In this paper, a memetic algorithm with competition(MAC) is proposed to solve the capacitated green vehicle routing problem(CGVRP). Firstly, the permutation array called traveling salesman problem(TSP) route is used t...In this paper, a memetic algorithm with competition(MAC) is proposed to solve the capacitated green vehicle routing problem(CGVRP). Firstly, the permutation array called traveling salesman problem(TSP) route is used to encode the solution, and an effective decoding method to construct the CGVRP route is presented accordingly. Secondly, the k-nearest neighbor(k NN) based initialization is presented to take use of the location information of the customers. Thirdly, according to the characteristics of the CGVRP, the search operators in the variable neighborhood search(VNS) framework and the simulated annealing(SA) strategy are executed on the TSP route for all solutions. Moreover, the customer adjustment operator and the alternative fuel station(AFS) adjustment operator on the CGVRP route are executed for the elite solutions after competition. In addition, the crossover operator is employed to share information among different solutions. The effect of parameter setting is investigated using the Taguchi method of design-ofexperiment to suggest suitable values. Via numerical tests, it demonstrates the effectiveness of both the competitive search and the decoding method. Moreover, extensive comparative results show that the proposed algorithm is more effective and efficient than the existing methods in solving the CGVRP.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
Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high ...Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.展开更多
Smart cities make use of a variety of smart technology to improve societies in better ways.Such intelligent technologies,on the other hand,pose sig-nificant concerns in terms of power usage and emission of carbons.The ...Smart cities make use of a variety of smart technology to improve societies in better ways.Such intelligent technologies,on the other hand,pose sig-nificant concerns in terms of power usage and emission of carbons.The suggested study is focused on technological networks for big data-driven systems.With the support of software-defined technologies,a transportation-aided multicast routing system is suggested.By using public transportation as another communication platform in a smart city,network communication is enhanced.The primary objec-tive is to use as little energy as possible while delivering as much data as possible.The Attribute Decision Making with Capacitated Vehicle(CV)Routing Problem(RP)and Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used in the proposed research.For the optimum network selection,a Multi-Attribute Decision Making(MADM)method is utilized.For the sake of reducing energy usage,the Capacitated Vehicle Routing Problem(CVRP)is employed.To reduce the transportation cost and risk,Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used.Moreover,a mixed-integer programming approach is used to deal with the problem.To produce Pareto optimal solutions,an intelligent algorithm based on the epsilon constraint approach and genetic algorithm is cre-ated.A scenario of Auckland Transport is being used to validate the concept of offloading the information onto the buses for energy-efficient and delay-tolerant data transfer.Therefore the experiments have demonstrated that the buses may be used effectively to carry out the data by customer requests while using 30%of less energy than the other systems.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
Purpose–The purpose of this paper is to solve the capacitated location routing problem(CLRP),which is an NP-hard problem that involves making strategic decisions as well as tactical and operational decisions,using a ...Purpose–The purpose of this paper is to solve the capacitated location routing problem(CLRP),which is an NP-hard problem that involves making strategic decisions as well as tactical and operational decisions,using a hybrid particle swarm optimization(PSO)algorithm.Design/methodology/approach–PSO,which is a population-based metaheuristic,is combined with a variable neighborhood strategy variable neighborhood search to solve the CLRP.Findings–The algorithm is tested on a set of instances available in the literature and gave good quality solutions,results are compared to those obtained by other metaheuristic,evolutionary and PSO algorithms.Originality/value–Local search is a time consuming phase in hybrid PSO algorithms,a set of neighborhood structures suitable for the solution representation used in the PSO algorithm is proposed in the VNS phase,moves are applied directly to particles,a clear decoding method is adopted to evaluate a particle(solution)and there is no need to re-encode solutions in the form of particles after applying local search.展开更多
In this paper,we address the k-Chinese postman problem under interdiction budget constraints(the k-CPIBC problem,for short),which is a further generalization of the k-Chinese postman problem and has many practical app...In this paper,we address the k-Chinese postman problem under interdiction budget constraints(the k-CPIBC problem,for short),which is a further generalization of the k-Chinese postman problem and has many practical applications in real life.Specifically,given a weighted graph G=(V,E;w,c;v_(1))equipped with a weight function w:E→R^(+)that satisfies the triangle inequality,an interdiction cost function c:E→Z^(+),a fixed depot v_(1)∈V,an integer k∈^Z^(+)and a budget B∈N,we are asked to find a subset S_(K)■E such that c(S_(K))=∑_(e∈S_(k)c_(e))≤B and that the subgraph G\S_(k)is connected,the objective is to minimize the value min_(C_(E)\S_(k))max{w(C_(i))|C_(i)∈C_(E)\S_(K)}among such all aforementioned subsets S_(k),where C_(E)S_(k)is a set of k-tours(of G\S_(k))starting and ending at the depot v_(1),jointly traversing each edge in G\S_(k)at least once,and w(C_(i))=∑e∈C_(i)w(e)for each tour C_(i)∈C_(E)\S_(k).We obtain the following main results:(1)Given an-approximation algorithm to solve the minimization knapsack problem,we design an(α+β)-approximation algorithm to solve the k-CPIBC problem,whereβ=7/2-1/k-[1/k].(2)We present aβ-approximation algorithm to solve the special version of the k-CPIBC problem,where c(e)1 for each edge e in G and is defined in(1).展开更多
提出一种新的蚁群算法(Multiple Ant Colonies Algorithm based on Sweep Algorithm, SbMACA)用以求解车辆路径问题(Capacitated Vehicle Routing Problem, CVRP)。该方法同以往蚁群算法的不同之处主要体现在两个方面:第一,首次将扫描...提出一种新的蚁群算法(Multiple Ant Colonies Algorithm based on Sweep Algorithm, SbMACA)用以求解车辆路径问题(Capacitated Vehicle Routing Problem, CVRP)。该方法同以往蚁群算法的不同之处主要体现在两个方面:第一,首次将扫描算法应用于蚁群算法,通过对蚂蚁所构造的初始解中的不同子回路之间的点进行交换优化,该算法可以有效地改进初始解的质量;第二,提出并采用了一种新的多蚁群技术,各个蚁群分别进行各自的搜索,在各个蚁群均停滞后,对蚁群之间的信息素进行交换与更新,以利于蚁群跳离局部最优值。实验结果表明,SbMACA算法具有很强的搜索能力,求取各CVRP的Benchmark问题所得解的质量同最好解相比较而言,平均仅有 0.28%的差距,是求解车辆路径问题的一种十分有效的方法。展开更多
基金supported by the National Science Fund for Distinguished Young Scholars of China(61525304)the National Natural Science Foundation of China(61873328)
文摘In this paper, a memetic algorithm with competition(MAC) is proposed to solve the capacitated green vehicle routing problem(CGVRP). Firstly, the permutation array called traveling salesman problem(TSP) route is used to encode the solution, and an effective decoding method to construct the CGVRP route is presented accordingly. Secondly, the k-nearest neighbor(k NN) based initialization is presented to take use of the location information of the customers. Thirdly, according to the characteristics of the CGVRP, the search operators in the variable neighborhood search(VNS) framework and the simulated annealing(SA) strategy are executed on the TSP route for all solutions. Moreover, the customer adjustment operator and the alternative fuel station(AFS) adjustment operator on the CGVRP route are executed for the elite solutions after competition. In addition, the crossover operator is employed to share information among different solutions. The effect of parameter setting is investigated using the Taguchi method of design-ofexperiment to suggest suitable values. Via numerical tests, it demonstrates the effectiveness of both the competitive search and the decoding method. Moreover, extensive comparative results show that the proposed algorithm is more effective and efficient than the existing methods in solving the CGVRP.
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Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.
基金supported by the National Research Foundation of Korea(NRF)Grant funded by the korea government(MSIT)(No.2022H1D8A3038040)and the Soonchunhyang University Research Fund.
文摘Smart cities make use of a variety of smart technology to improve societies in better ways.Such intelligent technologies,on the other hand,pose sig-nificant concerns in terms of power usage and emission of carbons.The suggested study is focused on technological networks for big data-driven systems.With the support of software-defined technologies,a transportation-aided multicast routing system is suggested.By using public transportation as another communication platform in a smart city,network communication is enhanced.The primary objec-tive is to use as little energy as possible while delivering as much data as possible.The Attribute Decision Making with Capacitated Vehicle(CV)Routing Problem(RP)and Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used in the proposed research.For the optimum network selection,a Multi-Attribute Decision Making(MADM)method is utilized.For the sake of reducing energy usage,the Capacitated Vehicle Routing Problem(CVRP)is employed.To reduce the transportation cost and risk,Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used.Moreover,a mixed-integer programming approach is used to deal with the problem.To produce Pareto optimal solutions,an intelligent algorithm based on the epsilon constraint approach and genetic algorithm is cre-ated.A scenario of Auckland Transport is being used to validate the concept of offloading the information onto the buses for energy-efficient and delay-tolerant data transfer.Therefore the experiments have demonstrated that the buses may be used effectively to carry out the data by customer requests while using 30%of less energy than the other systems.
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Purpose–The purpose of this paper is to solve the capacitated location routing problem(CLRP),which is an NP-hard problem that involves making strategic decisions as well as tactical and operational decisions,using a hybrid particle swarm optimization(PSO)algorithm.Design/methodology/approach–PSO,which is a population-based metaheuristic,is combined with a variable neighborhood strategy variable neighborhood search to solve the CLRP.Findings–The algorithm is tested on a set of instances available in the literature and gave good quality solutions,results are compared to those obtained by other metaheuristic,evolutionary and PSO algorithms.Originality/value–Local search is a time consuming phase in hybrid PSO algorithms,a set of neighborhood structures suitable for the solution representation used in the PSO algorithm is proposed in the VNS phase,moves are applied directly to particles,a clear decoding method is adopted to evaluate a particle(solution)and there is no need to re-encode solutions in the form of particles after applying local search.
基金supported by the National Natural Science Foundation of China(Nos.11861075,12101593)Project for Innovation Team(Cultivation)of Yunnan Province(No.202005AE-160006)+2 种基金Peng-Xiang Pan is also supported by Project of Yunnan Provincial Department of Education Science Research Fund(No.2020Y0040)Jun-Ran Lichen is also supported by Fundamental Research Funds for the Central Universities(No.buctrc202219)Jian-Ping Li is also supported by Project of Yunling Scholars Training of Yunnan Province(No.K264202011820).
文摘In this paper,we address the k-Chinese postman problem under interdiction budget constraints(the k-CPIBC problem,for short),which is a further generalization of the k-Chinese postman problem and has many practical applications in real life.Specifically,given a weighted graph G=(V,E;w,c;v_(1))equipped with a weight function w:E→R^(+)that satisfies the triangle inequality,an interdiction cost function c:E→Z^(+),a fixed depot v_(1)∈V,an integer k∈^Z^(+)and a budget B∈N,we are asked to find a subset S_(K)■E such that c(S_(K))=∑_(e∈S_(k)c_(e))≤B and that the subgraph G\S_(k)is connected,the objective is to minimize the value min_(C_(E)\S_(k))max{w(C_(i))|C_(i)∈C_(E)\S_(K)}among such all aforementioned subsets S_(k),where C_(E)S_(k)is a set of k-tours(of G\S_(k))starting and ending at the depot v_(1),jointly traversing each edge in G\S_(k)at least once,and w(C_(i))=∑e∈C_(i)w(e)for each tour C_(i)∈C_(E)\S_(k).We obtain the following main results:(1)Given an-approximation algorithm to solve the minimization knapsack problem,we design an(α+β)-approximation algorithm to solve the k-CPIBC problem,whereβ=7/2-1/k-[1/k].(2)We present aβ-approximation algorithm to solve the special version of the k-CPIBC problem,where c(e)1 for each edge e in G and is defined in(1).
文摘提出一种新的蚁群算法(Multiple Ant Colonies Algorithm based on Sweep Algorithm, SbMACA)用以求解车辆路径问题(Capacitated Vehicle Routing Problem, CVRP)。该方法同以往蚁群算法的不同之处主要体现在两个方面:第一,首次将扫描算法应用于蚁群算法,通过对蚂蚁所构造的初始解中的不同子回路之间的点进行交换优化,该算法可以有效地改进初始解的质量;第二,提出并采用了一种新的多蚁群技术,各个蚁群分别进行各自的搜索,在各个蚁群均停滞后,对蚁群之间的信息素进行交换与更新,以利于蚁群跳离局部最优值。实验结果表明,SbMACA算法具有很强的搜索能力,求取各CVRP的Benchmark问题所得解的质量同最好解相比较而言,平均仅有 0.28%的差距,是求解车辆路径问题的一种十分有效的方法。
