面向协同运输的车辆路径问题优化算法研究
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摘要
协同运输是近年发展并兴起的协同物流运作模式中的重要内容。协同运输要求相对独立的运输企业协同运作,共享物流资源和物流信息,共同承担客户需求,以达到减少车辆空载,降低整体物流成本,提高运行绩效和提高运输服务水平的目的。协同运输是一种新兴的运输模式和理念,面对此新型运输模式,产生诸多新问题有待研究。面向协同运输的车辆路径问题是其中一类基本而重要的问题。通过研究面向协同运输的车辆路径问题,可以确定运输企业在协同运输中最优车辆使用数目和车辆路径。同时,此问题也将为协同运输中的其他问题提供研究基础,对提高物流企业的生产经营管理水平和降低运作成本具有重要的理论意义和现实价值。
本文以面向协同运输的车辆路径问题为研究对象,提出面向协同运输的几类重要车辆路径问题,建立问题数学模型,综合运用组合优化、图论和启发式算法等方法和工具,设计求解问题的优化算法,并提出问题的有效不等式和紧凑下界,以定量评价所提出优化算法的求解精度。同时作为下一步研究的初步探讨,本文还以所研究的车辆路径问题作为基础,研究了面向协同运输的多企业利益分配问题。本文主要研究工作包括以下几点:
(1)综述了传统的车辆路径问题和面向协同运输的车辆路径问题。对车辆路径问题中两大基本问题,点路径问题和弧路径问题,以及面向协同运输特有的几类车辆路径问题,讨论分析了目前已经提出的数学模型、精确求解算法和启发式求解算法,分析了各种算法的求解性能。
(2)对基于任务选择的车辆路径问题进行研究。建立了此问题的混合整数规划数学模型。在分析问题数学模型特点的基础上,提出了问题的下界数学模型,采用数学规划软件Cplex实现分支定界算法求解下界数学模型,得到问题的下界。利用所研究问题的特性,基于简单启发式求解算法和最短路标签算法,设计了高效的现代现代启发式算法求解此问题。通过数值试验证明所提出启发式算法具有求解精度高,求解快速的特点,并验证了所提出的下界数学模型非常紧凑。
(3)首次提出开放-闭合混合式车辆路径问题。对此复杂问题建立精确数学模型,并设计现代启发式算法对此问题求解。启发式算法中嵌入利用了求解约束最短路问题的双标签算法,从而使得算法整体结构比较简单且易于实现。同时对此问题提出有效不等式,明显改进了分支定界算法求解问题的上界、下界效果和求解时间。数值试验证明,相对加入有效不等式提高后的Cplex求解结果,本文所提出的启发式算法在求解精度和求解时间两方面具有明显的优势。
(4)研究了两点间多次运输的多车场满载弧路径问题。针对目前精确算法求解此问题的不足,建立了该问题的全新数学规划模型和基于图论的模型,并设计了高效的两阶段启发式求解算法。第一阶段利用贪婪算法生成初始解,即形成完全覆盖运输任务弧的回路集;第二阶段组合和连接回路,构造起止于车场的闭通路。最后,利用局域搜索对求得的解改进,以得到最终解。同时,在分析问题特点性质基础上提出了新的下界数学规划模型。通过数值试验,定量分析了所提出启发式算法的求解效率和精度,同时分析对比了本文所提出的新下界模型和已有下界模型的效果。
(5)作为面向协同运输的车辆路径问题研究的扩展和进一步研究的探索,研究了面向协同运输的多企业利益分配问题。以面向协同运输的车辆路径问题优化结果为基础,同时采用Shapley值法对协同的利益在企业之间合理分配。对此问题研究深化了协同运输中利益分配问题的研究深度,为后续使用本论文的研究成果深入求解相关问题提供了借鉴和参考。
Collaborative transportation, as an emerging new mode, represents one of the major developing trends of transportation systems. Collaborative transportation brings together all participants to improve the overall performance of transportation planning and scheduling, share the information among the transportation companies, and reduce system-wide inefficiencies and cut down operational costs. Collaborative transportation was raised and adopted for only few years, thus there are many new problems that need to be studied. Among all these problems, vehicle routing problem, VRP, is an important and basic problem, which can help the companies in the collaborative transportation to utilize the vehicles and determine the optimal route scheme under some side constraints. Meanwhile, the VRPs are the basis of the collaborative transportation, since the results of the VRPs are necessary for other problems in the collaborative transportation. Therefore, in the collaborative transportation, developing solution algorithms with high quality and robustness for the VRPs is very necessary and significant to improve the management level and reduce the operation costs.
This dissertation focuses on some important variant problems of the VRP in the collaborative transportation. For these problems, this dissertation proposes mathematical models, develops sharp lower bounds and designs effective optimization algorithms. The major contributions are as follows:
(1) This dissertation shows a survey of the classical VRPs (i.e., the node routing problems and arc routing problems) and some special VRPs in the collaborative transportation. The mathematical models, exact algorithms and metaheuristics for these various problems are presented and discussed. Meanwhile, the implementation mechanisms and comparison of the different algorithms are given.
(2) The task selection and routing problem is introduced and studied in this dissertation, in which a truckload carrier receives tasks from shippers and other partners and makes a selection between a private vehicle and an external carrier to serve each task. The objective is to minimize the variable and fixed costs for operating the private fleet plus the total costs charged by the external carrier. Both the mathematical programming formulation and the lower bound are established. An effective memetic algorithm is developed to solve the problem. Computational experiments on a range of randomly generated instances are conducted. The results show that the proposed algorithm can produce high quality solutions within a reasonable computational time span.
(3) An optimization problem called the Closed-Open mixed vehicle routing problem is for the first time put forward, which can be used to assist in identifying routes when a carrier serves the customers through his private vehicles and vehicles hired from external carriers. The objective of the problem is to minimize the fixed and variable costs for operating the private vehicles and the hired vehicles. A mixed-integer programming model and an effective memetic algorithm are established for the problem. Computational experiments are conducted. The results show that the proposed algorithm is able to produce high reasonable solutions within an acceptable running time, and always outperforms the robust mixed-integer programming solver Cplex.
(4) A special optimization problem in the carrier collaboration system called the multi-depot capacitated arc routing problem with full truckloads is tackled in this dissertation. This dissertation proposes a mathematical programming model and its corresponding graph theory model, with the objective of minimizing empty vehicle movements. A two-phase greedy algorithm is given to solve practical large-scale problem instances. In the first phase, a set of directed cycles is created to fulfill the transportation orders. In the second phase, chains that are composed of cycles are generated. Furthermore, a set of local search strategies is put forward to improve the initial results. To evaluate the performance of the proposed algorithms, two lower bounds are developed. Finally, computational experiments on various randomly generated problems are conducted. The results show that the proposed methods are effective and the algorithms can provide reasonable solutions within an acceptable computational time.
(5) The profit sharing problem among transportation companies is also studied in this dissertation. This problem is studied on the basis of the optimization result of vehicle routing problems in the collaborative transportation. And, it is an extension of the vehicle routing problems in the collaborative transportation. In the first part, the profit margins resulting from cooperation among freight carriers are analyzed. In the second part, the possibilities of sharing these profit margins fairly among the partners are discussed. The Shapley value can be used to determine a fair allocation. Numerical results for test instances are presented. This study can promote the alliance of collaborative transportation. It can be absorbed and adapted by the future research about the related problems in the collaborative transportation.
本文以面向协同运输的车辆路径问题为研究对象,提出面向协同运输的几类重要车辆路径问题,建立问题数学模型,综合运用组合优化、图论和启发式算法等方法和工具,设计求解问题的优化算法,并提出问题的有效不等式和紧凑下界,以定量评价所提出优化算法的求解精度。同时作为下一步研究的初步探讨,本文还以所研究的车辆路径问题作为基础,研究了面向协同运输的多企业利益分配问题。本文主要研究工作包括以下几点:
(1)综述了传统的车辆路径问题和面向协同运输的车辆路径问题。对车辆路径问题中两大基本问题,点路径问题和弧路径问题,以及面向协同运输特有的几类车辆路径问题,讨论分析了目前已经提出的数学模型、精确求解算法和启发式求解算法,分析了各种算法的求解性能。
(2)对基于任务选择的车辆路径问题进行研究。建立了此问题的混合整数规划数学模型。在分析问题数学模型特点的基础上,提出了问题的下界数学模型,采用数学规划软件Cplex实现分支定界算法求解下界数学模型,得到问题的下界。利用所研究问题的特性,基于简单启发式求解算法和最短路标签算法,设计了高效的现代现代启发式算法求解此问题。通过数值试验证明所提出启发式算法具有求解精度高,求解快速的特点,并验证了所提出的下界数学模型非常紧凑。
(3)首次提出开放-闭合混合式车辆路径问题。对此复杂问题建立精确数学模型,并设计现代启发式算法对此问题求解。启发式算法中嵌入利用了求解约束最短路问题的双标签算法,从而使得算法整体结构比较简单且易于实现。同时对此问题提出有效不等式,明显改进了分支定界算法求解问题的上界、下界效果和求解时间。数值试验证明,相对加入有效不等式提高后的Cplex求解结果,本文所提出的启发式算法在求解精度和求解时间两方面具有明显的优势。
(4)研究了两点间多次运输的多车场满载弧路径问题。针对目前精确算法求解此问题的不足,建立了该问题的全新数学规划模型和基于图论的模型,并设计了高效的两阶段启发式求解算法。第一阶段利用贪婪算法生成初始解,即形成完全覆盖运输任务弧的回路集;第二阶段组合和连接回路,构造起止于车场的闭通路。最后,利用局域搜索对求得的解改进,以得到最终解。同时,在分析问题特点性质基础上提出了新的下界数学规划模型。通过数值试验,定量分析了所提出启发式算法的求解效率和精度,同时分析对比了本文所提出的新下界模型和已有下界模型的效果。
(5)作为面向协同运输的车辆路径问题研究的扩展和进一步研究的探索,研究了面向协同运输的多企业利益分配问题。以面向协同运输的车辆路径问题优化结果为基础,同时采用Shapley值法对协同的利益在企业之间合理分配。对此问题研究深化了协同运输中利益分配问题的研究深度,为后续使用本论文的研究成果深入求解相关问题提供了借鉴和参考。
Collaborative transportation, as an emerging new mode, represents one of the major developing trends of transportation systems. Collaborative transportation brings together all participants to improve the overall performance of transportation planning and scheduling, share the information among the transportation companies, and reduce system-wide inefficiencies and cut down operational costs. Collaborative transportation was raised and adopted for only few years, thus there are many new problems that need to be studied. Among all these problems, vehicle routing problem, VRP, is an important and basic problem, which can help the companies in the collaborative transportation to utilize the vehicles and determine the optimal route scheme under some side constraints. Meanwhile, the VRPs are the basis of the collaborative transportation, since the results of the VRPs are necessary for other problems in the collaborative transportation. Therefore, in the collaborative transportation, developing solution algorithms with high quality and robustness for the VRPs is very necessary and significant to improve the management level and reduce the operation costs.
This dissertation focuses on some important variant problems of the VRP in the collaborative transportation. For these problems, this dissertation proposes mathematical models, develops sharp lower bounds and designs effective optimization algorithms. The major contributions are as follows:
(1) This dissertation shows a survey of the classical VRPs (i.e., the node routing problems and arc routing problems) and some special VRPs in the collaborative transportation. The mathematical models, exact algorithms and metaheuristics for these various problems are presented and discussed. Meanwhile, the implementation mechanisms and comparison of the different algorithms are given.
(2) The task selection and routing problem is introduced and studied in this dissertation, in which a truckload carrier receives tasks from shippers and other partners and makes a selection between a private vehicle and an external carrier to serve each task. The objective is to minimize the variable and fixed costs for operating the private fleet plus the total costs charged by the external carrier. Both the mathematical programming formulation and the lower bound are established. An effective memetic algorithm is developed to solve the problem. Computational experiments on a range of randomly generated instances are conducted. The results show that the proposed algorithm can produce high quality solutions within a reasonable computational time span.
(3) An optimization problem called the Closed-Open mixed vehicle routing problem is for the first time put forward, which can be used to assist in identifying routes when a carrier serves the customers through his private vehicles and vehicles hired from external carriers. The objective of the problem is to minimize the fixed and variable costs for operating the private vehicles and the hired vehicles. A mixed-integer programming model and an effective memetic algorithm are established for the problem. Computational experiments are conducted. The results show that the proposed algorithm is able to produce high reasonable solutions within an acceptable running time, and always outperforms the robust mixed-integer programming solver Cplex.
(4) A special optimization problem in the carrier collaboration system called the multi-depot capacitated arc routing problem with full truckloads is tackled in this dissertation. This dissertation proposes a mathematical programming model and its corresponding graph theory model, with the objective of minimizing empty vehicle movements. A two-phase greedy algorithm is given to solve practical large-scale problem instances. In the first phase, a set of directed cycles is created to fulfill the transportation orders. In the second phase, chains that are composed of cycles are generated. Furthermore, a set of local search strategies is put forward to improve the initial results. To evaluate the performance of the proposed algorithms, two lower bounds are developed. Finally, computational experiments on various randomly generated problems are conducted. The results show that the proposed methods are effective and the algorithms can provide reasonable solutions within an acceptable computational time.
(5) The profit sharing problem among transportation companies is also studied in this dissertation. This problem is studied on the basis of the optimization result of vehicle routing problems in the collaborative transportation. And, it is an extension of the vehicle routing problems in the collaborative transportation. In the first part, the profit margins resulting from cooperation among freight carriers are analyzed. In the second part, the possibilities of sharing these profit margins fairly among the partners are discussed. The Shapley value can be used to determine a fair allocation. Numerical results for test instances are presented. This study can promote the alliance of collaborative transportation. It can be absorbed and adapted by the future research about the related problems in the collaborative transportation.
引文
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