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Although several surveys on Neural Combinatorial Optimization (NCO) solvers specifically designed to solve Vehicle Routing Problems (VRPs) have been conducted, they did not cover the state-of-the-art (SOTA) NCO solvers emerged recently.
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S. Yao, X. Lin, J. Wang, Q. Zhang, and Z. Wang, “Rethinking supervised learning based neural combinatorial optimization for routing problem,” ACM Transactions on Evolutionary Learning and Optimization , 2024
2024
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T. Dernedde, D. Thyssens, S. Dittrich, M. Stubbemann, and L. Schmidt-Thieme, “MOCO: A learnable meta optimizer for combinatorial optimization,” 2024, arXiv: 2402.04915
2024
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F. Liu, X. Tong, M. Yuan, X. Lin, F. Luo, Z. Wang, Z. Lu, and Q. Zhang, “Evolution of heuristics: Towards efficient automatic algorithm design using large language model,” in Proceedings of the International Conference on Machine Learning , 2024, pp. 32 201–32 223
2024
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H. Fang, Z. Song, P. Weng, and Y. Ban, “INViT: A generalizable routing problem solver with invariant nested view transformer,” in Proceedings of the International Conference on Machine Learning , 2024, pp. 12 973–12 992
2024
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S. Liu, X. Yan, and Y. Jin, “An edge-aware graph autoencoder trained on scale-imbalanced data for travelling salesman problems,” Knowledge-Based Systems , vol. 291, p. 111559, 2024
2024
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A. I. Garmendia, J. Ceberio, and A. Mendiburu, “Applicability of neural combinatorial optimization: A critical view,” ACM Transactions on Evolutionary Learning and Optimization , vol. 4, no. 3, 2024
2024
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J. Zhou, Z. Cao, Y. Wu, W. Song, Y. Ma, J. Zhang, and X. Chi, “MVMoE: Multi-task vehicle routing solver with mixture-of-experts,” in Proceedings of the International Conference on Machine Learning , 2024, pp. 61 804–61 824
2024
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Z. Zheng, C. Zhou, X. Tong, M. Yuan, and Z. Wang, “UDC: A unified neural divide-and-conquer framework for large-scale combinatorial optimization problems,” in Proceedings of Advances in Neural Information Processing Systems , 2024, pp. 6081–6125
2024
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C. Zhang, Z. Cao, W. Song, Y. Wu, and J. Zhang, “Deep reinforcement learning guided improvement heuristic for job shop scheduling,” in the International Conference on Learning Representations , 2024, pp. 1–20
2024
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H. Cheng, Y. Cong, W. Jiang, and S. Pu, “Learning to solve class-constrained bin packing problems via encoder-decoder model,” in the International Conference on Learning Representations , 2024, pp. 1–24
2024
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Y. Min and C. P. Gomes, “On size and hardness generalization in unsupervised learning for the travelling salesman problem,” 2024, arxiv: 2403.20212
2024
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R. Sun, Z. Zheng, and Z. Wang, “Learning encodings for constructive neural combinatorial optimization needs to regret,” in Proceedings of the AAAI Conference on Artificial Intelligence , 2024, pp. 20 803–20 811
2024
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J. Chen, Z. Gong, M. Liu, J. Wang, Y. Yu, and W. Zhang, “Looking ahead to avoid being late: Solving hard-constrained traveling salesman problem,” 2024, arXiv: 2403.05318
2024
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J. Bi, Y. Ma, J. Zhou, W. Song, Z. Cao, Y. Wu, and J. Zhang, “Learning to handle complex constraints for vehicle routing problems,” in Proceedings of Advances in Neural Information Processing Systems , 2024, pp. 93 479–93 509
2024
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Z. Wang, S. Yao, G. Li, and Q. Zhang, “Multiobjective combinatorial optimization using a single deep reinforcement learning model,” IEEE Transactions on Cybernetics , vol. 54, no. 3, pp. 1984–1996, 2024
2024
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G. Luo and J. Luo, “Multi-objective adaptive dynamics attention model to solve multi-objective vehicle routing problem,” in Proceedings of the Asian Conference on Machine Learning , 2024, pp. 834–849
2024
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Z. Zheng, S. Yao, Z. Wang, T. Xialiang, M. Yuan, and K. Tang, “DPN: Decoupling partition and navigation for neural solvers of min-max vehicle routing problems,” in Proceedings of the International Conference on Machine Learning , 2024, pp. 61 559–61 592
2024
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J. Son, M. Kim, S. Choi, H. Kim, and J. Park, “Equity-Transformer: Solving np-hard min-max routing problems as sequential generation with equity context,” in Proceedings of the AAAI Conference on Artificial Intelligence , 2024, pp. 20 265–20 273
2024
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A. Hottung, M. Mahajan, and K. Tierney, “PolyNet: Learning diverse solution strategies for neural combinatorial optimization,” 2024, arXiv: 2402.14048
2024
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J. Li, Y. Ma, Z. Cao, Y. Wu, W. Song, J. Zhang, and Y. M. Chee, “Learning feature embedding refiner for solving vehicle routing problems,” IEEE Transactions on Neural Networks and Learning Systems , vol. 35, no. 11, pp. 15 279–15 291, 2024
2024
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F. J. C. Verdù, L. Castelli, and L. Bortolussi, “Scaling combinatorial optimization neural improvement heuristics with online search and adaptation,” 2024, arXiv: 2412.10163
2024
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H. Ye, J. Wang, H. Liang, Z. Cao, Y. Li, and F. Li, “GLOP: Learning global partition and local construction for solving large-scale routing problems in real-time,” in Proceedings of the AAAI Conference on Artificial Intelligence , 2024, pp. 20 284–20 292
2024
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H. Ye, J. Wang, Z. Cao, F. Berto, C. Hua, H. KIM, J. Park, and G. Song, “Reevo: Large language models as hyper-heuristics with reflective evolution,” in Proceedings of Advances in Neural Information Processing Systems , 2024, pp. 43 571–43 608
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Y. Wang, Y.-H. Jia, W.-N. Chen, and Y. Mei, “Distance-aware attention reshaping: Enhance generalization of neural solver for large-scale vehicle routing problems,” 2024, arXiv: 2401.06979
2024
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C. Gao, H. Shang, K. Xue, D. Li, and C. Qian, “Towards generalizable neural solvers for vehicle routing problems via ensemble with transferrable local policy,” in Proceedings of the International Joint Conference on Artificial Intelligence , 2024, pp. 6914–6922
2024
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C. Wang, Z. Yu, S. McAleer, T. Yu, and Y. Yang, “ASP: Learn a universal neural solver!” IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 46, no. 6, pp. 4102–4114, 2024
2024
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F. Liu, X. Lin, W. Liao, Z. Wang, Q. Zhang, X. Tong, and M. Yuan, “Prompt learning for generalized vehicle routing,” in Proceedings of the International Joint Conference on Artificial Intelligence , 2024, pp. 6976–6984
2024
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J. Zhou, Y. Wu, Z. Cao, W. Song, J. Zhang, and Z. Shen, “Collaboration! Towards robust neural methods for routing problems,” in Proceedings of Advances in Neural Information Processing Systems , 2024, pp. 121 731–121 764
2024
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J. Pirnay and D. G. Grimm, “Self-improvement for neural combinatorial optimization: Sample without replacement, but improvement,” Transactions on Machine Learning Research , 2024
2024
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Y. Li, J. Guo, R. Wang, H. Zha, and J. Yan, “Fast T2T: Optimization consistency speeds up diffusion-based training-to-testing solving for combinatorial optimization,” in Proceedings of Advances in Neural Information Processing Systems , 2024, pp. 30 179–30 206
2024
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V.-A. Darvariu, S. Hailes, and M. Musolesi, “Graph reinforcement learning for combinatorial optimization: A survey and unifying perspective,” Transactions on Machine Learning Research , 2024
2024
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L. Luttmann and L. Xie, “Neural combinatorial optimization on heterogeneous graphs. An application to the picker routing problem in mixed-shelves warehouses,” in Proceedings of the International Conference on Automated Planning and Scheduling , 2024, pp. 1–9
2024
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Z. Lin, Y. Wu, B. Zhou, Z. Cao, W. Song, Y. Zhang, and S. Jayavelu, “Cross-problem learning for solving vehicle routing problems,” in Proceedings of the International Joint Conference on Artificial Intelligence , 2024, pp. 6958–6966
2024
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H. Li, F. Liu, Z. Zheng, Y. Zhang, and Z. Wang, “CaDA: Cross-problem routing solver with constraint-aware dual-attention,” 2024, arxiv: 2412.00346
2024
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Y. Xiao, D. Wang, Z. Cao, R. Cao, X. Wu, B. Li, and Y. Zhou, “From global assessment to local selection: Efficiently solving traveling salesman problems of all sizes,” 2025, openreview
2025
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P. Zhao, Y. Zhou, D. Wang, Z. Cao, Y. Xiao, X. Wu, Y. Li, H. Liu, W. Du, Y. Jiang, and L. Wang, “Dual operation aggregation graph neural networks for solving flexible job-shop scheduling problem with reinforcement learning,” in Proceedings of the Web Conference , 2025
2025
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Y. Lu, Z. Di, B. Li, S. Liu, H. Qian, P. Yang, K. Tang, and A. Zhou, “Context-aware diversity enhancement for neural multi-objective combinatorial optimization,” 2025, arXiv: 2405.08604
2025
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M. Fan, Y. Wu, Z. Cao, W. Song, G. Sartoretti, H. Liu, and G. Wu, “Conditional neural heuristic for multiobjective vehicle routing problems,” IEEE Transactions on Neural Networks and Learning Systems , vol. 36, no. 3, pp. 4677–4689, 2025
2025
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K. Li, F. Liu, Z. Wang, and Q. Zhang, “Destroy and repair using hyper graphs for routing,” in Proceedings of the AAAI Conference on Artificial Intelligence , 2025
2025
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M. Kim, S. Choi, H. Kim, J. Son, J. Park, and Y. Bengio, “Ant colony sampling with GFlownets for combinatorial optimization,” in Proceedings of the International Conference on Artificial Intelligence and Statistics , 2025
2025
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X. Wu, D. Wang, Z. Cao, C. Wu, L. Wen, C. Miao, Y. Xiao, and Y. Zhou, “Efficient heuristics generation for solving combinatorial optimization problems using large language models,” 2025, openreview
2025
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Y. Xiao, D. Wang, X. Wu, Y. Wu, B. Li, W. Du, L. Wang, and Y. Zhou, “Improving generalization of neural vehicle routing problem solvers through the lens of model architecture,” Neural Networks , vol. 187, p. 107380, 2025
2025
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M. Wang, Y. Zhou, Z. Cao, Y. Xiao, X. Wu, W. Pang, Y. Jiang, H. Yang, P. Zhao, and Y. Li, “An efficient diffusion-based non-autoregressive solver for traveling salesman problem,” in Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining , 2025
2025
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C. Zhou, X. Lin, Z. Wang, X. Tong, M. Yuan, and Q. Zhang, “ICAM: Rethinking instance-conditioned adaptation in neural vehicle routing solver,” 2025, openreview
2025
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F. Luo, X. Lin, Y. Wu, Z. Wang, X. Tong, M. Yuan, and Q. Zhang, “Boosting neural combinatorial optimization for large-scale vehicle routing problems,” in the International Conference on Learning Representations , 2025, pp. 1–27
2025
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C. Wang, Z. Cao, Y. Wu, L. Teng, and G. Wu, “Deep reinforcement learning for solving vehicle routing problems with backhauls,” IEEE Transactions on Neural Networks and Learning Systems , vol. 36, no. 3, pp. 4779–4793, 2025
2025
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J. Chen, J. Wang, Z. Cao, and Y. Wu, “Neural multi-objective combinatorial optimization via graph-image multimodal fusion,” in the International Conference on Learning Representations , 2025, pp. 1–20
2025
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F. Berto, C. Hua, N. G. Zepeda, A. Hottung, N. Wouda, L. Lan, J. Park, K. Tierney, and J. Park, “Routefinder: Towards foundation models for vehicle routing problems,” 2025, arxiv: 2406.15007
2025
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D. Drakulic, S. Michel, and J.-M. Andreoli, “GOAL: A generalist combinatorial optimization agent learner,” in the International Conference on Learning Representations , 2025, pp. 1–24
2025
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W. Pan, H. Xiong, J. Ma, W. Zhao, Y. Li, and J. Yan, “UniCO: On unified combinatorial optimization via problem reduction to matrix-encoded general TSP,” in the International Conference on Learning Representations , 2025, pp. 1–41
2025
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