A hybrid neural combinatorial optimization framework assisted by automated algorithm design
In recent years, the application of Neural Combinatorial Optimization (NCO) techniques in Combinatorial Optimization (CO) has emerged as a popular and promising research direction. Currently, there are mainly two types of NCO, namely, the Constructive Neural Combinatorial Optimization (CNCO) and the...
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| Vydané v: | Complex & intelligent systems Ročník 10; číslo 6; s. 8233 - 8247 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Springer International Publishing
01.12.2024
Springer Nature B.V Springer |
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| ISSN: | 2199-4536, 2198-6053 |
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| Abstract | In recent years, the application of Neural Combinatorial Optimization (NCO) techniques in Combinatorial Optimization (CO) has emerged as a popular and promising research direction. Currently, there are mainly two types of NCO, namely, the Constructive Neural Combinatorial Optimization (CNCO) and the Perturbative Neural Combinatorial Optimization (PNCO). The CNCO generally trains an encoder-decoder model via supervised learning to construct solutions from scratch. It exhibits high speed in construction process, however, it lacks the ability for sustained optimization due to the one-shot mapping, which bounds its potential for application. Instead, the PNCO generally trains neural network models via deep reinforcement learning (DRL) to intelligently select appropriate human-designed heuristics to improve existing solutions. It can achieve high-quality solutions but at the cost of high computational demand. To leverage the strengths of both approaches, we propose to hybrid the CNCO and PNCO by designing a hybrid framework comprising two stages, in which the CNCO is the first stage and the PNCO is the second. Specifically, in the first stage, we utilize the attention model to generate preliminary solutions for given CO instances. In the second stage, we employ DRL to intelligently select and combine appropriate algorithmic components from improvement pool, perturbation pool, and prediction pool to continuously optimize the obtained solutions. Experimental results on synthetic and real Capacitated Vehicle Routing Problems (CVRPs) and Traveling Salesman Problems(TSPs) demonstrate the effectiveness of the proposed hybrid framework with the assistance of automated algorithm design. |
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| AbstractList | Abstract In recent years, the application of Neural Combinatorial Optimization (NCO) techniques in Combinatorial Optimization (CO) has emerged as a popular and promising research direction. Currently, there are mainly two types of NCO, namely, the Constructive Neural Combinatorial Optimization (CNCO) and the Perturbative Neural Combinatorial Optimization (PNCO). The CNCO generally trains an encoder-decoder model via supervised learning to construct solutions from scratch. It exhibits high speed in construction process, however, it lacks the ability for sustained optimization due to the one-shot mapping, which bounds its potential for application. Instead, the PNCO generally trains neural network models via deep reinforcement learning (DRL) to intelligently select appropriate human-designed heuristics to improve existing solutions. It can achieve high-quality solutions but at the cost of high computational demand. To leverage the strengths of both approaches, we propose to hybrid the CNCO and PNCO by designing a hybrid framework comprising two stages, in which the CNCO is the first stage and the PNCO is the second. Specifically, in the first stage, we utilize the attention model to generate preliminary solutions for given CO instances. In the second stage, we employ DRL to intelligently select and combine appropriate algorithmic components from improvement pool, perturbation pool, and prediction pool to continuously optimize the obtained solutions. Experimental results on synthetic and real Capacitated Vehicle Routing Problems (CVRPs) and Traveling Salesman Problems(TSPs) demonstrate the effectiveness of the proposed hybrid framework with the assistance of automated algorithm design. In recent years, the application of Neural Combinatorial Optimization (NCO) techniques in Combinatorial Optimization (CO) has emerged as a popular and promising research direction. Currently, there are mainly two types of NCO, namely, the Constructive Neural Combinatorial Optimization (CNCO) and the Perturbative Neural Combinatorial Optimization (PNCO). The CNCO generally trains an encoder-decoder model via supervised learning to construct solutions from scratch. It exhibits high speed in construction process, however, it lacks the ability for sustained optimization due to the one-shot mapping, which bounds its potential for application. Instead, the PNCO generally trains neural network models via deep reinforcement learning (DRL) to intelligently select appropriate human-designed heuristics to improve existing solutions. It can achieve high-quality solutions but at the cost of high computational demand. To leverage the strengths of both approaches, we propose to hybrid the CNCO and PNCO by designing a hybrid framework comprising two stages, in which the CNCO is the first stage and the PNCO is the second. Specifically, in the first stage, we utilize the attention model to generate preliminary solutions for given CO instances. In the second stage, we employ DRL to intelligently select and combine appropriate algorithmic components from improvement pool, perturbation pool, and prediction pool to continuously optimize the obtained solutions. Experimental results on synthetic and real Capacitated Vehicle Routing Problems (CVRPs) and Traveling Salesman Problems(TSPs) demonstrate the effectiveness of the proposed hybrid framework with the assistance of automated algorithm design. |
| Author | Hao, Xingxing Ma, Liang Zhou, Wei Chen, Li Zhang, Ruibang He, Qianbao |
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| Cites_doi | 10.1007/BF00992696 10.1287/ijoc.3.4.376 10.1109/TII.2020.3031409 10.1007/s40747-022-00884-6 10.1016/j.eswa.2022.119461 10.1007/s40747-021-00635-z 10.1007/s40747-021-00507-6 10.1016/j.ins.2023.119639 10.1016/j.eswa.2021.115493 10.1109/TITS.2019.2929020 10.1007/978-3-319-93031-2_12 10.1109/TG.2019.2942773 10.1109/TEVC.2022.3197298 10.1145/3583133.3596303 10.1109/MCI.2020.2976182 10.1007/s40747-021-00288-y 10.1016/j.ejor.2016.08.012 |
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| References_xml | – reference: Vinyals O, Fortunato M, Jaitly N (2015) Pointer networks. In: 2015 Neural information processing systems (NIPS), pp 2692-2700 – reference: Kingma D P, Ba J et al (2014) Adam: A method for stochastic optimization. In: 3rd International conference on learning representations (ICLR) arXiv preprint http://arxiv.org/abs/1412.6980 – reference: Hottung A, Tierney K (2019) Neural large neighborhood search for the capacitated vehicle routing problem. In: 24th European Conference on Artificial Intelligence (ECAI).arXiv preprint http://arxiv.org/abs/1911.09539 – reference: HelsgaunKeldAn extension of the lin-kernighan-helsgaun tsp solver for constrained traveling salesman and vehicle routing problems2017RoskildeRoskilde University – reference: Gurobi Optimization, LLC (2023) Gurobi Optimizer Reference Manual. https://www.gurobi.com – reference: David A, Ribert B, Vasek C et al (2006) Concorde tsp solver. http://www.math.uwaterloo.ca/tsp/concorde/ – reference: Chen X, Tian Y (2019) Learning to perform local rewriting for combinatorial optimization. 33rd Conference on Neural Information Processing Systems (NIPS). Vancouver, Canada, pp 6278–6289 – reference: VeresMMoussaMDeep learning for intelligent transportation systems: A survey of emerging trendsIEEE Trans Intell Trans Syst20192183152316810.1109/TITS.2019.2929020 – reference: LloydHAmosMSolving Sudoku with ant colony optimizationIEEE Trans Games201912330231110.1109/TG.2019.2942773 – reference: Xin L, Song W, Cao Z et al (2020) Step-wise deep learning models for solving routing problems. IEEE Trans Ind Inform 17(7):4861–4871 – reference: Schulman J, Wolski F, Dhariwal P et al (2017). Proximal policy optimization algorithms. arXiv preprint http://arxiv.org/abs/1707.06347 – reference: Liu F, Tong X, Yuan M, et al (2024) Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model. arXiv preprint arXiv:2401.02051V2 – reference: Luo F, Lin X, Liu F et al (2023) Neural combinatorial optimization with heavy decoder: Toward large scale generalization. arXiv preprint http://arxiv.org/abs/2310.07985 – reference: KimMParkJLearning collaborative policies to solve NP-hard routing problemsAdv Neural Inform Process Syst2021341041810430 – reference: Zhou C, Lin X, Wang Z, et al (2024) Instance-Conditioned Adaptation for Large-scale Generalization of Neural Combinatorial Optimization. arXiv preprint arXiv:2405.01906 – reference: ReineltGerhardTSPLIB-a traveling salesman problem libraryORSA J Comput19913437638410.1287/ijoc.3.4.376 – reference: HongLWoodwardJRÖzcanEHyper-heuristic approach: automatically designing adaptive mutation operators for evolutionary programmingComplex Intell Syst2021763135316310.1007/s40747-021-00507-6 – reference: LiSLuoTWangLTourism route optimization based on improved knowledge ant colony algorithmComplex Intell Syst2022853973398810.1007/s40747-021-00635-z – reference: Du Y, Fu T, Sun J, et al (2022) Molgensurvey: a systematic survey in machine learning models for molecule design. arXiv preprint http://arxiv.org/abs/2203.14500 – reference: Lu H, Zhang X, Yang S (2019) A learning-based iterative method for solving vehicle routing problems. In: 8th International conference on learning representations (ICLR) – reference: KwonYDChooJYoonIMatrix encoding networks for neural combinatorial optimizationAdv Neural Inform Process Syst20213451385149 – reference: Cheng H, Zheng H, Cong Y et al (2023) Select and Optimize: Learning to aolve large-scale TSP instances. In: 26th International Conference on Artificial Intelligence and Statistics 206:1219-1231 – reference: QuRKendallGPillayNThe General Combinatorial Optimization Problem: Towards Automated Algorithm DesignIEEE Comput Intell Mag2020152142310.1109/MCI.2020.2976182 – reference: WilliamsRJSimple statistical gradient-following algorithms for connectionist reinforcement learningMach Learn1992822925610.1007/BF00992696 – reference: Meng W, Qu R (2023) Sequential Rule Mining for Automated Design of Meta-heuristics. In: Proceedings of the Companion Conference on Genetic and Evolutionary Computation (GECCO). arXiv preprint https://doi.org/10.1145/3583133.3596303 – reference: XinLSongWCaoZMulti-decoder attention model with embedding glimpse for solving vehicle routing problemsProc AAAI Conf Artificial Intell202135131204212049 – reference: UchoaEPecinDPessoaANew benchmark instances for the capacitated vehicle routing problemEuro J Oper Res20172573845858357112710.1016/j.ejor.2016.08.012 – reference: YiWQuRAutomated design of search algorithms based on reinforcement learningInform Sci202364910.1016/j.ins.2023.119639 – reference: KwonYDChooJKimBPomo: Policy optimization with multiple optima for reinforcement learningAdv Neural Inform Process Syst2020332118821198 – reference: YiWQuRJiaoLAutomated design of metaheuristics using reinforcement learning within a novel general search frameworkIEEE Trans Evol Comput20232741072108410.1109/TEVC.2022.3197298 – reference: ZhongJFengYTangSA collaborative neurodynamic optimization algorithm to traveling salesman problemComplex Intell Syst2023921809182110.1007/s40747-022-00884-6 – reference: YiWQuRJiaoLAutomated algorithm design using proximal policy optimisation with identified featuresExpert Syst Appl202321610.1016/j.eswa.2022.119461 – reference: Chen X, Tian Y et al (2019) Learning to perform local rewriting for combinatorial optimization. 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| SubjectTerms | Algorithms Automated algorithm design Automation Combinatorial analysis Complexity Computational Intelligence Data Structures and Information Theory Deep learning Design optimization Encoders-Decoders Engineering Machine learning Neural combinatorial optimization Neural networks Optimization Original Article Reinforcement learning Supervised learning Transformer Traveling salesman problem Vehicle routing |
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| Title | A hybrid neural combinatorial optimization framework assisted by automated algorithm design |
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