On the complexity of the k-customer vehicle routing problem

We investigate the complexity of the k-CUSTOMER VEHICLE ROUTING PROBLEM: Given an edge weighted graph, the problem requires to compute a minimum weight set of cyclic routes such that each contains a distinguished depot vertex and at most other k customer vertices, and every customer belongs to exactly one route.     

Evolutionary Algorithms for the Vehicle Routing Problem with Time Windows

This paper surveys the research on evolutionary algorithms for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from a single depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval. All routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. The main types of evolutionary algorithms for the VRPTW are genetic algorithms and evolution strategies. In addition to describing the basic features of each method, experimental results for the benchmark test problems of Solomon (1987) and Gehring and Homberger (1999) are presented and analyzed.     

Scheduling orders for multiple product types to minimize total weighted completion time

We consider the problem of scheduling orders for multiple different product types in an environment with m dedicated machines in parallel. The objective is to minimize the total weighted completion time. Each product type is produced by one and only one of the m dedicated machines; that is, each machine is dedicated to a specific product type. Each order has a weight and may also have a release date. Each order asks for certain amounts of various different product types. The different products for an order can be produced concurrently. Preemptions are not allowed. Even when all orders are available at time 0, the problem has been shown to be strongly NP-hard for any fixed number (?2) of machines. This paper focuses on the design and analysis of efficient heuristics for the case without release dates. Occasionally, however, we extend our results to the case with release dates. The heuristics considered include some that have already been proposed in the literature as well as several new ones. They include various static and dynamic priority rules as well as two more sophisticated LP-based algorithms. We analyze the performance bounds of the priority rules and of the algorithms and present also an in-depth comparative analysis of the various rules and algorithms. The conclusions from this empirical analysis provide insights into the trade-offs with regard to solution quality, speed, and memory space.     

多行程车辆路径问题和配送中心定位问题的研究

为了同时解决多行程车辆路径问题和配送中心的定位问题,首先开发了一个以最小化总成本为目标的数学模型,其中总成本包括运输成本和车辆启动成本.然后设计了一个启发式算法解决这个问题,包括三个阶段:第一阶段是找到初始定位并进行路线安排,第二阶段采用模拟退火(SA)的逻辑和交换算法来获得更好的路线,最后阶段是改善由模拟退火算法中当前温度控制的位置.通过标准样例进行的实验结果表明,该算法可以更好地获得一个配送中心定位和有效的相关路线安排.最后,数值实验指出:1)选择不同类型行程的配送方式取决于每辆车的启动成本和单位距离的运输成本;2)使用大容量车辆可以更好地减少运输距离.3)增加服务时间可以有效地减少所需车辆的数量,这三个结果对于多行程车辆路径问题和配送中心的定位问题的管理决策都具有一定的实用价值.     

A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows

Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize the objectives of traveling distance and number of vehicles. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW. The proposed HMOEA is featured with specialized genetic operators and variable-length chromosome representation to accommodate the sequence-oriented optimization in VRPTW. Unlike existing VRPTW approaches that often aggregate multiple criteria and constraints into a compromise function, the proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace. The HMOEA is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, which yields 20 routing solutions better than or competitive as compared to the best solutions published in literature.     

改进的二进制粒子群算法求解车辆路径问题

设计了一种改进的二进制粒子群优化算法来求解车辆路径问题,算法基于粒子群算法的寻优模式充分考虑粒子之间的导向作用,改进二进制粒子群算法的位取值方式,减小了在进化过程中停滞于局部最优解的概率,并通过构造辅助函数处理优化问题的约束条件,基于分层次实现多个目标的思路来寻优,提高了算法的搜索效率和计算速度.实验测试结果验证了该算法对求解车辆路径问题的适用性和有效性.     

考虑外协服务的车辆路径优化问题

降低零售企业的末端配送成本是控制物流成本的关键,共享经济的发展为此提供了新思路。因此,针对零售企业末端上门配送服务成本较高的情况,提出了考虑外协的车辆服务策略,将有意愿进行单次交付的线下客户作为协作车辆配合普通车辆来完成线上客户订单的配送,建立了以最小化普通车辆路径成本,普通车辆使用成本,时间窗惩罚成本和协作车辆补偿成本为目标函数的数学模型,并设计匹配算法和混合遗传算子的模拟退火算法对该模型进行求解,最后结合算例对提出的算法进行检验与分析。     

车辆路径问题的改进遗传算法

提出一种基于遗传算法的求解车辆路径问题的新算法,避免传统遗传算法处理不可行约束条件中惩罚项系数选取不当所出现的问题.同时,通过现实例子分析该算法的优劣性,实验结果表明该算法是一种有效的算法.     

基于遗传算法的物流配送车辆调度问题研究

研究使用遗传算法求解物流配送组织过程中车辆调度问题 .通过把时间窗约束和车辆容量约束转嫁到最小费用目标函数中去 ,建立适合于遗传算法的车辆调度模型 .阐述放回式随机复制算子和适应度函数 ,设计描述行驶线路的染色体结构、初始群体生成方法、独特的交叉算子和交换变异算子 ,构造完整的遗传算法 .并给出算例 ,验证调度模型和遗传算法 .     

有时间窗的车辆路径问题的局部下降搜索算法

介绍了一个求解有时间窗的车辆路径问题(vehicle routing problem with time windows,VRPTW)的启发式算法——基于λ-交换的局部下降搜索算法(Local search descent method based on λ-interchange).VRPTW是指合理安排车辆行驶路线,为一组预先设定有时间限制的客户运送货物,在不违反时间要求和车辆容量限制的条件下使得成本最小.它是一个典型的NP-难题,可以通过启发式算法获得近优解来解决.通过两个实验验证,显示了局部下降搜索算法的优良性能,取得了很好的效果,可以作为进一步研究复杂算法的基础.     

Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method

An alternate formulation of the classical vehicle routing problem with stochastic demands (VRPSD) is considered. We propose a new heuristic method to solve the problem, based on the Cross-Entropy method. In order to better estimate the objective function at each point in the domain, we incorporate Monte Carlo sampling. This creates many practical issues, especially the decision as to when to draw new samples and how many samples to use. We also develop a framework for obtaining exact solutions and tight lower bounds for the problem under various conditions, which include specific families of demand distributions. This is used to assess the performance of the algorithm. Finally, numerical results are presented for various problem instances to illustrate the ideas.     

需求可分的车辆路径问题模型与算法

需求可分的车辆路径问题(SDVRP)无论是从运输距离还是派车数量上,都可进一步优化传统的车辆路径问题。为了降低SDVRP的求解难度,本文在分析最优解性质的基础上,加强模型的约束条件,将原模型转变为等价的改进SDVRP,并在使用蚂蚁算法求解改进SDVRP模型的过程中,采用开发新路径和2-opt相结合的方法,以避免出现迭代停滞的现象。实验表明,算法计算结果稳定,最差解与最好解的偏差仅为1.80%。     

求解车辆路径问题的离散蝙蝠算法

根据车辆路径问题的数学模型,分析了它的具体特征,从而对BA的操作算子又进行了重新定义,设计了求解VRP问题的离散蝙蝠算法,并通过实例测试将离散蝙蝠算法与其他算法进行比较,验证了该算法求解VRP问题的有效性与可行性.     

基于油耗的带有车容限制弧路径问题的模型及优化

提出了一种基于油耗的带有车容限制的弧路径问题(Capacitated Arc RoutingProblem,CARP),建立了以降低油耗为目标的问题模型,构造了相应的遗传算法.基于标准测试问题,同传统以距离为优化目标的遗传算法求得的油耗进行比较,实验结果表明,此算法可以快速、有效的求得以油耗为优化目标的CARP问题的优化解,为实际中降低车辆运输服务成本提供了较好方案.     

成品油配送多车舱车辆指派及路径优化问题研究

针对成品油配送中多车型、多车舱的车辆优化调度难题,综合考虑多车型车辆指派、多车舱车辆装载及路径安排等决策,以派车成本与油耗成本之和的总成本最小为目标,建立了多车型多车舱的车辆优化调度模型。为降低模型求解的复杂性,本文提出一种基于C-W节约算法的“需求拆分→合并装载”的车辆装载策略,并综合利用Relocate和Exchange算子进行并行邻域搜索改进,获得优化的成品油配送方案。最后,通过算例验证了本文提出的模型与算法用于求解大规模成品油配送问题的有效性。并通过数据实验揭示了以下规律:1)多车舱车辆相对于单车舱车辆在运营成本上具有优越性;2)大型车辆适合远距离配送,小型车辆适合近距离配送;3)多车型车辆混合配送相对于单车型车辆配送在运营成本上具有优越性。这些规律可为成品油配送公司的车辆配置提供决策参考。     

求解车辆路径问题的免疫算法

将免疫算法用于求解车辆路径问题,并根据车辆路径问题的具体情况提出了一种基于分组匹配的亲和力计算方法.实验结果表明,免疫算法能有效地应用于车辆路径问题.     

Approximation algorithms for a vehicle routing problem

In this paper we investigate a vehicle routing problem motivated by a real-world application in cooperation with the German Automobile Association (ADAC). The general task is to assign service requests to service units and to plan tours for the units such as to minimize the overall cost. The characteristics of this large-scale problem due to the data volume involve strict real-time requirements. We show that the problem of finding a feasible dispatch for service units starting at their current position and serving at most k requests is NP-complete for each fixed k ≥ 2. We also present a polynomial time (2k − 1)-approximation algorithm, where again k denotes the maximal number of requests served by a single service unit. For the boundary case when k equals the total number |E| of requests (and thus there are no limitations on the tour length), we provide a -approximation. Finally, we extend our approximation results to include linear and quadratic lateness costs.     

多商品分批次取送货的模糊需求车辆路径问题

为解决连锁企业库存不平衡问题,本文研究了考虑多商品多批次取送货的模糊需求车辆路径问题。该问题综合考虑了多货混装、多次访问、供需未匹配、客户需求不唯一以及需求不确定等因素。本文以运营成本最小为目标,构建MCVRPSPDFD数学模型,模型利用可信测度理论应对决策环境中的不确定因素,通过改进的禁忌搜索算法进行求解。为适应模型需求和提升运算效率,算法设计了合理的初始种群形成过程及编码解码方式,并通过参数测试选取合适的参数。算例结果显示,本文成果能有效解决连锁企业库存不平衡问题,决策者偏好值的变动会对运营成本产生影响。     

一种部分约束满足车辆路线问题及其求解算法

描述了一类过度约束车辆路线问题，其中可用车辆数较少而时间窗口等其它约束又不允许放松，因而导致不存在满足所有约束的可行解。此时问题求解可以转化为一类部分约束满足问题来处理，相应的优化目标是最小化未访问顾客的损失和。本给出了求解这类特殊问题的一种禁忌搜索算法设计，并通过规模不同的几个算例与其它常用方法进行了比较。最后分析了模型和算法的实用意义。