Stochastic vehicle routing problems ( VRPs) play important roles in logistics, though they have not been studied systematically yet. The paper summaries the definition, properties and classification of stochastic VRPs...Stochastic vehicle routing problems ( VRPs) play important roles in logistics, though they have not been studied systematically yet. The paper summaries the definition, properties and classification of stochastic VRPs, makes further discussion about two strategies in stochastic VRPs, and at last overviews dynamic and stochastic VRPs.展开更多
In the context of the COVID-19 epidemic,a"double-hazard scenario"consisting of a natural disaster and a public health event simultaneously accurring is more likely to arise.However,compared with single-hazar...In the context of the COVID-19 epidemic,a"double-hazard scenario"consisting of a natural disaster and a public health event simultaneously accurring is more likely to arise.However,compared with single-hazard,multiple disasters confront the challenges of complexity,diversity,and demand urgency.To improve the efficiency of emergency material distribution under multiple disasters,this study first divided multiple disasters into three categoriles:independent scenario,sequential scenario,and coupling scenario.A set of evaluation index systems for multiple disasters was established to quantify the urgency of demand.The routing optimization model of emergency vehicles for multiple disasters was proposed by combining demand urgency and road damage,and the non-dominated sorting genetic algorithm II(NSGA-I)was used to simulate and validate the model.A coupling scenario considering two typical disasters of hurricanes and epidemics was selected as a validation example,and sensitivity analysis was also performed for different algorithms,scenarios,and constraints.The results demonstrated that the proposed model could effectively address the vehicle routing problem of emer-gency materials in the context of multiple disasters.Compared to the NSGA,the NSGA-II was used to reduce the total delivery time,cost,and penalty cost by 15.98%6,13.60%,and 16.14%,respectively.Compared with the independent scenario,the coupling scenario increased the total delivery time and cost by 186.28%and 132.48%during the epidemic.However,it reduced the total delivery time by 4.00%and increased the delivery cost by 23.55%compared with the hurricane.Compared with the model without consideration,the model considering demand urgency and road damage reduced the total delivery time and cost by 17.88%and 8.73%,respectively.The model constructed in this study addressed the vehicle routing problem considering the demand urgency and road damage in the optimization process,particularly in the context of multiple disasters.展开更多
We propose a multi-crossover and adaptive island based population algorithm(MAIPA).This technique divides the entire population into subpopulations,or demes,each with a different crossover function,which can be switch...We propose a multi-crossover and adaptive island based population algorithm(MAIPA).This technique divides the entire population into subpopulations,or demes,each with a different crossover function,which can be switched according to the efficiency.In addition,MAIPA reverses the philosophy of conventional genetic algorithms.It gives priority to the autonomous improvement of the individuals(at the mutation phase),and introduces dynamism in the crossover probability.Each subpopulation begins with a very low value of crossover probability,and then varies with the change of the current generation number and the search performance on recent generations.This mechanism helps prevent premature convergence.In this research,the effectiveness of this technique is tested using three well-known routing problems,i.e.,the traveling salesman problem(TSP),capacitated vehicle routing problem(CVRP),and vehicle routing problem with backhauls(VRPB).MAIPA proves to be better than a traditional island based genetic algorithm for all these three problems.展开更多
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
Unmanned Aerial Vehicle(UAV)stands as a burgeoning electric transportation carrier,holding substantial promise for the logistics sector.A reinforcement learning framework Centralized-S Proximal Policy Optimization(C-S...Unmanned Aerial Vehicle(UAV)stands as a burgeoning electric transportation carrier,holding substantial promise for the logistics sector.A reinforcement learning framework Centralized-S Proximal Policy Optimization(C-SPPO)based on centralized decision process and considering policy entropy(S)is proposed.The proposed framework aims to plan the best scheduling scheme with the objective of minimizing both the timeout of order requests and the flight impact of UAVs that may lead to conflicts.In this framework,the intents of matching act are generated through the observations of UAV agents,and the ultimate conflict-free matching results are output under the guidance of a centralized decision maker.Concurrently,a pre-activation operation is introduced to further enhance the cooperation among UAV agents.Simulation experiments based on real-world data from New York City are conducted.The results indicate that the proposed CSPPO outperforms the baseline algorithms in the Average Delay Time(ADT),the Maximum Delay Time(MDT),the Order Delay Rate(ODR),the Average Flight Distance(AFD),and the Flight Impact Ratio(FIR).Furthermore,the framework demonstrates scalability to scenarios of different sizes without requiring additional training.展开更多
The Vehicle Routing Problem with Time Windows(VRPTW)presents a significant challenge in combinatorial optimization,especially under real-world uncertainties such as variable travel times,service durations,and dynamic ...The Vehicle Routing Problem with Time Windows(VRPTW)presents a significant challenge in combinatorial optimization,especially under real-world uncertainties such as variable travel times,service durations,and dynamic customer demands.These uncertainties make traditional deterministic models inadequate,often leading to suboptimal or infeasible solutions.To address these challenges,this work proposes an adaptive hybrid metaheuristic that integrates Genetic Algorithms(GA)with Local Search(LS),while incorporating stochastic uncertainty modeling through probabilistic travel times.The proposed algorithm dynamically adjusts parameters—such as mutation rate and local search probability—based on real-time search performance.This adaptivity enhances the algorithm’s ability to balance exploration and exploitation during the optimization process.Travel time uncertainties are modeled using Gaussian noise,and solution robustness is evaluated through scenario-based simulations.We test our method on a set of benchmark problems from Solomon’s instance suite,comparing its performance under deterministic and stochastic conditions.Results show that the proposed hybrid approach achieves up to a 9%reduction in expected total travel time and a 40% reduction in time window violations compared to baseline methods,including classical GA and non-adaptive hybrids.Additionally,the algorithm demonstrates strong robustness,with lower solution variance across uncertainty scenarios,and converges faster than competing approaches.These findings highlight the method’s suitability for practical logistics applications such as last-mile delivery and real-time transportation planning,where uncertainty and service-level constraints are critical.The flexibility and effectiveness of the proposed framework make it a promising candidate for deployment in dynamic,uncertainty-aware supply chain environments.展开更多
This paper addresses the Multi-Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery(MVRPTWSPD),aiming to optimize logistics distribution routes and minimize total costs.A vehicle routing opti...This paper addresses the Multi-Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery(MVRPTWSPD),aiming to optimize logistics distribution routes and minimize total costs.A vehicle routing optimization model is developed based on the operational requirements of the KS Logistics Center,focusing on minimizing vehicle dispatch,loading and unloading,operating,and time window penalty costs.The model incorporates constraints such as vehicle capacity,time windows,and travel distance,and is solved using a genetic algorithm to ensure optimal route planning.Through MATLAB simulations,34 customer points are analyzed,demonstrating that the simultaneous pickup and delivery model reduces total costs by 30.13%,increases vehicle loading rates by 20.04%,and decreases travel distance compared to delivery-only or pickup-only models.The results demonstrate the significant advantages of the simultaneous pickup and delivery mode in reducing logistics costs and improving vehicle utilization,offering valuable insights for enhancing the operational efficiency of the KS Logistics Center.展开更多
This paper systematically reviews the latest research developments in Vehicle Routing Problems(VRP).It examines classical VRP models and their classifications across different dimensions,including load capacity,operat...This paper systematically reviews the latest research developments in Vehicle Routing Problems(VRP).It examines classical VRP models and their classifications across different dimensions,including load capacity,operational characteristics,optimization objectives,vehicle types,and time constraints.Based on literature retrieval results from the Web of Science database,the paper analyzes the current state and trends in VRP research,providing detailed explanations of VRP models and algorithms applied to various scenarios in recent years.Additionally,the article discusses limitations in existing research and provides perspectives on future development trends in VRP research.This review offers researchers in the VRP field a comprehensive overview while identifying future research directions.展开更多
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
Efficient warehouse management is critical for modern supply chain systems,particularly in the era of e-commerce and automation.The Multi-Picker Robot Routing Problem(MPRRP)presents a complex challenge involving the o...Efficient warehouse management is critical for modern supply chain systems,particularly in the era of e-commerce and automation.The Multi-Picker Robot Routing Problem(MPRRP)presents a complex challenge involving the optimization of routes for multiple robots assigned to retrieve items from distinct locations within a warehouse.This study introduces optimized metaheuristic strategies to address MPRRP,with the aim of minimizing travel distances,energy consumption,and order fulfillment time while ensuring operational efficiency.Advanced algorithms,including an enhanced Particle Swarm Optimization(PSO-MPRRP)and a tailored Genetic Algorithm(GA-MPRRP),are specifically designed with customized evolutionary operators to effectively solve the MPRRP.Comparative experiments are conducted to evaluate the proposed strategies against benchmark approaches,demonstrating significant improvements in solution quality and computational efficiency.The findings contribute to the development of intelligent,scalable,and environmentally friendly warehouse systems,paving the way for future advances in robotics and automated logistics management.展开更多
Considering that the vehicle routing problem （VRP） with many extended features is widely used in actual life, such as multi-depot, heterogeneous types of vehicles, customer service priority and time windows etc., a ...Considering that the vehicle routing problem （VRP） with many extended features is widely used in actual life, such as multi-depot, heterogeneous types of vehicles, customer service priority and time windows etc., a mathematical model for multi-depot heterogeneous vehicle routing problem with soft time windows （MDHVRPSTW） is established. An improved ant colony optimization （IACO） is proposed for solving this model. First, MDHVRPSTW is transferred into different groups according to the nearest principle, and then the initial route is constructed by the scanning algorithm （SA）. Secondly, genetic operators are introduced, and crossover probability and mutation probability are adaptively adjusted in order to improve the global search ability of the algorithm. Moreover, the smooth mechanism is used to improve the performance of the ant colony optimization （ACO）. Finally, the 3-opt strategy is used to improve the local search ability. The proposed IACO was tested on three new instances that were generated randomly. The experimental results show that IACO is superior to the other three existing algorithms in terms of convergence speed and solution quality. Thus, the proposed method is effective and feasible, and the proposed model is meaningful.展开更多
In this paper, we propose a new packet routing strategy that incorporates memory information for reducing congestion in communication networks. First, we study the conventional routing strategy which selects the paths...In this paper, we propose a new packet routing strategy that incorporates memory information for reducing congestion in communication networks. First, we study the conventional routing strategy which selects the paths for transmitting packets to destinations using the distance information and the dynamical information such as the number of accumulating packets at adjacent nodes. Then, we evaluate the effectiveness of this routing strategy for the scale-free networks. From results of numerical simulations, we conclude that this routing strategy is not effective when the density of the packets increases due to the impermeability of the communication network. To avoid this undesirable problem, we incorporate memory information to the routing strategy. By using memory information effectively, packets are spread into the communication networks, achieving a higher performance than conventional routing strategies for various network topologies, such as scale-free networks, small-world networks, and scale-free networks with community展开更多
Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational comp...Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid ap- proximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimiza- tion (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.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)algorithms is propose...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 vehicle routing problem(VRP)is a typical discrete combinatorial optimization problem,and many models and algorithms have been proposed to solve the VRP and its variants.Although existing approaches have contribute...The vehicle routing problem(VRP)is a typical discrete combinatorial optimization problem,and many models and algorithms have been proposed to solve the VRP and its variants.Although existing approaches have contributed significantly to the development of this field,these approaches either are limited in problem size or need manual intervention in choosing parameters.To solve these difficulties,many studies have considered learning-based optimization(LBO)algorithms to solve the VRP.This paper reviews recent advances in this field and divides relevant approaches into end-to-end approaches and step-by-step approaches.We performed a statistical analysis of the reviewed articles from various aspects and designed three experiments to evaluate the performance of four representative LBO algorithms.Finally,we conclude the applicable types of problems for different LBO algorithms and suggest directions in which researchers can improve LBO algorithms.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
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
Vehicle routing problem in distribution(VRPD)is a widely used type of vehicle routing problem(VRP),which has been proved as NP-Hard,and it is usually modeled as single objective optimization problem when modeling.For ...Vehicle routing problem in distribution(VRPD)is a widely used type of vehicle routing problem(VRP),which has been proved as NP-Hard,and it is usually modeled as single objective optimization problem when modeling.For multi-objective optimization model,most researches consider two objectives.A multi-objective mathematical model for VRP is proposed,which considers the number of vehicles used,the length of route and the time arrived at each client.Genetic algorithm is one of the most widely used algorithms to solve VRP.As a type of genetic algorithm(GA),non-dominated sorting in genetic algorithm-Ⅱ(NSGA-Ⅱ)also suffers from premature convergence and enclosure competition.In order to avoid these kinds of shortage,a greedy NSGA-Ⅱ(GNSGA-Ⅱ)is proposed for VRP problem.Greedy algorithm is implemented in generating the initial population,cross-over and mutation.All these procedures ensure that NSGA-Ⅱis prevented from premature convergence and refine the performance of NSGA-Ⅱat each step.In the distribution problem of a distribution center in Michigan,US,the GNSGA-Ⅱis compared with NSGA-Ⅱ.As a result,the GNSGA-Ⅱis the most efficient one and can get the most optimized solution to VRP problem.Also,in GNSGA-Ⅱ,premature convergence is better avoided and search efficiency has been improved sharply.展开更多
As a new variant of vehicle routing problem( VRP),a finished vehicle routing problem with time windows in finished vehicle logistics( FVRPTW) is modeled and solved. An optimization model for FVRPTW is presented with t...As a new variant of vehicle routing problem( VRP),a finished vehicle routing problem with time windows in finished vehicle logistics( FVRPTW) is modeled and solved. An optimization model for FVRPTW is presented with the objective of scheduling multiple transport routes considering loading constraints along with time penalty function to minimize the total cost. Then a genetic algorithm( GA) is developed. The specific encoding and genetic operators for FVRPTW are devised.Especially,in order to accelerate its convergence,an improved termination condition is given. Finally,a case study is used to evaluate the effectiveness of the proposed algorithm and a series of experiments are conducted over a set of finished vehicle routing problems. The results demonstrate that the proposed approach has superior performance and satisfies users in practice. Contributions of the study are the modeling and solving of a complex FVRPTW in logistics industry.展开更多
The school bus routing problem(SBRP)is a central issue in transportation planning and optimization systems.SBRP seeks to plan an efficient schedule for a fleet of school buses where each bus picks up students from var...The school bus routing problem(SBRP)is a central issue in transportation planning and optimization systems.SBRP seeks to plan an efficient schedule for a fleet of school buses where each bus picks up students from various bus stops and delivers them to their designated schools while satisfying various constraints such as the maximum capacity of a bus,and the time window of a school.Due to its inherent complexity,many heuristics have been proposed to solve this combinatorial problem in an effective way.In this paper,a novel geographic information systems(GIS)-based decisionmaking framework that combines GIS,clustering techniques,network cutting techniques,and a hybrid ant colony optimization metaheuristic with the iterated Lin–Kernighan local improvement heuristic is proposed for solving the SBRP as a split delivery vehicle routing problem(SDVRP).Experiments were conducted for evaluating the proposed framework by comparing the results for solving 11 routing problems using both the proposed decision-making framework and Arc-GIS 9.2 Network Analyst which uses the greedy Dijkstra’s algorithm.The reported results of the proposed framework generally outperform that of the ArcGIS Network Analyst.In addition,the proposed decision-making framework was applied to solve a real life SBRP to demonstrate its application.展开更多
基金Supported by the National Natural Science Fundation of China( No. 70071028 and 79700019).
文摘Stochastic vehicle routing problems ( VRPs) play important roles in logistics, though they have not been studied systematically yet. The paper summaries the definition, properties and classification of stochastic VRPs, makes further discussion about two strategies in stochastic VRPs, and at last overviews dynamic and stochastic VRPs.
基金funded by the Natural Science Foundation of Zhejiang Province,China(No.MS25E080023)the Natural Science Foundation of Ningbo City,China(No.2024J130)+6 种基金the Fundamental Research Funds for the Provincial Universities of Zhejiang(No.SJLY2023009)the National"111"Center on Safety and Intelligent Operation of Sea Bridge(D21013)National Natural Science Foundation of China(Nos.71971059,52262047,52302388,52272334,and 61963011)the Natural Science Foundation of Jiangsu Province,China(No.BK20230853)the Specific Research Project of Guangxi for Research Bases and Talents(No.AD20159035)the Guilin Key R&D Program[No.20210214-1]the Liuzhou Key R&D Program(No.2022AAA0103).
文摘In the context of the COVID-19 epidemic,a"double-hazard scenario"consisting of a natural disaster and a public health event simultaneously accurring is more likely to arise.However,compared with single-hazard,multiple disasters confront the challenges of complexity,diversity,and demand urgency.To improve the efficiency of emergency material distribution under multiple disasters,this study first divided multiple disasters into three categoriles:independent scenario,sequential scenario,and coupling scenario.A set of evaluation index systems for multiple disasters was established to quantify the urgency of demand.The routing optimization model of emergency vehicles for multiple disasters was proposed by combining demand urgency and road damage,and the non-dominated sorting genetic algorithm II(NSGA-I)was used to simulate and validate the model.A coupling scenario considering two typical disasters of hurricanes and epidemics was selected as a validation example,and sensitivity analysis was also performed for different algorithms,scenarios,and constraints.The results demonstrated that the proposed model could effectively address the vehicle routing problem of emer-gency materials in the context of multiple disasters.Compared to the NSGA,the NSGA-II was used to reduce the total delivery time,cost,and penalty cost by 15.98%6,13.60%,and 16.14%,respectively.Compared with the independent scenario,the coupling scenario increased the total delivery time and cost by 186.28%and 132.48%during the epidemic.However,it reduced the total delivery time by 4.00%and increased the delivery cost by 23.55%compared with the hurricane.Compared with the model without consideration,the model considering demand urgency and road damage reduced the total delivery time and cost by 17.88%and 8.73%,respectively.The model constructed in this study addressed the vehicle routing problem considering the demand urgency and road damage in the optimization process,particularly in the context of multiple disasters.
文摘We propose a multi-crossover and adaptive island based population algorithm(MAIPA).This technique divides the entire population into subpopulations,or demes,each with a different crossover function,which can be switched according to the efficiency.In addition,MAIPA reverses the philosophy of conventional genetic algorithms.It gives priority to the autonomous improvement of the individuals(at the mutation phase),and introduces dynamism in the crossover probability.Each subpopulation begins with a very low value of crossover probability,and then varies with the change of the current generation number and the search performance on recent generations.This mechanism helps prevent premature convergence.In this research,the effectiveness of this technique is tested using three well-known routing problems,i.e.,the traveling salesman problem(TSP),capacitated vehicle routing problem(CVRP),and vehicle routing problem with backhauls(VRPB).MAIPA proves to be better than a traditional island based genetic algorithm for all these three problems.
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.
基金the support of the Chinese Special Research Project for Civil Aircraft(No.MJZ17N22)the National Natural Science Foundation of China(Nos.U2133207,U2333214)+1 种基金the China Postdoctoral Science Foundation(No.2023M741687)the National Social Science Fund of China(No.22&ZD169)。
文摘Unmanned Aerial Vehicle(UAV)stands as a burgeoning electric transportation carrier,holding substantial promise for the logistics sector.A reinforcement learning framework Centralized-S Proximal Policy Optimization(C-SPPO)based on centralized decision process and considering policy entropy(S)is proposed.The proposed framework aims to plan the best scheduling scheme with the objective of minimizing both the timeout of order requests and the flight impact of UAVs that may lead to conflicts.In this framework,the intents of matching act are generated through the observations of UAV agents,and the ultimate conflict-free matching results are output under the guidance of a centralized decision maker.Concurrently,a pre-activation operation is introduced to further enhance the cooperation among UAV agents.Simulation experiments based on real-world data from New York City are conducted.The results indicate that the proposed CSPPO outperforms the baseline algorithms in the Average Delay Time(ADT),the Maximum Delay Time(MDT),the Order Delay Rate(ODR),the Average Flight Distance(AFD),and the Flight Impact Ratio(FIR).Furthermore,the framework demonstrates scalability to scenarios of different sizes without requiring additional training.
文摘The Vehicle Routing Problem with Time Windows(VRPTW)presents a significant challenge in combinatorial optimization,especially under real-world uncertainties such as variable travel times,service durations,and dynamic customer demands.These uncertainties make traditional deterministic models inadequate,often leading to suboptimal or infeasible solutions.To address these challenges,this work proposes an adaptive hybrid metaheuristic that integrates Genetic Algorithms(GA)with Local Search(LS),while incorporating stochastic uncertainty modeling through probabilistic travel times.The proposed algorithm dynamically adjusts parameters—such as mutation rate and local search probability—based on real-time search performance.This adaptivity enhances the algorithm’s ability to balance exploration and exploitation during the optimization process.Travel time uncertainties are modeled using Gaussian noise,and solution robustness is evaluated through scenario-based simulations.We test our method on a set of benchmark problems from Solomon’s instance suite,comparing its performance under deterministic and stochastic conditions.Results show that the proposed hybrid approach achieves up to a 9%reduction in expected total travel time and a 40% reduction in time window violations compared to baseline methods,including classical GA and non-adaptive hybrids.Additionally,the algorithm demonstrates strong robustness,with lower solution variance across uncertainty scenarios,and converges faster than competing approaches.These findings highlight the method’s suitability for practical logistics applications such as last-mile delivery and real-time transportation planning,where uncertainty and service-level constraints are critical.The flexibility and effectiveness of the proposed framework make it a promising candidate for deployment in dynamic,uncertainty-aware supply chain environments.
文摘This paper addresses the Multi-Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery(MVRPTWSPD),aiming to optimize logistics distribution routes and minimize total costs.A vehicle routing optimization model is developed based on the operational requirements of the KS Logistics Center,focusing on minimizing vehicle dispatch,loading and unloading,operating,and time window penalty costs.The model incorporates constraints such as vehicle capacity,time windows,and travel distance,and is solved using a genetic algorithm to ensure optimal route planning.Through MATLAB simulations,34 customer points are analyzed,demonstrating that the simultaneous pickup and delivery model reduces total costs by 30.13%,increases vehicle loading rates by 20.04%,and decreases travel distance compared to delivery-only or pickup-only models.The results demonstrate the significant advantages of the simultaneous pickup and delivery mode in reducing logistics costs and improving vehicle utilization,offering valuable insights for enhancing the operational efficiency of the KS Logistics Center.
文摘This paper systematically reviews the latest research developments in Vehicle Routing Problems(VRP).It examines classical VRP models and their classifications across different dimensions,including load capacity,operational characteristics,optimization objectives,vehicle types,and time constraints.Based on literature retrieval results from the Web of Science database,the paper analyzes the current state and trends in VRP research,providing detailed explanations of VRP models and algorithms applied to various scenarios in recent years.Additionally,the article discusses limitations in existing research and provides perspectives on future development trends in VRP research.This review offers researchers in the VRP field a comprehensive overview while identifying future research directions.
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funded by Hanoi University of Industry,Hanoi,Vietnam,under contract number 25−2024−RD/HD−DHCN.
文摘Efficient warehouse management is critical for modern supply chain systems,particularly in the era of e-commerce and automation.The Multi-Picker Robot Routing Problem(MPRRP)presents a complex challenge involving the optimization of routes for multiple robots assigned to retrieve items from distinct locations within a warehouse.This study introduces optimized metaheuristic strategies to address MPRRP,with the aim of minimizing travel distances,energy consumption,and order fulfillment time while ensuring operational efficiency.Advanced algorithms,including an enhanced Particle Swarm Optimization(PSO-MPRRP)and a tailored Genetic Algorithm(GA-MPRRP),are specifically designed with customized evolutionary operators to effectively solve the MPRRP.Comparative experiments are conducted to evaluate the proposed strategies against benchmark approaches,demonstrating significant improvements in solution quality and computational efficiency.The findings contribute to the development of intelligent,scalable,and environmentally friendly warehouse systems,paving the way for future advances in robotics and automated logistics management.
基金The National Natural Science Foundation of China(No.61074147)the Natural Science Foundation of Guangdong Province(No.S2011010005059)+2 种基金the Foundation of Enterprise-University-Research Institute Cooperation from Guangdong Province and Ministry of Education of China(No.2012B091000171,2011B090400460)the Science and Technology Program of Guangdong Province(No.2012B050600028)the Science and Technology Program of Huadu District,Guangzhou(No.HD14ZD001)
文摘Considering that the vehicle routing problem （VRP） with many extended features is widely used in actual life, such as multi-depot, heterogeneous types of vehicles, customer service priority and time windows etc., a mathematical model for multi-depot heterogeneous vehicle routing problem with soft time windows （MDHVRPSTW） is established. An improved ant colony optimization （IACO） is proposed for solving this model. First, MDHVRPSTW is transferred into different groups according to the nearest principle, and then the initial route is constructed by the scanning algorithm （SA）. Secondly, genetic operators are introduced, and crossover probability and mutation probability are adaptively adjusted in order to improve the global search ability of the algorithm. Moreover, the smooth mechanism is used to improve the performance of the ant colony optimization （ACO）. Finally, the 3-opt strategy is used to improve the local search ability. The proposed IACO was tested on three new instances that were generated randomly. The experimental results show that IACO is superior to the other three existing algorithms in terms of convergence speed and solution quality. Thus, the proposed method is effective and feasible, and the proposed model is meaningful.
文摘In this paper, we propose a new packet routing strategy that incorporates memory information for reducing congestion in communication networks. First, we study the conventional routing strategy which selects the paths for transmitting packets to destinations using the distance information and the dynamical information such as the number of accumulating packets at adjacent nodes. Then, we evaluate the effectiveness of this routing strategy for the scale-free networks. From results of numerical simulations, we conclude that this routing strategy is not effective when the density of the packets increases due to the impermeability of the communication network. To avoid this undesirable problem, we incorporate memory information to the routing strategy. By using memory information effectively, packets are spread into the communication networks, achieving a higher performance than conventional routing strategies for various network topologies, such as scale-free networks, small-world networks, and scale-free networks with community
基金Project (No. 60174009) supported by the National Natural ScienceFoundation of China
文摘Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid ap- proximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimiza- tion (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.
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.
文摘The vehicle routing problem(VRP)is a typical discrete combinatorial optimization problem,and many models and algorithms have been proposed to solve the VRP and its variants.Although existing approaches have contributed significantly to the development of this field,these approaches either are limited in problem size or need manual intervention in choosing parameters.To solve these difficulties,many studies have considered learning-based optimization(LBO)algorithms to solve the VRP.This paper reviews recent advances in this field and divides relevant approaches into end-to-end approaches and step-by-step approaches.We performed a statistical analysis of the reviewed articles from various aspects and designed three experiments to evaluate the performance of four representative LBO algorithms.Finally,we conclude the applicable types of problems for different LBO algorithms and suggest directions in which researchers can improve LBO algorithms.
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(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.
基金supported by National Natural Science Foundation of China(No.60474059)Hi-tech Research and Development Program of China(863 Program,No.2006AA04Z160).
文摘Vehicle routing problem in distribution(VRPD)is a widely used type of vehicle routing problem(VRP),which has been proved as NP-Hard,and it is usually modeled as single objective optimization problem when modeling.For multi-objective optimization model,most researches consider two objectives.A multi-objective mathematical model for VRP is proposed,which considers the number of vehicles used,the length of route and the time arrived at each client.Genetic algorithm is one of the most widely used algorithms to solve VRP.As a type of genetic algorithm(GA),non-dominated sorting in genetic algorithm-Ⅱ(NSGA-Ⅱ)also suffers from premature convergence and enclosure competition.In order to avoid these kinds of shortage,a greedy NSGA-Ⅱ(GNSGA-Ⅱ)is proposed for VRP problem.Greedy algorithm is implemented in generating the initial population,cross-over and mutation.All these procedures ensure that NSGA-Ⅱis prevented from premature convergence and refine the performance of NSGA-Ⅱat each step.In the distribution problem of a distribution center in Michigan,US,the GNSGA-Ⅱis compared with NSGA-Ⅱ.As a result,the GNSGA-Ⅱis the most efficient one and can get the most optimized solution to VRP problem.Also,in GNSGA-Ⅱ,premature convergence is better avoided and search efficiency has been improved sharply.
基金Supported by the National Natural Science Foundation of China(No.51565036)
文摘As a new variant of vehicle routing problem( VRP),a finished vehicle routing problem with time windows in finished vehicle logistics( FVRPTW) is modeled and solved. An optimization model for FVRPTW is presented with the objective of scheduling multiple transport routes considering loading constraints along with time penalty function to minimize the total cost. Then a genetic algorithm( GA) is developed. The specific encoding and genetic operators for FVRPTW are devised.Especially,in order to accelerate its convergence,an improved termination condition is given. Finally,a case study is used to evaluate the effectiveness of the proposed algorithm and a series of experiments are conducted over a set of finished vehicle routing problems. The results demonstrate that the proposed approach has superior performance and satisfies users in practice. Contributions of the study are the modeling and solving of a complex FVRPTW in logistics industry.
文摘The school bus routing problem(SBRP)is a central issue in transportation planning and optimization systems.SBRP seeks to plan an efficient schedule for a fleet of school buses where each bus picks up students from various bus stops and delivers them to their designated schools while satisfying various constraints such as the maximum capacity of a bus,and the time window of a school.Due to its inherent complexity,many heuristics have been proposed to solve this combinatorial problem in an effective way.In this paper,a novel geographic information systems(GIS)-based decisionmaking framework that combines GIS,clustering techniques,network cutting techniques,and a hybrid ant colony optimization metaheuristic with the iterated Lin–Kernighan local improvement heuristic is proposed for solving the SBRP as a split delivery vehicle routing problem(SDVRP).Experiments were conducted for evaluating the proposed framework by comparing the results for solving 11 routing problems using both the proposed decision-making framework and Arc-GIS 9.2 Network Analyst which uses the greedy Dijkstra’s algorithm.The reported results of the proposed framework generally outperform that of the ArcGIS Network Analyst.In addition,the proposed decision-making framework was applied to solve a real life SBRP to demonstrate its application.
