As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in mult...As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(VRP-mmD).The problem aims at making schedules for the trucks and drones such that the total travel time is minimized.This paper formulate the problem with a mixed integer program-ming model and propose a two-phase algorithm,i.e.,a parallel route construction heuristic(PRCH)for the first phase and an adaptive neighbor searching heuristic(ANSH)for the second phase.The PRCH generates an initial solution by con-currently assigning as many nodes as possible to the truck–drone pair to progressively reduce the waiting time at the rendezvous node in the first phase.Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase.Numerical tests on some benchmark data are conducted to verify the performance of the algorithm.The results show that the proposed algorithm can found better solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.展开更多
The multi-compartment electric vehicle routing problem(EVRP)with soft time window and multiple charging types(MCEVRP-STW&MCT)is studied,in which electric multi-compartment vehicles that are environmentally friendl...The multi-compartment electric vehicle routing problem(EVRP)with soft time window and multiple charging types(MCEVRP-STW&MCT)is studied,in which electric multi-compartment vehicles that are environmentally friendly but need to be recharged in course of transport process,are employed.A mathematical model for this optimization problem is established with the objective of minimizing the function composed of vehicle cost,distribution cost,time window penalty cost and charging service cost.To solve the problem,an estimation of the distribution algorithm based on Lévy flight(EDA-LF)is proposed to perform a local search at each iteration to prevent the algorithm from falling into local optimum.Experimental results demonstrate that the EDA-LF algorithm can find better solutions and has stronger robustness than the basic EDA algorithm.In addition,when comparing with existing algorithms,the result shows that the EDA-LF can often get better solutions in a relatively short time when solving medium and large-scale instances.Further experiments show that using electric multi-compartment vehicles to deliver incompatible products can produce better results than using traditional fuel vehicles.展开更多
The time dependent vehicle routing problem with time windows（TDVRPTW） is considered. A multi-type ant system（MTAS） algorithm hybridized with the ant colony system（ACS）and the max-min ant system（MMAS） algorithm...The time dependent vehicle routing problem with time windows（TDVRPTW） is considered. A multi-type ant system（MTAS） algorithm hybridized with the ant colony system（ACS）and the max-min ant system（MMAS） algorithms is proposed. This combination absorbs the merits of the two algorithms in solutions construction and optimization separately. In order to improve the efficiency of the insertion procedure, a nearest neighbor selection（NNS） mechanism, an insertion local search procedure and a local optimization procedure are specified in detail. And in order to find a balance between good scouting performance and fast convergence rate, an adaptive pheromone updating strategy is proposed in the MTAS. Computational results confirm the MTAS algorithm＇s good performance with all these strategies on classic vehicle routing problem with time windows（VRPTW） benchmark instances and the TDVRPTW instances, and some better results especially for the number of vehicles and travel times of the best solutions are obtained in comparison with the previous research.展开更多
The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency...The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.展开更多
This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the ...This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the total distance. This problem exists widely in real-life logistics distribution process.We propose a hybrid column generation algorithm(HCGA) for the OVRPTW, embedding both exact algorithm and metaheuristic. In HCGA, a label setting algorithm and an intelligent algorithm are designed to select columns from small and large subproblems, respectively. Moreover, a branch strategy is devised to generate the final feasible solution for the OVRPTW. The computational results show that the proposed algorithm has faster speed and can obtain the approximate optimal solution of the problem with 100 customers in a reasonable time.展开更多
The vehicle routing problem (VRP) can be described as the problem of designing the optimal delivery or collection routes from one or several depots to a number of geographically scattered customers, subject to load co...The vehicle routing problem (VRP) can be described as the problem of designing the optimal delivery or collection routes from one or several depots to a number of geographically scattered customers, subject to load constraints. The routing decision involves determining which of the demand s will be satisfied by each vehicle and what route each vehicle will follow in s erving its assigned demand in order to minimize total delivery cost. In this pap er, a methodology for the design of VRP by integrating optimization and simulate d annealing (SA) approach is presented hierarchically. To express the problem of vehicle routing, a new mathematical formulation is first conducted. The objecti ve function involves both the delivery cost and the vehicle acquisition cost wit h load constraints. A heuristic is then proposed to solve this problem by using SA procedure in conjunction with any solution procedure of travelling salesman p roblem (TSP). The initial configuration is arranged as one vehicle route ser ving one customer. The SA searching procedure is then developed to combine custo mer to any one of the vehicle routes existed in the system if the capacity and c ost are attractive. An important concept of this proposed heuristic is that it attempts to minimize total number of vehicle required in the system on the b asis of the fixed cost and the variable cost view points. In addition, this appr oach can be easily adapted to accommodate many additional problem complexities.展开更多
The route optimization problem for road networks was applied to pedestrian flow.Evacuation path networks with nodes and arcs considering the traffic capacities of facilities were built in metro hubs,and a path impedan...The route optimization problem for road networks was applied to pedestrian flow.Evacuation path networks with nodes and arcs considering the traffic capacities of facilities were built in metro hubs,and a path impedance function for metro hubs which used the relationships among circulation speed,density and flow rate for pedestrians was defined.Then,a route optimization model which minimizes the movement time of the last evacuee was constructed to optimize evacuation performance.Solutions to the proposed mathematical model were obtained through an iterative optimization process.The route optimization model was applied to Xidan Station of Beijing Metro Line 4 based on the actual situations,and the calculation results of the model were tested using buildingExodus microscopic evacuation simulation software.The simulation result shows that the proposed model shortens the evacuation time by 16.05%,3.15% and 2.78% compared with all or none method,equally split method and Logit model,respectively.Furthermore,when the population gets larger,evacuation efficiency in the proposed model has a greater advantage.展开更多
文摘As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(VRP-mmD).The problem aims at making schedules for the trucks and drones such that the total travel time is minimized.This paper formulate the problem with a mixed integer program-ming model and propose a two-phase algorithm,i.e.,a parallel route construction heuristic(PRCH)for the first phase and an adaptive neighbor searching heuristic(ANSH)for the second phase.The PRCH generates an initial solution by con-currently assigning as many nodes as possible to the truck–drone pair to progressively reduce the waiting time at the rendezvous node in the first phase.Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase.Numerical tests on some benchmark data are conducted to verify the performance of the algorithm.The results show that the proposed algorithm can found better solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.
基金supported by the National Natural Science Foundation of China(71571076)the National Key R&D Program for the 13th-Five-Year-Plan of China(2018YFF0300301).
文摘The multi-compartment electric vehicle routing problem(EVRP)with soft time window and multiple charging types(MCEVRP-STW&MCT)is studied,in which electric multi-compartment vehicles that are environmentally friendly but need to be recharged in course of transport process,are employed.A mathematical model for this optimization problem is established with the objective of minimizing the function composed of vehicle cost,distribution cost,time window penalty cost and charging service cost.To solve the problem,an estimation of the distribution algorithm based on Lévy flight(EDA-LF)is proposed to perform a local search at each iteration to prevent the algorithm from falling into local optimum.Experimental results demonstrate that the EDA-LF algorithm can find better solutions and has stronger robustness than the basic EDA algorithm.In addition,when comparing with existing algorithms,the result shows that the EDA-LF can often get better solutions in a relatively short time when solving medium and large-scale instances.Further experiments show that using electric multi-compartment vehicles to deliver incompatible products can produce better results than using traditional fuel vehicles.
文摘The time dependent vehicle routing problem with time windows（TDVRPTW） is considered. A multi-type ant system（MTAS） algorithm hybridized with the ant colony system（ACS）and the max-min ant system（MMAS） algorithms is proposed. This combination absorbs the merits of the two algorithms in solutions construction and optimization separately. In order to improve the efficiency of the insertion procedure, a nearest neighbor selection（NNS） mechanism, an insertion local search procedure and a local optimization procedure are specified in detail. And in order to find a balance between good scouting performance and fast convergence rate, an adaptive pheromone updating strategy is proposed in the MTAS. Computational results confirm the MTAS algorithm＇s good performance with all these strategies on classic vehicle routing problem with time windows（VRPTW） benchmark instances and the TDVRPTW instances, and some better results especially for the number of vehicles and travel times of the best solutions are obtained in comparison with the previous research.
基金Project(50775089)supported by the National Natural Science Foundation of ChinaProject(2007AA04Z190,2009AA043301)supported by the National High Technology Research and Development Program of ChinaProject(2005CB724100)supported by the National Basic Research Program of China
文摘The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.
基金supported by the National Natural Science Foundation of China (61963022,51665025,61873328)。
文摘This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the total distance. This problem exists widely in real-life logistics distribution process.We propose a hybrid column generation algorithm(HCGA) for the OVRPTW, embedding both exact algorithm and metaheuristic. In HCGA, a label setting algorithm and an intelligent algorithm are designed to select columns from small and large subproblems, respectively. Moreover, a branch strategy is devised to generate the final feasible solution for the OVRPTW. The computational results show that the proposed algorithm has faster speed and can obtain the approximate optimal solution of the problem with 100 customers in a reasonable time.
文摘The vehicle routing problem (VRP) can be described as the problem of designing the optimal delivery or collection routes from one or several depots to a number of geographically scattered customers, subject to load constraints. The routing decision involves determining which of the demand s will be satisfied by each vehicle and what route each vehicle will follow in s erving its assigned demand in order to minimize total delivery cost. In this pap er, a methodology for the design of VRP by integrating optimization and simulate d annealing (SA) approach is presented hierarchically. To express the problem of vehicle routing, a new mathematical formulation is first conducted. The objecti ve function involves both the delivery cost and the vehicle acquisition cost wit h load constraints. A heuristic is then proposed to solve this problem by using SA procedure in conjunction with any solution procedure of travelling salesman p roblem (TSP). The initial configuration is arranged as one vehicle route ser ving one customer. The SA searching procedure is then developed to combine custo mer to any one of the vehicle routes existed in the system if the capacity and c ost are attractive. An important concept of this proposed heuristic is that it attempts to minimize total number of vehicle required in the system on the b asis of the fixed cost and the variable cost view points. In addition, this appr oach can be easily adapted to accommodate many additional problem complexities.
基金Project(51078086)supported by the National Natural Science Foundation of China
文摘The route optimization problem for road networks was applied to pedestrian flow.Evacuation path networks with nodes and arcs considering the traffic capacities of facilities were built in metro hubs,and a path impedance function for metro hubs which used the relationships among circulation speed,density and flow rate for pedestrians was defined.Then,a route optimization model which minimizes the movement time of the last evacuee was constructed to optimize evacuation performance.Solutions to the proposed mathematical model were obtained through an iterative optimization process.The route optimization model was applied to Xidan Station of Beijing Metro Line 4 based on the actual situations,and the calculation results of the model were tested using buildingExodus microscopic evacuation simulation software.The simulation result shows that the proposed model shortens the evacuation time by 16.05%,3.15% and 2.78% compared with all or none method,equally split method and Logit model,respectively.Furthermore,when the population gets larger,evacuation efficiency in the proposed model has a greater advantage.
