电子学报 ›› 2022, Vol. 50 ›› Issue (2): 480-492.DOI: 10.12263/DZXB.20201154
蒋华伟1,2, 郭陶1,2, 杨震1,2
收稿日期:
2020-10-19
修回日期:
2021-01-30
出版日期:
2022-02-25
发布日期:
2022-02-25
作者简介:
基金资助:
JIANG Hua-wei1,2, GUO Tao1,2, YANG Zhen1,2
Received:
2020-10-19
Revised:
2021-01-30
Online:
2022-02-25
Published:
2022-02-25
摘要:
车辆路径作为经典的组合优化问题一直是研究的热点与难点,无论是在应急管理工作还是物流配送中,对它的合理规划都至关重要.为了今后更好地开展相关工作,本文回顾了精确算法、启发式算法和机器学习算法在车辆路径优化问题中的研究进展,并基于Solomon标准数据集对六种经典算法的求解性能进行了比较分析;分别从局部最优和收敛速度间的平衡关系、个体评价函数、动态车辆路径问题以及机器学习算法在车辆路径问题中的应用等四个方面对其发展趋势进行了展望.
中图分类号:
蒋华伟, 郭陶, 杨震. 车辆路径问题研究进展[J]. 电子学报, 2022, 50(2): 480-492.
JIANG Hua-wei, GUO Tao, YANG Zhen. Research Progress of Vehicle Routing Problem[J]. Acta Electronica Sinica, 2022, 50(2): 480-492.
VRP求解算法 | 优点 | 缺点 | 适用规模 | 参考来源 |
---|---|---|---|---|
分支定界法 | 不需要评价所有可能的可行解即可找到最优解 | 求解速率慢,适用性差 | 小规模VRP | Desrochers等[ 1992 |
列生成法 | 可求解大规模线性规划问题,具有较高的求解速度 | 只能求解线性松弛问题,子问题的求解速度较慢 | 较大规模VRP | Irnich等[ 2005 |
动态规划法 | 可利用实际知识和经验提高求解速率 | 没有统一的标准模型,数值方法求解时存在维数灾难 | 小规模VRP | Secomandi[ 2000 |
蚁群算法 | 鲁棒性强,具有内在并行性 | 收敛速度慢,易陷入局部最优,初始信息素匮乏 | 大规模VRP | 吴华锋等[ 2013 |
禁忌搜索算法 | 搜索速度快,局部“爬山”能力强 | 对初始解具有较强的依赖性 | 大规模VRP | 王燕等[ 2018 |
SOM神经 网络 | 既可以学习训练数据输入向量的分布特征,也可以学习训练数据输入向量数据的拓扑结构 | 收敛速度慢,泛化性能低 | 大规模动态VRP | Ghaziri等[ 2006 |
强化学习 | 通过智能体与环境的交互可反复学习行为 | 维数灾难 | 大规模动态VRP | Sutton等[ 1998 |
表1 启发式算法及其优缺点比较
VRP求解算法 | 优点 | 缺点 | 适用规模 | 参考来源 |
---|---|---|---|---|
分支定界法 | 不需要评价所有可能的可行解即可找到最优解 | 求解速率慢,适用性差 | 小规模VRP | Desrochers等[ 1992 |
列生成法 | 可求解大规模线性规划问题,具有较高的求解速度 | 只能求解线性松弛问题,子问题的求解速度较慢 | 较大规模VRP | Irnich等[ 2005 |
动态规划法 | 可利用实际知识和经验提高求解速率 | 没有统一的标准模型,数值方法求解时存在维数灾难 | 小规模VRP | Secomandi[ 2000 |
蚁群算法 | 鲁棒性强,具有内在并行性 | 收敛速度慢,易陷入局部最优,初始信息素匮乏 | 大规模VRP | 吴华锋等[ 2013 |
禁忌搜索算法 | 搜索速度快,局部“爬山”能力强 | 对初始解具有较强的依赖性 | 大规模VRP | 王燕等[ 2018 |
SOM神经 网络 | 既可以学习训练数据输入向量的分布特征,也可以学习训练数据输入向量数据的拓扑结构 | 收敛速度慢,泛化性能低 | 大规模动态VRP | Ghaziri等[ 2006 |
强化学习 | 通过智能体与环境的交互可反复学习行为 | 维数灾难 | 大规模动态VRP | Sutton等[ 1998 |
算法 | 最好解/km | 最差解/km | 平均解/km | 平均运算时间/s | 偏差 /% | 求解次数/次 |
---|---|---|---|---|---|---|
BAC | 828.94 | ― | ― | 25.2 | 0 | 10 |
CG | 828.94 | ― | ― | 23.7 | 0 | 10 |
ACA | 851.46 | 921.49 | 877.21 | 15.1 | 2.7 | 10 |
TS | 855.37 | 936.32 | 893.27 | 13.8 | 3.2 | 10 |
SOM | 847.22 | 858.09 | 852.16 | 3.3 | 2.2 | 10 |
RL | 846.82 | 861.51 | 856.47 | 3.6 | 2.1 | 10 |
表2 六种算法所求解对比
算法 | 最好解/km | 最差解/km | 平均解/km | 平均运算时间/s | 偏差 /% | 求解次数/次 |
---|---|---|---|---|---|---|
BAC | 828.94 | ― | ― | 25.2 | 0 | 10 |
CG | 828.94 | ― | ― | 23.7 | 0 | 10 |
ACA | 851.46 | 921.49 | 877.21 | 15.1 | 2.7 | 10 |
TS | 855.37 | 936.32 | 893.27 | 13.8 | 3.2 | 10 |
SOM | 847.22 | 858.09 | 852.16 | 3.3 | 2.2 | 10 |
RL | 846.82 | 861.51 | 856.47 | 3.6 | 2.1 | 10 |
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