基于深度强化学习的组合优化研究进展

李凯文; 张涛; 王锐; 覃伟健; 贺惠晖; 黄鸿

doi:10.16383/j.aas.c200551

基于深度强化学习的组合优化研究进展

doi: 10.16383/j.aas.c200551

李凯文^{1, 2,},
张涛^{1, 2,},
王锐^{1, 2,},
覃伟健^{1, 2,},
贺惠晖^{1, 2,},
黄鸿^{1, 2,}

1.
国防科技大学系统工程学院长沙 410073
2.
多能源系统智慧互联技术湖南省重点实验室长沙 410073

基金项目: 国家自然科学基金面上项目(61773390), 湖湘青年英才计划(2018RS3081), 科技委国防创新特区项目(193-A11-101-03-01), 国防科技大学自主科研计划(ZZKY-ZX-11-04)资助

详细信息

作者简介:
李凯文：国防科技大学系统工程学院博士研究生. 主要研究方向为能源互联网技术, 深度强化学习与优化技术. E-mail: likaiwen@nudt.edu.cn

张涛：国防科技大学系统工程学院教授. 主要研究方向为能源互联网技术, 基于计算智能的优化与决策技术. E-mail: zhangtao@nudt.edu.cn

王锐：国防科技大学系统工程学院副研究员. 主要研究方向为能源互联网技术, 计算智能理论与方法, 多目标进化算法. 本文通信作者. E-mail: ruiwangnudt@gmail.com

覃伟健：国防科技大学系统工程学院硕士研究生. 主要研究方向为能源互联网技术, 深度强化学习与优化技术. E-mail: qinweijian@nudt.edu.cn

贺惠晖：国防科技大学系统工程学院硕士研究生. 主要研究方向为能源互联网技术, 基于计算智能的优化与决策技术. E-mail: hehuihui@nudt.edu.cn

黄鸿：国防科技大学系统工程学院硕士研究生. 主要研究方向为能源互联网技术, 基于计算智能的优化与决策技术. E-mail: huanghong@nudt.edu.cn

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出版历程
- 收稿日期: 2020-07-14
- 录用日期: 2020-11-04
- 网络出版日期: 2020-12-10
- 刊出日期: 2021-11-18

Research Reviews of Combinatorial Optimization Methods Based on Deep Reinforcement Learning

LI Kai-Wen^{1, 2
,},
ZHANG Tao^{1, 2
,},
WANG Rui^{1, 2
,},
QIN Wei-Jian^{1, 2
,},
HE Hui-Hui^{1, 2
,},
HUANG Hong^{1, 2
,}

1.
College of System Engineering, National University of Defense Technology, Changsha 410073
2.
Hunan Key Laboratory of Multi-Energy System Intelligent Interconnection Technology, Changsha 410073

Funds: Supported by National Natural Science Foundation of China (61773390), the Hunan Youth Elite Program (2018RS3081), the National Defense Innovation Zone Project of Science and Technology Committee (193-A11-101-03-01), and the Scientific Project of National University of Defense Technology (ZZKY-ZX-11-04)

More Information

Author Bio:
LI Kai-Wen　Ph. D. candidate at College of System Engineering, National University of Defense Technology. His research interest covers energy internet technology, deep reinforcement learning and optimization

ZHANG Tao　Professor at College of System Engineering, National University of Defense Technology. His research interest covers energy internet technology, optimization and decision making based on computational intelligence

WANG Rui　Associate professor at College of System Engineering, National University of Defense Technology. His research interest covers energy internet technology, computational intelligence methodologies, multi-objective evolutionary optimizations. Corresponding author of this paper

QIN Wei-Jian　Master student at College of System Engineering, National University of Defense Technology. His research interest covers energy internet technology, deep reinforcement learning and optimization

HE Hui-Hui　Master student at College of System Engineering, National University of Defense Technology. His research interest covers energy internet technology, optimization and decision making based on computational intelligence

HUANG Hong　Master student at College of System Engineering, National University of Defense Technology. His research interest covers energy internet technology, optimization and decision making based on computational intelligence

摘要

摘要: 组合优化问题广泛存在于国防、交通、工业、生活等各个领域, 几十年来, 传统运筹优化方法是解决组合优化问题的主要手段, 但随着实际应用中问题规模的不断扩大、求解实时性的要求越来越高, 传统运筹优化算法面临着很大的计算压力, 很难实现组合优化问题的在线求解. 近年来随着深度学习技术的迅猛发展, 深度强化学习在围棋、机器人等领域的瞩目成果显示了其强大的学习能力与序贯决策能力. 鉴于此, 近年来涌现出了多个利用深度强化学习方法解决组合优化问题的新方法, 具有求解速度快、模型泛化能力强的优势, 为组合优化问题的求解提供了一种全新的思路. 因此本文总结回顾近些年利用深度强化学习方法解决组合优化问题的相关理论方法与应用研究, 对其基本原理、相关方法、应用研究进行总结和综述, 并指出未来该方向亟待解决的若干问题.
- 深度强化学习 /
- 组合优化问题 /
- 深度神经网络 /
- 图神经网络 /
- 指针网络
Abstract: Combinatorial optimization problems widely exist in various fields such as national defense, transportation, industry and life. For decades, traditional operational research methods are the main means to solve combinatorial optimization problems. However, with the increase of problem size in practical applications and the increasing demands for real-time optimization, traditional methods suffer from great computational burdens, and it is difficult to realize the online solution of combinatorial optimization problems. In recent years, with the rapid development of deep learning technology, the achievements of deep reinforcement learning in AlphaGo, robot and other fields show its strong learning ability and sequential decision-making ability. In view of this, in recent years, a number of new methods using deep reinforcement learning to solve combinatorial optimization problems have emerged, which have the advantages of fast solving speed and strong model generalization ability. It provides a new idea for solving combinatorial optimization problems. Therefore, this paper summarizes and reviews the theoretical methods and application researches of this kind of methods in recent years.
- Deep reinforcement learning /
- combinatorial optimization problems /
- deep neural network /
- graph neural networks /
- pointer networks

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图 1 Pointer network模型示意图

Fig. 1 Schematic diagram of pointer network model

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表 1 现有算法模型、训练方法、求解问题、以及优化效果比较

Table 1 Comparison of model, training method, solving problems and performance with existing algorithms

方法类别	研究	模型以及训练方法	求解问题及优化效果
基于 Pointer network 的端到端方法	2015 年 Vinyals 等^[30]	Ptr-Net + 监督式训练	30 TSP问题: 接近最优解, 优于启发式算法. 40, 50-TSP: 与最优解存在一定差距. 凸包问题、三角剖分问题.
	2017 年 Bello 等^[31]	Ptr-Net + REINFORCE & Critic baseline	50-TSP: 优于文献 [30]. 100-TSP: 接近 Concorde 最优解. 200-Knapsack: 达到最优解.
	2018 年 Nazari 等^[32]	Ptr-Net + REINFORCE & Critic baseline	100-TSP: 与文献 [31]优化效果相近, 训练时间降低约60 %. 100-CVRP/随机CVRP: 优于多个启发式算法.
	2018 年 Deudon 等^[33]	Transformer attention + REINFORCE & Critic baseline	20, 50-TSP: 优于文献 [31]. 100-TSP: 与文献 [31]优化效果相近.
	2019 年 Kool 等^[34]	Transformer attention + REINFORCE & Rollout baseline	100-TSP: 优于文献 [30-33, 37, 40]. 100-CVRP、100-SDVRP、100-OP、100-PCTSP、SPCTSP: 接近 Gurobi 最优解, 优于多种启发式方法.
	2020 年 Ma 等^[35]	Graph pointer network + HRL	20, 50-TSP: 优于文献 [31, 37], 劣于文献 [34]. 250, 500, 1000-TSP: 优于文献 [31, 34]. 20-TSPTW: 优于OR-Tools、蚁群算法.
	2021 年 Li 等^[36]	Ptr-Net + REINFORCE & Critic baseline & 分解策略/参数迁移	40, 100, 150, 200, 500-两目标/三目标TSP : 优于 MOEA/D、NSGA-II、MOGLS.
基于图神经网络的端到端方法	2017 年 Dai 等^[37]	structure2vec + DQN	1200-TSP: 接近文献 [31]. 1200-MVC (最小顶点覆盖): 接近最优解. 1200-MAXCUT (最大割集): 接近最优解.
	2020 年 Manchanda 等^[38]	GCN + DQN	2k至20k-MCP (最大覆盖问题): 优于文献 [37]. 10k, 20k, 50k-MVC: 优于文献 [37].
	2018 年 Li 等^[39]	GCN + 监督式训练 + 引导树搜索	实际数据集 MVC、MIS (最大独立点集)、MC (极大团)、 Satisfiability (适定性问题): 优于文献 [37].
	2017 年 Nowak 等^[40]	GNN + 监督式训练 + 波束搜索	20-TSP: 劣于文献 [30].
	2019 年 Joshi 等^[41]	GCN + 监督式训练 + 波束搜索	20, 50, 100-TSP: 略微优于文献 [30-31, 33-34], 优于文献 [37].
深度强化学习改进的局部搜索方法	2019 年 Chen 等^[47]	Ptr-Net + Actor-critic	20-CVRP: 达到最优解. 50, 100-CVRP: 优于文献 [32, 34]、OR-Tools. 作业车间调度: 优于OR-Tools、DeepRM.
	2019 年 Yolcu 等^[48]	GNN + REINFORCE	实际数据集 Satisfiability、MIS、MVC、MC、图着色问题: 更少搜索步数得到最优解、但单步运行时间长于传统算法.
	2020 年 Gao 等^[49]	Graph attention + PPO	100-CVPR: 优于文献 [34]. 100-CVPRTW: 优于多个启发式方法. 400-CVRPTW: 劣于单个启发式方法, 优于其他.
	2020 年 Lu 等^[50]	Transformer attention + REINFORCE	20, 50, 100-CVRP: 优于文献 [32, 34, 47], 以及优于 OR Tools、 LKH3. 且运行时间远低于 LKH3.

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表 2 端到端模型在TSP问题上优化性能比较

Table 2 Comparison of end-to-end model on TSP

方法类别	模型	TSP-20	TSP-50	TSP-100
最优	Concorde	3.84	5.70	7.76
基于指针网络 (Attention 机制)	Vinyals 等^[30]	3.88	7.66	—
	Bello 等^[31]	3.89	5.95	8.30
	Nazari 等^[32]	3.97	6.08	8.44
	Deudon 等^[33]	3.86	5.81	8.85
	Deudon 等^[33] + 2OPT	3.85	5.85	8.17
	Kool 等^[34] (Greedy)	3.85 (0 s)	5.80 (2 s)	8.12 (6 s)
	Kool 等^[34] (Sampling)	3.84 (5 m)	5.73 (24 m)	7.94 (1 h)
基于图神经网络	Dai 等^[37]	3.89	5.99	8.31
	Nowak 等^[40]	3.93	—	—
	Joshi 等^[41] (Greedy)	3.86 (6 s)	5.87 (55 s)	8.41 (6 m)
	Joshi 等^[41] (BS)	3.84 (12 m)	5.70 (18 m)	7.87 (40 m)

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表 3 多个模型在VRP问题上优化性能比较

Table 3 Comparison of models on VRP

模型	VRP-20	VRP-50	VRP-100
LKH3	6.14 (2 h)	10.38 (7 h)	15.65 (13 h)
Nazari 等^[32]	6.40	11.15	16.96
Kool 等^[34] (Greedy)	6.40 (1 s)	10.98 (3 s)	16.80 (8 s)
Kool 等^[34] (Sampling)	6.25 (6 m)	10.62 (28 m)	16.23 (2 h)
Chen 等^[47]	6.12	10.51	16.10
Lu 等^[50]	6.12 (12 m)	10.35 (17 m)	15.57 (24 m)

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表 4 不同组合优化问题求解算法统计与比较

Table 4 Summary and comparison of algorithms on different combinatorial optimization problems

组合优化问题	文献	模型细节
TSP 问题	[30–36]	基于 Ptr-Net 架构 (Encoder-decoder-attention)
	[37]	GNN + DQN
	[40–41]	GNN + 监督式训练 + 波束搜索
VRP 问题	[32, 34]	基于Ptr-Net 架构 (Encoder- decoder-attention)
VRP 问题	[47, 49–50]	DRL 训练局部搜索算子. [47]: Ptr-Net 模型, [49]: Graph attention 模型, [50]: Transformer attention 模型.
最小顶点覆盖问题(MVC)	[37–38, 48]	GNN + RL
最小顶点覆盖问题(MVC)	[39]	GNN + 监督式训练 + 树搜索
最大割集问题(MaxCut)	[37]	GNN + DQN
	[57]	Message passing neural network (MPNN) + DQN
	[58] ^*	CNN&RNN + PPO
适定性问题(Satisfiability)	[39, 48]	GNN + 监督式训练/RL
最小支配集问题 (MDS)	[48]	GNN + RL
最小支配集问题 (MDS)	[59] ^*	Decision diagram + RL
极大团问题 (MC)	[39, 48]	GNN + 监督式训练/RL
最大独立集问题 (MIS)	[39]	GNN + 监督式训练 + 树搜索
最大独立集问题 (MIS)	[60] ^*	GNN + RL + 蒙特卡洛树搜索
背包问题 (Knapsack)	[31]	Ptr-Net + RL
车间作业调度问题	[47]	LSTM + RL 训练局部搜索算子
装箱问题 (BPP)	[61] ^*	LSTM + RL
装箱问题 (BPP)	[62] ^*	NN + RL + 蒙特卡洛树搜索
图着色问题	[48]	GNN + RL
图着色问题	[63] ^*	LSTM + RL + 蒙特卡洛树搜索

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