大规模动态车辆路径问题优化方法研究
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摘要
随着因特网络、电子技术和信息技术的发展,电子商务(Electronic Commerce, EC)、全球定位系统(Global Positioning System, GPS)、智能交通系统(Intelligence Transport System, ITS)和全球移动通讯系统(Global System of Mobile communication, GSM)得到了越来越广泛的应用。当前,通过借助这些技术工具,在物流配送的过程中,物流企业能够便捷的获取到在线顾客、交通状况、车队状况等实时配送信息。由于事先的配送方案在新信息出现后可能变的次优甚至不可行,所以如何根据实时动态信息不断的合理调整车辆配送路线,已成为当代物流配送企业提升竞争力的关键因素。另外,如今顾客需求特征呈少批量多批次的发展趋势,并且随着物流配送企业间的合作逐渐加强,配送中的顾客数量规模也越来越大。因此,在这两方面的背景下,大规模动态车辆路径问题随之产生。
求解大规模动态车辆路径问题要求算法能够不断的合并实时信息,快速的求解得到新的车辆配送行驶路径计划,这要求算法的求解速度非常快。然而当前算法大多是为求解静态车辆路径问题设计,因此导致当前算法的特点是求解质量非常精确,但求解速度不够理想,所以,直接采用当前算法难于有效的求解大规模动态车辆路径问题。
本研究针对大规模动态车辆路径问题特征,提出了相应的优化方法。首先将大规模动态车辆路径问题转化为一系列的经典静态车辆路径问题；然后提出一个速度非常快且能确保求解质量较为满意的改进贪婪算法,用于在出现实时信息后快速的求解得到初始满意方案；最后设计了混合大邻域算法,用于继续优化改进贪婪算法的求解方案,直到下一条实时信息出现。具体研究工作如下：
(1)大规模动态车辆路径问题分析及求解思路研究。首先界定了本文研究的大规模动态车辆路径问题所属的类型,并通过分析大规模动态车辆路径问题发现,在配送过程中出现新顾客、老顾客取消订单、交通中断和配送车辆抛锚等不同类型动态事件后,重新决策生成新的配送方案,等价于一个静态的多车型开放式车辆路径问题；然后,以正在执行配送任务车辆位置作为虚拟顾客的方式,将多车型开放式车辆路径问题转化为经典的静态车辆路径问题,因此求解大规模动态车辆路径问题,等价于求解一系列经典静态车辆路径问题；最后,基于经典车辆路径问题模型,提出了大规模动态车辆路径问题的模型及其求解思路。
(2)求解车辆路径问题的改进贪婪算法研究。首先,基于贪婪算法的思想,提出求解车辆路径问题的贪婪算法规则,通过分析和求解算例发现,该算法求解规则简洁但求解质量和求解速度均不够理想；然后,分别基于Held Karp模型和K-D Tree区域分割法提出了改进贪婪算法的求解质量和速度两个策略,原始贪婪算法结合提出的两个策略从而得到改进贪婪算法;最后,分析改进贪婪算法的复杂度发现仅为O(nlogn),并且采用改进贪婪算法求解了当前世界上最大的24个车辆路径问题标准算例,其平均求解质量在10%之内。
(3)基于复杂网络理论的混合大邻域算法设计。首先提出了采用复杂网络分析算法解空间结构的方法,并分析了常用的几种k-opt算法的解空间结构发现,优秀算法的解空间结构类似于小世界网络；然后,以该研究成果为理论依据,设计了一个混合大邻域算法,使其算法解空间的结构更类似于小世界网络,从而具有更好的算法性能,并且设计了执行该算法的数据结构以进一步提高其执行速度减少内存需求；最后,采用改进贪婪算法与混合大邻域算法联合使用的方式求解了众多算例,并与当前经典算法进行了比较发现这种求解方式的综合性能非常具有竞争力。
本优化方法的主要贡献是,由于提出的改进贪婪算法的速度非常快速,能够在每次出现新的配送信息后从全局的角度重新优化得到最新的执行方案,并且利用提出的混合大邻域算法可以不断继续优化当前的执行方案。相对于目前通过局部调整当前方案处理新信息以减少当前配送计划变动程度的方式,本优化方法为求解大规模动态车辆路径问题提供了一种新的方法和求解思路。
With development of Internet, electronic and information technology, Electronic Commerce (EC), Global Positioning System (GPS), Intelligence Transport System (ITS) and Global System of Mobile (GSM) communication are being applied more broadly. Recently, with these tools in the process of logistics, it is convenient for logistics enterprises to get real-time information of delivery such as on-line customers, traffic conditions, fleet conditions, etc. Since the prior delivery scheme may become suboptimal or even infeasible when new information comes, so how to adjust the vehicle delivery route reasonably according to the real-time dynamic informationhas become a key issue for logistics enterprises to enhance their competitiveness. In addition, logistics enterprises get more small-batches of customer need, and with the gradual strengthening of the cooperation between the logistics enterprises, the number of customers are becoming larger and larger. Therefore, the large-scale dynamic vehicle routing problem (DVRP) comes up in this context.
To solve this problem, the algorithm needs to continuously conjoin the real-time information, and to fastly get solution of new vehicle routing plan. However, the current algorithms are mostly designed to solve static vehicle routing problem, which leads the solving quality of the current algorithms to be accurate, but the unsatisfactory speed, therefore. the current algorithms are not effective enough for solving the large-scale dynamic vehicle routing problem.
According to characteristics of the large-scale dynamic vehicle routing problem, in this dissertation an optimization method is proposed. Firstly, the dynamic vehicle routing problem is converted into a series of classic static vehicle routing problems; Then an Improved Greedy Algorithm (IMGR) is developed, with both fast solving speed and satisfactory solving quality. IMGR can get an initial satisfactory solution when new real-time information comes along; Finally, a Hybrid Large Neighborhood Algorithm (HLNA) is designed to optimize the solution of the IMGR until another real-time information comes up. The specific research work is as follows:
(1) Analysis of the large-scaledynamic vehicle routing problem and ideas of solving the problem. Firstly, it is confirmed what the category this problem belonges to. Through the analysis of large-scale dynamic vehicle routing problem, we find out that after such different types of dynamic events as the emergence of new customers, cancellation of orders. disruption of traffic and vehicle's breaking down, how to design new delivery plan is equivalent to a static Heterogeneous Fleet Open Vehicle Routing Problem (HFOVRP); Secondly, by making the strategy that take position of the vehicles which are executing delivery task as some dummy customers. HFOVRP can be converted into the classical static VRP.Thus solving the large-scale dynamic vehicle routing problem is equivalent to solving a series of classical static vehicle routing problem as well; Finally, based on the classical vehicle routing problem model, we propose a large-scale dynamic vehicle routing problem model and come up with new ideas of solving the problem.
(2) The research on IMGR for solving VRP. Firstly, based on the idea of the greedy algorithm, the rules of greedy algorithm for vehicle routing problem are proposed, and the rules are simple but not good in solution quality and speed. Then two strategies are put forwarded to improve greedy algorithm solution quality and speed based on Held Karp model and K-D Tree method respectively. Hence the greedy algorithm combines the two strategies results in the IMGR. Finally, it is found that the complexity of IMGR is only O(nlogn) according to the algorithm complexity theory. By using IMGR to solve the largest24benchmark instances of VRP in the current world, it is shown that the average solution quality-is less than10%deviating from the theoretical optimal solutions.
(3) The design for HLNA based on complex network theory. Firstly, the method using the complex network analysis algorithm to solve the space structure is proposed, and the space structures of several common k-opt algorithm are analyzed, it is indicated the solution space structures of the excellent algorithms are similar to the small-world networks. Then, we develop HLNA according to the theoretical basis of the research results, making the algorithm solution space structure is more similar to the small-world networks, thus to have a better performance of the algorithm. In addition, the data structure of HLNA is designed to reduce the memory requirements and to further improve its execution speed. Finally, we solve some benchmark instances of VRP by using the combination of IMGR and HLNA, and it is demonstrated that the overall performance of this solution method is very competitive comparing with the current classical algorithms.
The main contribution of this optimization method is to get the latest implementation of the program by re-optimization from a global perspective after each new distribution information appeares and continue to optimize the current implementation of the program by using HLNA, because of IMGR which we proposed is very fast. Comparing with current methods which adjust the local scheme in order to minimize the disruption, this optimization method provides a new idea for solving large-scale dynamic vehicle routing problem.
求解大规模动态车辆路径问题要求算法能够不断的合并实时信息,快速的求解得到新的车辆配送行驶路径计划,这要求算法的求解速度非常快。然而当前算法大多是为求解静态车辆路径问题设计,因此导致当前算法的特点是求解质量非常精确,但求解速度不够理想,所以,直接采用当前算法难于有效的求解大规模动态车辆路径问题。
本研究针对大规模动态车辆路径问题特征,提出了相应的优化方法。首先将大规模动态车辆路径问题转化为一系列的经典静态车辆路径问题；然后提出一个速度非常快且能确保求解质量较为满意的改进贪婪算法,用于在出现实时信息后快速的求解得到初始满意方案；最后设计了混合大邻域算法,用于继续优化改进贪婪算法的求解方案,直到下一条实时信息出现。具体研究工作如下：
(1)大规模动态车辆路径问题分析及求解思路研究。首先界定了本文研究的大规模动态车辆路径问题所属的类型,并通过分析大规模动态车辆路径问题发现,在配送过程中出现新顾客、老顾客取消订单、交通中断和配送车辆抛锚等不同类型动态事件后,重新决策生成新的配送方案,等价于一个静态的多车型开放式车辆路径问题；然后,以正在执行配送任务车辆位置作为虚拟顾客的方式,将多车型开放式车辆路径问题转化为经典的静态车辆路径问题,因此求解大规模动态车辆路径问题,等价于求解一系列经典静态车辆路径问题；最后,基于经典车辆路径问题模型,提出了大规模动态车辆路径问题的模型及其求解思路。
(2)求解车辆路径问题的改进贪婪算法研究。首先,基于贪婪算法的思想,提出求解车辆路径问题的贪婪算法规则,通过分析和求解算例发现,该算法求解规则简洁但求解质量和求解速度均不够理想；然后,分别基于Held Karp模型和K-D Tree区域分割法提出了改进贪婪算法的求解质量和速度两个策略,原始贪婪算法结合提出的两个策略从而得到改进贪婪算法;最后,分析改进贪婪算法的复杂度发现仅为O(nlogn),并且采用改进贪婪算法求解了当前世界上最大的24个车辆路径问题标准算例,其平均求解质量在10%之内。
(3)基于复杂网络理论的混合大邻域算法设计。首先提出了采用复杂网络分析算法解空间结构的方法,并分析了常用的几种k-opt算法的解空间结构发现,优秀算法的解空间结构类似于小世界网络；然后,以该研究成果为理论依据,设计了一个混合大邻域算法,使其算法解空间的结构更类似于小世界网络,从而具有更好的算法性能,并且设计了执行该算法的数据结构以进一步提高其执行速度减少内存需求；最后,采用改进贪婪算法与混合大邻域算法联合使用的方式求解了众多算例,并与当前经典算法进行了比较发现这种求解方式的综合性能非常具有竞争力。
本优化方法的主要贡献是,由于提出的改进贪婪算法的速度非常快速,能够在每次出现新的配送信息后从全局的角度重新优化得到最新的执行方案,并且利用提出的混合大邻域算法可以不断继续优化当前的执行方案。相对于目前通过局部调整当前方案处理新信息以减少当前配送计划变动程度的方式,本优化方法为求解大规模动态车辆路径问题提供了一种新的方法和求解思路。
With development of Internet, electronic and information technology, Electronic Commerce (EC), Global Positioning System (GPS), Intelligence Transport System (ITS) and Global System of Mobile (GSM) communication are being applied more broadly. Recently, with these tools in the process of logistics, it is convenient for logistics enterprises to get real-time information of delivery such as on-line customers, traffic conditions, fleet conditions, etc. Since the prior delivery scheme may become suboptimal or even infeasible when new information comes, so how to adjust the vehicle delivery route reasonably according to the real-time dynamic informationhas become a key issue for logistics enterprises to enhance their competitiveness. In addition, logistics enterprises get more small-batches of customer need, and with the gradual strengthening of the cooperation between the logistics enterprises, the number of customers are becoming larger and larger. Therefore, the large-scale dynamic vehicle routing problem (DVRP) comes up in this context.
To solve this problem, the algorithm needs to continuously conjoin the real-time information, and to fastly get solution of new vehicle routing plan. However, the current algorithms are mostly designed to solve static vehicle routing problem, which leads the solving quality of the current algorithms to be accurate, but the unsatisfactory speed, therefore. the current algorithms are not effective enough for solving the large-scale dynamic vehicle routing problem.
According to characteristics of the large-scale dynamic vehicle routing problem, in this dissertation an optimization method is proposed. Firstly, the dynamic vehicle routing problem is converted into a series of classic static vehicle routing problems; Then an Improved Greedy Algorithm (IMGR) is developed, with both fast solving speed and satisfactory solving quality. IMGR can get an initial satisfactory solution when new real-time information comes along; Finally, a Hybrid Large Neighborhood Algorithm (HLNA) is designed to optimize the solution of the IMGR until another real-time information comes up. The specific research work is as follows:
(1) Analysis of the large-scaledynamic vehicle routing problem and ideas of solving the problem. Firstly, it is confirmed what the category this problem belonges to. Through the analysis of large-scale dynamic vehicle routing problem, we find out that after such different types of dynamic events as the emergence of new customers, cancellation of orders. disruption of traffic and vehicle's breaking down, how to design new delivery plan is equivalent to a static Heterogeneous Fleet Open Vehicle Routing Problem (HFOVRP); Secondly, by making the strategy that take position of the vehicles which are executing delivery task as some dummy customers. HFOVRP can be converted into the classical static VRP.Thus solving the large-scale dynamic vehicle routing problem is equivalent to solving a series of classical static vehicle routing problem as well; Finally, based on the classical vehicle routing problem model, we propose a large-scale dynamic vehicle routing problem model and come up with new ideas of solving the problem.
(2) The research on IMGR for solving VRP. Firstly, based on the idea of the greedy algorithm, the rules of greedy algorithm for vehicle routing problem are proposed, and the rules are simple but not good in solution quality and speed. Then two strategies are put forwarded to improve greedy algorithm solution quality and speed based on Held Karp model and K-D Tree method respectively. Hence the greedy algorithm combines the two strategies results in the IMGR. Finally, it is found that the complexity of IMGR is only O(nlogn) according to the algorithm complexity theory. By using IMGR to solve the largest24benchmark instances of VRP in the current world, it is shown that the average solution quality-is less than10%deviating from the theoretical optimal solutions.
(3) The design for HLNA based on complex network theory. Firstly, the method using the complex network analysis algorithm to solve the space structure is proposed, and the space structures of several common k-opt algorithm are analyzed, it is indicated the solution space structures of the excellent algorithms are similar to the small-world networks. Then, we develop HLNA according to the theoretical basis of the research results, making the algorithm solution space structure is more similar to the small-world networks, thus to have a better performance of the algorithm. In addition, the data structure of HLNA is designed to reduce the memory requirements and to further improve its execution speed. Finally, we solve some benchmark instances of VRP by using the combination of IMGR and HLNA, and it is demonstrated that the overall performance of this solution method is very competitive comparing with the current classical algorithms.
The main contribution of this optimization method is to get the latest implementation of the program by re-optimization from a global perspective after each new distribution information appeares and continue to optimize the current implementation of the program by using HLNA, because of IMGR which we proposed is very fast. Comparing with current methods which adjust the local scheme in order to minimize the disruption, this optimization method provides a new idea for solving large-scale dynamic vehicle routing problem.
引文
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