In this work,we investigate a generalization of the classical capacitated arc routing problem,called the Multi-depot Capacitated Arc Routing Problem(MCARP).We give exact and approximation algorithms for different vari...In this work,we investigate a generalization of the classical capacitated arc routing problem,called the Multi-depot Capacitated Arc Routing Problem(MCARP).We give exact and approximation algorithms for different variants of the MCARP.First,we obtain the first constant-ratio approximation algorithms for the MCARP and its nonfixed destination version.Second,for the multi-depot rural postman problem,i.e.,a special case of the MCARP where the vehicles have infinite capacity,we develop a(2-1/2k+1)-approximation algorithm(k denotes the number of depots).Third,we show the polynomial solvability of the equal-demand MCARP on a line and devise a 2-approximation algorithm for the multi-depot capacitated vehicle routing problem on a line.Lastly,we conduct extensive numerical experiments on the algorithms for the multi-depot rural postman problem to show their effectiveness.展开更多
The multi-depot vehicle routing problem(MDVRP)is one of the most essential and useful variants of the traditional vehicle routing problem(VRP)in supply chain management(SCM)and logistics studies.Many supply chains(SC)...The multi-depot vehicle routing problem(MDVRP)is one of the most essential and useful variants of the traditional vehicle routing problem(VRP)in supply chain management(SCM)and logistics studies.Many supply chains(SC)choose the joint distribution of multiple depots to cut transportation costs and delivery times.However,the ability to deliver quality and fast solutions for MDVRP remains a challenging task.Traditional optimization approaches in operation research(OR)may not be practical to solve MDVRP in real-time.With the latest developments in artificial intelligence(AI),it becomes feasible to apply deep reinforcement learning(DRL)for solving combinatorial routing problems.This paper proposes a new multi-agent deep reinforcement learning(MADRL)model to solve MDVRP.Extensive experiments are conducted to evaluate the performance of the proposed approach.Results show that the developed MADRL model can rapidly capture relative information embedded in graphs and effectively produce quality solutions in real-time.展开更多
针对多仓库异质车队带时间窗的车辆路径问题(Multi-Depot Heterogeneous Fleet Vehicle Routing Problem with Time Windows,MDHFVRPTW),以车辆数费用和物流成本最小为目标,综合客户需求、时间约束等因素构建数学模型,并提出改进智能水...针对多仓库异质车队带时间窗的车辆路径问题(Multi-Depot Heterogeneous Fleet Vehicle Routing Problem with Time Windows,MDHFVRPTW),以车辆数费用和物流成本最小为目标,综合客户需求、时间约束等因素构建数学模型,并提出改进智能水滴算法(Improved Intelligent Waterdrop Algorithm,IIWD)求解。引入大邻域搜索方法及模拟退火可接受概率准则,重新定义了算法的水滴路径,有效优化智能水滴算法的局部搜索能力。Cordeau标准测试算例和实际算例的求解结果显示,算法在寻优能力上较其他算法更强,求解时间也有明显提升,充分验证了算法的有效性与可行性。展开更多
基金supported by the National Natural Science Foundation of China(Nos.11671135,11871213,11901255)the Natural Science Foundation of Shanghai(No.19ZR1411800)。
文摘In this work,we investigate a generalization of the classical capacitated arc routing problem,called the Multi-depot Capacitated Arc Routing Problem(MCARP).We give exact and approximation algorithms for different variants of the MCARP.First,we obtain the first constant-ratio approximation algorithms for the MCARP and its nonfixed destination version.Second,for the multi-depot rural postman problem,i.e.,a special case of the MCARP where the vehicles have infinite capacity,we develop a(2-1/2k+1)-approximation algorithm(k denotes the number of depots).Third,we show the polynomial solvability of the equal-demand MCARP on a line and devise a 2-approximation algorithm for the multi-depot capacitated vehicle routing problem on a line.Lastly,we conduct extensive numerical experiments on the algorithms for the multi-depot rural postman problem to show their effectiveness.
文摘The multi-depot vehicle routing problem(MDVRP)is one of the most essential and useful variants of the traditional vehicle routing problem(VRP)in supply chain management(SCM)and logistics studies.Many supply chains(SC)choose the joint distribution of multiple depots to cut transportation costs and delivery times.However,the ability to deliver quality and fast solutions for MDVRP remains a challenging task.Traditional optimization approaches in operation research(OR)may not be practical to solve MDVRP in real-time.With the latest developments in artificial intelligence(AI),it becomes feasible to apply deep reinforcement learning(DRL)for solving combinatorial routing problems.This paper proposes a new multi-agent deep reinforcement learning(MADRL)model to solve MDVRP.Extensive experiments are conducted to evaluate the performance of the proposed approach.Results show that the developed MADRL model can rapidly capture relative information embedded in graphs and effectively produce quality solutions in real-time.
文摘针对多仓库异质车队带时间窗的车辆路径问题(Multi-Depot Heterogeneous Fleet Vehicle Routing Problem with Time Windows,MDHFVRPTW),以车辆数费用和物流成本最小为目标,综合客户需求、时间约束等因素构建数学模型,并提出改进智能水滴算法(Improved Intelligent Waterdrop Algorithm,IIWD)求解。引入大邻域搜索方法及模拟退火可接受概率准则,重新定义了算法的水滴路径,有效优化智能水滴算法的局部搜索能力。Cordeau标准测试算例和实际算例的求解结果显示,算法在寻优能力上较其他算法更强,求解时间也有明显提升,充分验证了算法的有效性与可行性。
