Choo et al., 2022] Jinho Choo, Yeong-Dae Kwon, Jihoon Kim, Jeongwoo Jae, André Hottung, Kevin Tierney, and Youngjune Gwon. Simulation-guided beam search for neural combinatorial optimization. In NeurIPS, 2022.","title":"Simulation-guided beam search for neural combinatorial optimization","authors":"Jinho Choo, Yeong-Dae Kwon, Jihoon Kim, Jeongwoo Jae, André Hottung, Kevin Tierney, Youngjune Gwon","year":"2022","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Dai et al., 2017] Hanjun Dai, Elias B. Khalil, Yuyu Zhang, Bistra Dilkina, and Le Song. Learning combinatorial opti- mization algorithms over graphs. In NeurIPS, 2017.","title":"Learning combinatorial optimization algorithms over graphs","authors":"Hanjun Dai, Elias B Khalil, Yuyu Zhang, Bistra Dilkina, Le Song","year":"2017","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Devlin et al., 2018] Jacob Devlin, Ming-Wei Chang, Ken- ton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understand- ing. arXiv preprint arXiv:1810.04805, 2018.","title":"Bert: Pre-training of deep bidirectional transformers for language understanding","authors":"Jacob Devlin, Ming-Wei Chang, Kenton Lee, Kristina Toutanova","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Dong et al., 2019] Li Dong, Nan Yang, Wenhui Wang, Furu Wei, Xiaodong Liu, Yu Wang, Jianfeng Gao, Ming Zhou, and Hsiao-Wuen Hon. Unified language model pre- training for natural language understanding and genera- tion. In NeurIPS, pages 13063-13075, 2019.","title":"Unified language model pretraining for natural language understanding and generation","authors":"Li Dong, Nan Yang, Wenhui Wang, Furu Wei, Xiaodong Liu, Yu Wang, Jianfeng Gao, Ming Zhou, Hsiao-Wuen Hon","year":"2019","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Dosovitskiy et al., 2021] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Min- derer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. In ICLR, 2021.","title":"An image is worth 16x16 words: Transformers for image recognition at scale","authors":"Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly","year":"2021","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Fu et al., 2021] Zhang-Hua Fu, Kai-Bin Qiu, and Hongyuan Zha. Generalize a small pre-trained model to arbitrarily large tsp instances. In AAAI, pages 7474-7482, 2021.","title":"Generalize a small pre-trained model to arbitrarily large tsp instances","authors":"Zhang-Hua Fu, Kai-Bin Qiu, Hongyuan Zha","year":"2021","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Gao et al., 2020] Lei Gao, Mingxiang Chen, Qichang Chen, Ganzhong Luo, Nuoyi Zhu, and Zhixin Liu. Learn to design the heuristics for vehicle routing problem. arXiv preprint arXiv:2002.08539, 2020.","title":"Learn to design the heuristics for vehicle routing problem","authors":"Lei Gao, Mingxiang Chen, Qichang Chen, Ganzhong Luo, Nuoyi Zhu, Zhixin Liu","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Geisler et al., 2022] Simon Geisler, Johanna Sommer, Jan Schuchardt, Aleksandar Bojchevski, and Stephan Günnemann. Generalization of neural combinatorial solvers through the lens of adversarial robustness. In ICLR, 2022.","title":"Generalization of neural combinatorial solvers through the lens of adversarial robustness","authors":"Simon Geisler, Johanna Sommer, Jan Schuchardt, Aleksandar Bojchevski, Stephan Günnemann","year":"2022","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2022.","title":"Gurobi Optimization","authors":null,"year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Hottung and Tierney, 2020] André Hottung and Kevin Tier- ney. Neural large neighborhood search for the capacitated vehicle routing problem. In ECAI, pages 443-450, 2020.","title":"Neural large neighborhood search for the capacitated vehicle routing problem","authors":"Tierney ; Hottung, André Hottung, Kevin Tierney","year":"2020","venue":"ECAI","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Hottung et al., 2022] André Hottung, Yeong-Dae Kwon, and Kevin Tierney. Efficient active search for combina- torial optimization problems. In ICLR, 2022.","title":"Efficient active search for combinatorial optimization problems","authors":"Hottung","year":"2022","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Houlsby et al., 2019] Neil Houlsby, Andrei Giurgiu, Stanis- law Jastrzebski, Bruna Morrone, Quentin De Laroussilhe, Andrea Gesmundo, Mona Attariyan, and Sylvain Gelly. Parameter-efficient transfer learning for nlp. In ICML, pages 2790-2799, 2019.","title":"Parameter-efficient transfer learning for nlp","authors":"Neil Houlsby, Andrei Giurgiu, Stanislaw Jastrzebski, Bruna Morrone, Quentin De Laroussilhe, Andrea Gesmundo, Mona Attariyan, Sylvain Gelly","year":"2019","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Hu et al., 2020] Weihua Hu, Bowen Liu, Joseph Gomes, Marinka Zitnik, Percy Liang, Vijay Pande, and Jure Leskovec. Strategies for pre-training graph neural net- works. In ICLR, 2020.","title":"Strategies for pre-training graph neural networks","authors":"Weihua Hu, Bowen Liu, Joseph Gomes, Marinka Zitnik, Percy Liang, Vijay Pande, Jure Leskovec","year":"2020","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Hu et al., 2021] Edward J Hu, Phillip Wallis, Zeyuan Allen- Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. Lora: Low-rank adaptation of large language models. In ICLR, 2021.","title":"Lora: Low-rank adaptation of large language models","authors":"J Edward, Phillip Hu, Zeyuan Wallis, Yuanzhi Allen-Zhu, Shean Li, Lu Wang, Weizhu Wang, Chen","year":"2021","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Hudson et al., 2022] Benjamin Hudson, Qingbiao Li, Matthew Malencia, and Amanda Prorok. Graph neural network guided local search for the traveling salesperson problem. In ICLR, 2022.","title":"Graph neural network guided local search for the traveling salesperson problem","authors":"Benjamin Hudson, Qingbiao Li, Matthew Malencia, Amanda Prorok","year":"2022","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Kim et al., 2021] Minsu Kim, Jinkyoo Park, et al. Learning collaborative policies to solve np-hard routing problems. In NeurIPS, pages 10418-10430, 2021.","title":"Learning collaborative policies to solve np-hard routing problems","authors":"Minsu Kim, Jinkyoo Park","year":"2021","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Kim et al., 2022a] Minjun Kim, Junyoung Park, and Jinkyoo Park. Learning to cross exchange to solve min- max vehicle routing problems. In ICLR, 2022.","title":"Learning to cross exchange to solve minmax vehicle routing problems","authors":"Kim","year":"2022","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Kim et al., 2022b] Minsu Kim, Junyoung Park, and Jinkyoo Park. Sym-NCO: Leveraging symmetricity for neural combinatorial optimization. In NeurIPS, 2022.","title":"Sym-NCO: Leveraging symmetricity for neural combinatorial optimization","authors":"Kim","year":"2022","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Kitaev et al., 2020] Nikita Kitaev, Lukasz Kaiser, and Anselm Levskaya. Reformer: The efficient transformer. In ICLR, 2020.","title":"Reformer: The efficient transformer","authors":"Nikita Kitaev, Lukasz Kaiser, Anselm Levskaya","year":"2020","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Kobeaga et al., 2018] Gorka Kobeaga, María Merino, and Jose A Lozano. An efficient evolutionary algorithm for the orienteering problem. Computers & Operations Research, 90:42-59, 2018.","title":"An efficient evolutionary algorithm for the orienteering problem","authors":"Gorka Kobeaga, María Merino, Jose A Lozano","year":"2018","venue":"Computers & Operations Research","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Konstantakopoulos et al., 2022] Grigorios D Konstanta- kopoulos, Sotiris P Gayialis, and Evripidis P Kechagias. Vehicle routing problem and related algorithms for logis- tics distribution: A literature review and classification. Operational research, pages 1-30, 2022.","title":"Vehicle routing problem and related algorithms for logistics distribution: A literature review and classification","authors":"Grigorios D Konstantakopoulos, P Sotiris, Evripidis P Gayialis, Kechagias","year":"2022","venue":"Operational research","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Kool et al., 2018] Wouter Kool, Herke van Hoof, and Max Welling. Attention, learn to solve routing problems! In ICLR, 2018.","title":"Attention, learn to solve routing problems! In ICLR","authors":"Wouter Kool, Herke Van Hoof, Max Welling","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Kwon et al., 2020] Yeong-Dae Kwon, Jinho Choo, By- oungjip Kim, Iljoo Yoon, Youngjune Gwon, and Seungjai Min. Pomo: Policy optimization with multiple optima for reinforcement learning. In NeurIPS, pages 21188-21198, 2020.","title":"Pomo: Policy optimization with multiple optima for reinforcement learning","authors":"Yeong-Dae Kwon, Jinho Choo, Byoungjip Kim, Iljoo Yoon, Youngjune Gwon, Seungjai Min","year":"2020","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Kwon et al., 2021] Yeong-Dae Kwon, Jinho Choo, Iljoo Yoon, Minah Park, Duwon Park, and Youngjune Gwon. Matrix encoding networks for neural combinatorial opti- mization. In NeurIPS, pages 5138-5149, 2021.","title":"Matrix encoding networks for neural combinatorial optimization","authors":"Yeong-Dae Kwon, Jinho Choo, Iljoo Yoon, Minah Park, Duwon Park, Youngjune Gwon","year":"2021","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Li et al., 2021] Sirui Li, Zhongxia Yan, and Cathy Wu. Learning to delegate for large-scale vehicle routing. In NeurIPS, pages 26198-26211, 2021.","title":"Learning to delegate for large-scale vehicle routing","authors":"Sirui Li, Zhongxia Yan, Cathy Wu","year":"2021","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Luo et al., 2023] Fu Luo, Xi Lin, Fei Liu, Qingfu Zhang, and Zhenkun Wang. Neural combinatorial optimization with heavy decoder: Toward large scale generalization. In NeurIPS, 2023.","title":"Neural combinatorial optimization with heavy decoder: Toward large scale generalization","authors":"Xi Fu Luo, Fei Lin, Qingfu Liu, Zhenkun Zhang, Wang","year":"2023","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Ma et al., 2021] Yining Ma, Jingwen Li, Zhiguang Cao, Wen Song, Le Zhang, Zhenghua Chen, and Jing Tang. Learning to iteratively solve routing problems with dual- aspect collaborative transformer. In NeurIPS, pages 11096-11107, 2021.","title":"Learning to iteratively solve routing problems with dualaspect collaborative transformer","authors":"Yining Ma, Jingwen Li, Zhiguang Cao, Wen Song, Le Zhang, Zhenghua Chen, Jing Tang","year":"2021","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Ma et al., 2023] Zeyuan Ma, Hongshu Guo, Jiacheng Chen, Zhenrui Li, Guojun Peng, Yue-Jiao Gong, Yining Ma, and Zhiguang Cao. Metabox: A benchmark platform for meta- black-box optimization with reinforcement learning. In Advances in Neural Information Processing Systems, vol- ume 36, 2023.","title":"Metabox: A benchmark platform for metablack-box optimization with reinforcement learning","authors":"Ma","year":"2023","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Nazari et al., 2018] Mohammadreza Nazari, Afshin Oroo- jlooy, Lawrence Snyder, and Martin Takác. Reinforce- ment learning for solving the vehicle routing problem. In NeurIPS, page 9861-9871, 2018.","title":"Reinforcement learning for solving the vehicle routing problem","authors":"Mohammadreza Nazari, Afshin Oroojlooy, Lawrence Snyder, Martin Takác","year":"2018","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Pfeiffer et al., 2021] Jonas Pfeiffer, Aishwarya Kamath, Andreas Rücklé, Kyunghyun Cho, and Iryna Gurevych. Adapterfusion: Non-destructive task composition for transfer learning. In EACL, pages 487-503, 2021.","title":"Adapterfusion: Non-destructive task composition for transfer learning","authors":"Pfeiffer","year":"2021","venue":"EACL","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Qiu et al., 2020] Jiezhong Qiu, Qibin Chen, Yuxiao Dong, Jing Zhang, Hongxia Yang, Ming Ding, Kuansan Wang, and Jie Tang. Gcc: Graph contrastive coding for graph neural network pre-training. In KDD, pages 1150-1160, 2020.","title":"Gcc: Graph contrastive coding for graph neural network pre-training","authors":"Qiu","year":"2020","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Qiu et al., 2022] Ruizhong Qiu, Zhiqing Sun, and Yiming Yang. DIMES: A differentiable meta solver for combina- torial optimization problems. In NeurIPS, 2022.","title":"DIMES: A differentiable meta solver for combinatorial optimization problems","authors":"Qiu","year":"2022","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Ribeiro et al., 2020] Marco Tulio Ribeiro, Tongshuang Wu, Carlos Guestrin, and Sameer Singh. Beyond accuracy: Behavioral testing of nlp models with checklist. In ACL, pages 4902-4912, 2020.","title":"Beyond accuracy: Behavioral testing of nlp models with checklist","authors":"Marco Tulio Ribeiro, Tongshuang Wu, Carlos Guestrin, Sameer Singh","year":"2020","venue":"ACL","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Santana et al., 2022] Ítalo Santana, Andrea Lodi, and Thibaut Vidal. Neural networks for local search and crossover in vehicle routing: A possible overkill? arXiv preprint arXiv:2210.12075, 2022.","title":"Neural networks for local search and crossover in vehicle routing: A possible overkill","authors":"Ítalo Santana, Andrea Lodi, Thibaut Vidal","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":40,"raw":"[Sung et al., 2022] Yi-Lin Sung, Jaemin Cho, and Mohit Bansal. Lst: Ladder side-tuning for parameter and mem- ory efficient transfer learning. In NeurIPS, pages 12991- 13005, 2022.","title":"Lst: Ladder side-tuning for parameter and memory efficient transfer learning","authors":"Sung","year":"2022","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Sutton and Barto, 2018] Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction. MIT press, 2018.","title":"Reinforcement learning: An introduction","authors":"S Richard, Andrew G Sutton, Barto","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":42,"raw":"[Touvron et al., 2021] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablay- rolles, and Hervé Jégou. Training data-efficient image transformers & distillation through attention. In ICML, pages 10347-10357, 2021.","title":"Training data-efficient image transformers & distillation through attention","authors":"Touvron","year":"2021","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":43,"raw":"[Tsiligirides, 1984] Theodore Tsiligirides. Heuristic meth- ods applied to orienteering. Journal of the Operational Research Society, 35:797-809, 1984.","title":"Theodore Tsiligirides. Heuristic methods applied to orienteering","authors":"Tsiligirides","year":"1984","venue":"Journal of the Operational Research Society","doi":null,"url":null,"internal_url":null},{"position":44,"raw":"[Vaswani et al., 2017] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In NeurIPS, page 6000-6010, 2017.","title":"Attention is all you need","authors":"Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, Illia Polosukhin","year":"2017","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":45,"raw":"[Wang and Sheu, 2019] Zheng Wang and Jiuh-Biing Sheu. Vehicle routing problem with drones. Transportation re- search part B: methodological, 122:350-364, 2019.","title":"Vehicle routing problem with drones","authors":"Wang, Sheu, Zheng Wang, Jiuh-Biing Sheu","year":"2019","venue":"Transportation research part B: methodological","doi":null,"url":null,"internal_url":null},{"position":46,"raw":"[Wang et al., 2021] Runzhong Wang, Zhigang Hua, Gan Liu, Jiayi Zhang, Junchi Yan, Feng Qi, Shuang Yang, Jun Zhou, and Xiaokang Yang. A bi-level framework for learning to solve combinatorial optimization on graphs. In NeurIPS, pages 21453-21466, 2021.","title":"A bi-level framework for learning to solve combinatorial optimization on graphs","authors":"Runzhong Wang, Zhigang Hua, Gan Liu, Jiayi Zhang, Junchi Yan, Feng Qi, Shuang Yang, Jun Zhou, Xiaokang Yang","year":"2021","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":47,"raw":"[Williams, 1992] Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforce- ment learning. Machine learning, 8(3):229-256, 1992.","title":"Simple statistical gradient-following algorithms for connectionist reinforcement learning","authors":"Williams Ronald","year":"1992","venue":"Machine learning","doi":null,"url":null,"internal_url":null},{"position":48,"raw":"[Wu et al., 2021] Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang, and Andrew Lim. Learning improvement heuris- tics for solving routing problems. IEEE transactions on neural networks and learning systems, 2021.","title":"Learning improvement heuristics for solving routing problems","authors":"Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang, Andrew Lim","year":"2021","venue":"IEEE transactions on neural networks and learning systems","doi":null,"url":null,"internal_url":null},{"position":49,"raw":"[Xin et al., 2021a] Liang Xin, Wen Song, Zhiguang Cao, and Jie Zhang. Multi-decoder attention model with embedding glimpse for solving vehicle routing problems. In AAAI, pages 12042-12049, 2021.","title":"Multi-decoder attention model with embedding glimpse for solving vehicle routing problems","authors":"Xin","year":"2021","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":50,"raw":"[Xin et al., 2021b] Liang Xin, Wen Song, Zhiguang Cao, and Jie Zhang. Neurolkh: Combining deep learning model with lin-kernighan-helsgaun heuristic for solving the trav- eling salesman problem. In NeurIPS, pages 7472-7483, 2021.","title":"Neurolkh: Combining deep learning model with lin-kernighan-helsgaun heuristic for solving the traveling salesman problem","authors":"Xin","year":"2021","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":51,"raw":"[You et al., 2020] Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. Graph con- trastive learning with augmentations. In NeurIPS, pages 5812-5823, 2020.","title":"Graph contrastive learning with augmentations","authors":"Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, Yang Shen","year":"2020","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":52,"raw":"[Zhang et al., 2020] Jeffrey O Zhang, Alexander Sax, Amir Zamir, Leonidas Guibas, and Jitendra Malik. Side-tuning: a baseline for network adaptation via additive side net- works. In ECCV, pages 698-714. Springer, 2020.","title":"Side-tuning: a baseline for network adaptation via additive side networks","authors":"Alexander Jeffrey O Zhang, Amir Sax, Leonidas Zamir, Jitendra Guibas, Malik","year":"2020","venue":"ECCV","doi":null,"url":null,"internal_url":null},{"position":53,"raw":"[Zhao et al., 2020] Mengjie Zhao, Tao Lin, Fei Mi, Martin Jaggi, and Hinrich Schütze. Masking as an efficient al- ternative to finetuning for pretrained language models. In EMNLP, pages 2226-2241, 2020.","title":"Masking as an efficient alternative to finetuning for pretrained language models","authors":"Mengjie Zhao, Tao Lin, Fei Mi, Martin Jaggi, Hinrich Schütze","year":"2020","venue":"EMNLP","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}