基于粒子群算法的集送货一体化车辆路径问题研究
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摘要
近年来,随着可利用自然资源的日趋减少以及人们环保意识的增强,能源的回收利用越来越受到人们的重视。在政府构建集约型社会政策指引下,正向物流和逆向物流相结合成为时代的要求,由此衍生的集送货一体化车辆路径问题已成为当前国内外物流领域的一个研究热点。
对于集送货一体化车辆路径问题,目前的研究尚不够深入,并且,实际的车辆路径问题往往规模较大,这就需要一种耗费时间较少、求解质量较优的算法来满足实际工作的需要。本文针对这一要求,提出了“先预分派,后优化”的启发式算法。首先,借鉴扫描算法的思想对客户进行预分派。根据实际中距离相对较近的客户由同一辆车提供服务的特点,把在一定扫描范围内的客户分派给同一辆车；然后,运用改进的粒子群算法分派并优化配送线路。在优化过程中,为保证粒子所代表的配送线路是可行的,对于配送线路不可行的粒子,及时进行调整。这种基于客户预分派的粒子群算法,优化效果优于客户车辆随机分派的基本粒子群算法,从而能够保证粒子在飞行中快速收敛,有利于在较短的时间内找到较优的解决方案。
为验证该算法的有效性,本文进行了大量的仿真实验。实验主要包括两部分：对车辆路径问题和集送货一体化的车辆路径问题的数据集分别进行了测试。实验结果表明,这种基于客户预分派的改进粒子群算法具有较高的计算效率,能够在合理的时间内得到较优解,这为解决实际生活中客户规模较大的车辆路径问题提供了一种很好的解决思路。
最后,本文对于改进粒子群算法的应用前景进行了展望,并给出了进一步的研究方向。
In recent years, with the reduction of renewable resources and the growing awareness of environmental protection, people increasingly pay attention to the energy recovery and utilization. Besides, the "Saving Society" policy supported by the government makes the combination of forward logistics together with reverse logistics become a requirement of the times. Therefore, a great many of research interests have been shown on vehicle routing problem with simultaneous pickup and delivery (VRPSPD).
Current research on VRPSPD is still not deep enough. Moreover, due to the large scalability in current practical problem, algorithms with less running time and relative acceptable problem-solving ability are needed in practice. With the aim of the difficulties in solving them, a customer pre-assigned two-phase heuristic algorithm is developed. We first deploy different vehicles, with algorithm used to assign customer groups to delivery vehicles, so customers are assigned to the same vehicle, the angle of which with the datum mark is only slightly different. Secondly we propose a modified particle swarm optimization to arrange customers visiting sequences for every vehicle. In process of optimization, the infeasible routes which violate the capability constraint are not abjured but adjusted before the next iteration. So the number of infeasible routes decreases through this adjustment, and it can help the particle to move forward to a more feasible solution.
In order to verify the effectiveness and efficiency of the proposed algorithm, a large number of simulation experiments have been carried out. They can be divided into two parts:experiments on vehicle routing problem and vehicle routing problem with simultaneous pickup and delivery. The experimental results prove the feasibility and validity of the proposed method which can obtain the efficient solution within short time. Therefore, it can be used to solve the real-life large-scale vehicle routing problem.
At last, the thesis predicts the application prospect of the improved particle swarm optimization and gives some directions of future research.
对于集送货一体化车辆路径问题,目前的研究尚不够深入,并且,实际的车辆路径问题往往规模较大,这就需要一种耗费时间较少、求解质量较优的算法来满足实际工作的需要。本文针对这一要求,提出了“先预分派,后优化”的启发式算法。首先,借鉴扫描算法的思想对客户进行预分派。根据实际中距离相对较近的客户由同一辆车提供服务的特点,把在一定扫描范围内的客户分派给同一辆车；然后,运用改进的粒子群算法分派并优化配送线路。在优化过程中,为保证粒子所代表的配送线路是可行的,对于配送线路不可行的粒子,及时进行调整。这种基于客户预分派的粒子群算法,优化效果优于客户车辆随机分派的基本粒子群算法,从而能够保证粒子在飞行中快速收敛,有利于在较短的时间内找到较优的解决方案。
为验证该算法的有效性,本文进行了大量的仿真实验。实验主要包括两部分：对车辆路径问题和集送货一体化的车辆路径问题的数据集分别进行了测试。实验结果表明,这种基于客户预分派的改进粒子群算法具有较高的计算效率,能够在合理的时间内得到较优解,这为解决实际生活中客户规模较大的车辆路径问题提供了一种很好的解决思路。
最后,本文对于改进粒子群算法的应用前景进行了展望,并给出了进一步的研究方向。
In recent years, with the reduction of renewable resources and the growing awareness of environmental protection, people increasingly pay attention to the energy recovery and utilization. Besides, the "Saving Society" policy supported by the government makes the combination of forward logistics together with reverse logistics become a requirement of the times. Therefore, a great many of research interests have been shown on vehicle routing problem with simultaneous pickup and delivery (VRPSPD).
Current research on VRPSPD is still not deep enough. Moreover, due to the large scalability in current practical problem, algorithms with less running time and relative acceptable problem-solving ability are needed in practice. With the aim of the difficulties in solving them, a customer pre-assigned two-phase heuristic algorithm is developed. We first deploy different vehicles, with algorithm used to assign customer groups to delivery vehicles, so customers are assigned to the same vehicle, the angle of which with the datum mark is only slightly different. Secondly we propose a modified particle swarm optimization to arrange customers visiting sequences for every vehicle. In process of optimization, the infeasible routes which violate the capability constraint are not abjured but adjusted before the next iteration. So the number of infeasible routes decreases through this adjustment, and it can help the particle to move forward to a more feasible solution.
In order to verify the effectiveness and efficiency of the proposed algorithm, a large number of simulation experiments have been carried out. They can be divided into two parts:experiments on vehicle routing problem and vehicle routing problem with simultaneous pickup and delivery. The experimental results prove the feasibility and validity of the proposed method which can obtain the efficient solution within short time. Therefore, it can be used to solve the real-life large-scale vehicle routing problem.
At last, the thesis predicts the application prospect of the improved particle swarm optimization and gives some directions of future research.
引文
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[2]邱佩兰.降低运输成本促进物流发展[J].宁波经济,2009,(5)：45-46.
[3]李军,郭耀煌.物流配送车辆优化调度理论与方法[M].北京：中国物资出版社,2001.
[4]Katoh N, Yano T. An approximation algorithm for the pickup and delivery vehicle routing problem on trees [J]. Discrete Applied Mathematics,2006, 154(16):2335-2349.
[5]龙磊,陈秋双,华彦宁,徐亚.具有同时集送货需求的车辆路径问题的自适应混合遗传算法[J].计算机集成制造系统,2008,14(3)：548-556.
[6]齐姿.集货和送货一体化车辆配送路径问题研究[D].北京：北京科技大学,2007.
[7]Dantzig G B, Ramser J H. The Truck Dispatching Problem [J]. Management Science,1959,6(1):80-91.
[8]孙丽君,胡祥培,王征.车辆路径规划问题及其求解方法研究进展[J].系统工程,2006,24(11)：31-37.
[9]袁正磊.基于聚类的车辆线路优化算法研究[D].济南：山东大学,2008.
[10]Dell'Amico M, Righini G, Salani M.A branch-and-price approach to the vehicle routing problem with simultaneous distribution and collection [J]. Transportation Science,2006,40(2):235-247.
[11]Laporte G, Semet F. Classical Heuristics for the Vehicle Routing Problem [J]. Les Cahiers du GERAD G-89-04,Ecole des Hautes Etudes Commerciales de Montreal,1999.
[12]Clarke G, Wright J W. Scheduling of vehicles from a central depot to a number of delivery points [J]. Operations Research,1964, (12):568-581.
[13]Gillett B E, Miller L R. A heuristic algorithm for the vehicle dispatch problem [J]. Operations Research,1974, (22):340-349.
[14]Wren A, Holliday A. Computer scheduling of vehicles from one or more depots to a number of delivery points [J]. Operational Research Quarterly, 1972, (23):333-344.
[15]Fisher M L, Jaikumar R. A generalized assignment heuristic for vehicle routing [J]. Networks,1981, (11):109-124.
[16]Bramel J, Simchi-Levi D. A location based heuristics for general routing problems [J]. Operation Research,1995, (43):649-660.
[17]Min H. The multiple the vehicle routing problem with simultaneous delivery and pick-up points [J]. Transportation Research Part A,1989,5:377-386.
[18]Halse K. Modeling and Solving Complex Vehicle Routing Problems [D]. Technical University of Denmark, Lyngby,1992.
[19]Dethloff J. Vehicle routing and reverse logistics:The vehicle routing problem with simultaneous delivery and pick-up [J]. OR Spektrum,2001,23:79-96.
[20]Salhi S, Nagy G. A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling [J]. Journal of the Operational Research Society,1999,50(10):1034-1042.
[21]Nagy G, Salhi S. Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries[J]. European Journal of Operational Research,2005,162(1):126-141.
[22]Michel Gendreau, Gilbert Laporte, Jean-Yves Potvin. Meta-heuristics for the Vehicle Routing Problem [J]. Les Cahiers du GERAD G-89-04, Ecole des Hautes Etudes Commerciales de Montreal,1999.
[23]曾华.真实道路下大规模车辆路径问题算法研究与应用[D].济南：山东大学,2006.
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