Mathematical Modelling for a Multi-Product Inventory Routing Problem with Split Delivery

In this article, a multi-product inventory routing problem is studied. One-depot and many retailers in a finite time period are considered, and split delivery is allowed as well for the addressed problem. The objective is to minimize the overall cost including vehicle cost, inventory holding cost and transportation cost while the delivery schedule and the quantity of each product for each retailer have to be decided simultaneously. A mathematical model is presented for solving the addressed optimally and example is illustrated as well.

Enhanced solution representations for vehicle routing problems with split deliveries

In this study,we investigate a forest-based solution representation for split delivery vehicle routing problems(SDVRPs),which have several practical applications and are among the most difficult vehicle routing problems.The new solution representation fully reflects the nature of split delivery,and can help reduce the search space when used in heuristic algorithms.Based on the forest structure,we devise three neighborhood search operators.To highlight the effectiveness of this solution representation,we integrate these operators into a standard tabu search framework.We conduct extensive experiments on three main SDVRPs addressed in the literature:The basic SDVRP,the multidepot SDVRP,and the SDVRP with time windows.The experimental results show that the new forest-based solution representation is particularly effective in designing and implementing neighborhood operators,and that our new approach outperforms state-of-the-art algorithms on standard datasets.

A two-stage heuristic method for vehicle routing problem with split deliveries and pickups

The vehicle routing problem(VRP) is a well-known combinatorial optimization issue in transportation and logistics network systems. There exist several limitations associated with the traditional VRP. Releasing the restricted conditions of traditional VRP has become a research focus in the past few decades. The vehicle routing problem with split deliveries and pickups(VRPSPDP) is particularly proposed to release the constraints on the visiting times per customer and vehicle capacity, that is, to allow the deliveries and pickups for each customer to be simultaneously split more than once. Few studies have focused on the VRPSPDP problem. In this paper we propose a two-stage heuristic method integrating the initial heuristic algorithm and hybrid heuristic algorithm to study the VRPSPDP problem. To validate the proposed algorithm, Solomon benchmark datasets and extended Solomon benchmark datasets were modified to compare with three other popular algorithms. A total of 18 datasets were used to evaluate the effectiveness of the proposed method. The computational results indicated that the proposed algorithm is superior to these three algorithms for VRPSPDP in terms of total travel cost and average loading rate.

Integrated multi-item packaging and vehicle routing with split delivery problem for fresh agri-product emergency supply at large-scale epidemic disease context

Fresh agri-product emergency supply is crucial to secure the basic livelihood of residents at large-scale epidemic disease context. Considering the massive demand and limited transportation resources, this study integrates multi-item packaging and vehicle routing with split delivery to improve the emergency supply capacity. Firstly, three specific objectives of fresh agri-product emergency supply at large-scale epidemic disease context are formulated, i.e., average response time, infectious risk possibility and transportation resource utilization. Then, a multi-item packaging strategy is proposed to consolidate different categories of fresh agri-products according to the food cold chain temperatures.An optimization model integrating multi-item packaging and vehicle routing with split delivery is developed to jointly decide the optimal packaging scheduling, vehicle assignment and delivery routing. Next, an improved genetic algorithm based on solution features (IGA-SF) is designed to solve the integrated model with multiple decision variables. Finally,a case on fresh agri-product emergency supply of Huangpi District, Wuhan in the context of the Corona Virus Disease 2019(COVID-19) is carried out to illustrate the efficiency and feasibility of the proposed model. The numerical results of medium-to-largescale cases demonstrate that the proposed IGA-SF could save 23.91% CPU time and 37.80% iteration number on average than genetic algorithm. This study could satisfy different emergency scenario requirements flexibly, and provide scientific decision support for provincial and national governments on fresh agri-product emergency supply.

基于离散混合蛙跳算法的地震应急物资调度

建立震后应急物资调度数学模型。该模型根据各灾区的受灾情况评估其救援紧急程度,并设计一种需求拆分供应的运输机制,提高车辆的利用效率。为求解该模型,提出一种多源信息学习的离散混合蛙跳算法。所提算法引入多种信息源以扩展算法的搜索方向,降低种群的同化速度。同时,让子组最差个体学习种群中的有效信息,提高算法的收敛精度。实验结果表明,所提算法能够搜索到精度更优的调度方案,对问题规模具有良好的可扩展性。

面向复杂物流配送场景的车辆路径规划多任务辅助进化算法

在现代社会中,复杂物流配送场景的车辆路径规划问题(Vehicle routing problem,VRP)一般带有时间窗约束且需要提供同时取送货的服务.这种复杂物流配送场景的车辆路径规划问题是NP-难问题.当其规模逐渐增大时,一般的数学规划方法难以求解,通常使用启发式方法在限定时间内求得较优解.然而,传统的启发式方法从原大规模问题直接开始搜索,无法利用先前相关的优化知识,导致收敛速度较慢.因此,提出面向复杂物流配送场景的车辆路径规划多任务辅助进化算法(Multitask-based assisted evolutionary algorithm,MBEA),通过使用迁移优化方法加快算法收敛速度,其主要思想是通过构造多个简单且相似的子任务用于辅助优化原大规模问题.首先从原大规模问题中随机选择一部分客户订单用于构建多个不同的相似优化子任务,然后使用进化多任务(Evolutional multitasking,EMT)方法用于生成原大规模问题和优化子任务的候选解.由于优化子任务相对简单且与原大规模问题相似,其搜索得到的路径特征可以通过任务之间的知识迁移辅助优化原大规模问题,从而加快其求解速度.最后,提出的算法在京东物流公司快递取送货数据集上进行验证,其路径规划效果优于当前最新提出的路径规划算法.

考虑个体客户满意度的多车程生鲜品配送路径优化

随着生鲜电商的兴起,生鲜品的道路运输量越来越大,其配送任务越来越复杂,提升客户满意度是生鲜品配送的重要目标组成。文章以一个具有配送自主权的生鲜品供应商为研究对象,以整个计划周期内生鲜品配送的车辆运输成本最小及客户满意度最大为双目标,且客户满意度从顾客的个体视角考虑,构建双目标多车程带时间窗及考虑订单打包时间的车辆路径优化模型。基于ε-约束方法,设计了两阶段变邻域搜索(VNS)和模拟退火(SA)相结合的元启发式算法,基于车辆构造初始路线,并针对性地提出了3点改进措施,包括通过数学性质推导下界、减少求解过程中不必要的搜索空间以及规避求解过程中被支配解的后优化处理。最后,以Solomon标准算例为基础构造算例对所设计的算法进行了计算实验,其求解结果表明:其设计的算法具有有效性,并通过敏感性分析得出相关管理启示。

多中心半开放式同时送取货的车辆路径问题研究

研究了带软时间窗约束的多配送中心半开放式同时送取货的车辆路径问题,所有客户点均存在送取两种需求,并采用同一辆车同时提供送取服务.车辆服务完路线上所有客户点后,不一定返回起始配送中心,可就近返回任意配送中心.在此条件下,构建了以车辆运输成本、车辆租赁成本、时间窗惩罚成本等总和最小为目标的优化模型.根据问题特征,设计了自适应精英遗传算法对该问题进行求解,引入自适应机制,根据个体的适应度动态地调节交叉和变异概率,采用精英保留策略将优秀个体进行遗传保留,不仅增强了算法的全局优化能力,还均衡了算法的局部搜索能力.通过案例仿真,验证了模型和算法的可行性和有效性.研究成果丰富了车辆路径问题的相关研究,为物流企业提供了一种决策参考.

DCS算法求解带软时间窗的送取货一体化VRP

为求解带软时间窗的送取货一体化车辆路径问题,提出一种离散布谷鸟(DCS)搜索算法。该算法在基本布谷鸟搜索算法基础之上,对莱维飞行获取新鸟巢和以一定概率抛弃鸟巢的迭代公式进行重新定义;同时设计客户序列和车辆序列双倍体鸟巢,并对客户序列采用交换、逆序、插入操作和对每辆车的访问路线采用2-Opt操作。通过5个算例的仿真实验和相关文献比较,结果表明所提DCS算法行之有效。

面向多行程取送货车辆路径问题的混合NSGA-Ⅱ

针对多行程取送货车辆路径问题(VRP)收敛性与多样性相互制约的问题,提出一种融合自适应大邻域搜索(ALNS)算法和自适应邻域选择(ANS)的混合快速非支配排序遗传算法(NSGA-Ⅱ-ALNS-ANS)。首先,考虑初始解对算法收敛速度的影响,提出一种改进的后悔插入法以获得高质量初始解;其次,结合取送货问题特性,设计多组破坏和修复算子,以及多种邻域结构,提高算法的全局搜索能力和局部搜索能力;最后,设计基于随机采样的最佳拟合下降(BFD)算法与高效的可行解评价标准,生成路径分配方案。采用不同规模的标准公开算例进行仿真实验,与模因算法(MA)相比,所提算法的最优解质量提升了27%。实验结果表明,所提算法可快速得到满足多重约束的高质量车辆多行程路径分配方案,并在收敛性与多样性上优于对比算法。

外卖配送路径优化问题研究现状与趋势

外卖配送路径优化问题一直是外卖配送研究领域的难点和热点。由于配送成本在总成本中占有较大的占比,所以至今以来国内外学者不断提出外卖配送路径优化相关的目标及算法的改进以提高配送效率。为了进一步梳理国内外研究现状,文章针对外卖配送路径优化问题的时间窗、取送要求、随机性、开放型等特点特性,分别针对不同类型的外卖配送路径优化问题,从优化目标和优化算法两个方面进行了较为全面的综述。最后,对外卖配送路径优化领域一些新的研究方向进行了展望。

基于残差图卷积网络与深度强化学习的需求可拆分车辆路径优化算法

需求可拆分车辆路径问题(SDVRP)出现在广泛的物流配送场景中,具有重要的研究价值.高效的SDVRP优化算法能够提高车辆装载率,降低物流配送成本.为提高SDVRP的求解效率,本文提出基于残差图卷积神经网络(RGCN)和多头注意力的深度强化学习算法(REINFORCE),逐步构建可行解序列.首先,从强化学习的角度出发,文章对SDVRP建立马尔科夫决策模型,定义序列预测过程的环境状态、智能体动作空间、状态转移函数等.其次,建立编–解码模型求解节点选择策略,其中使用残差图卷积神经网络的编码器重构配送中心和客户节点的特征,将配送网络中节点间的连接关系与节点特征相互关联,获得差异性显著的特征嵌入向量;利用注意力网络解码器在重构后的嵌入向量基础上融合动态变化的车辆剩余装载量和客户需求等信息执行解码任务,实现每次迭代为单个案例提供多个可行解.最后,提出基于平均基准值的REINFORCE算法更新模型参数,通过求解不同问题规模测试集、标准SDVRP数据集,以及京东物流实际配送任务,验证了所提算法的有效性.

深度强化学习Memetic算法求解取送货车辆路径问题

带时间窗约束的同时取送货车辆路径问题(VRPSPDTW)是NP难问题,属于约束较复杂的车辆路径问题,在现代物流中有广泛应用。提出深度强化学习Memetic算法求解该问题,将Memetic算法求解VRPSPDTW问题中的大邻域搜索过程建模成马尔可夫决策过程,构建编码器-解码器架构的深度神经网络模型完成大邻域搜索中的移除操作。编码器对当前解中各结点的个体特征和位置特征进行信息交互,解码器输出需要移除的结点,设计了非自回归和自回归两种网络结构,采用强化学习算法训练神经网络模型。设计了混合策略,将人工设计的启发式策略与深度强化学习到的策略相结合,以提高寻优能力。实验结果显示提出的算法具有更强的跳出局部最优的能力,能在有效的时间内获得比对比算法更优的解,特别是在大规模问题上。最后,对提出算法的新组件进行了消融实验,证明了算法的有效性。

转向限制网络下考虑订单平均配送时间的取送货路径优化

研究考虑城市通行限制的即时配送策略对减少订单平均配送时间,提高配送时间一致性及客户满意度具有重要意义。通过设置可转向节点构建转向限制性配送网络,以平均配送时间最小化为目标,在具有转向限制的配送网络下,建立考虑订单动态性的多车辆实时取送货路径优化模型,并基于滚动时域设计IGNORE和W&R(wait&return)两种延迟配送策略。在算例分析中,调整可转向节点个数及距离模拟密集型、稀疏型两种道路网络。通过数值仿真及遗传算法求解,验证了模型的稳定性及策略的适用性,得到了IGNORE和W&R策略分别在这两种网络及不同订单数量、配送员人数和滚动时域的时长下的平均配送时间,并分析了平均配送时间波动的原因。结果表明:IGNORE策略适用于网络小订单少的情形,且随着滚动时域时长缩短,订单平均配送时间减少;W&R策略适用于配送网络较大的情形,网络可转向节点数越多,订单平均配送时间减少。研究结论对即时配送平台优化配送策略和提升客户满意度有一定的参考意义。

基于改进遗传算法的末端共同配送车辆路径优化

为解决共同配送路径优化问题,提出一个具有可操作性的共同配送策略,基于此构建了以考虑车辆使用成本、车辆行驶成本和碳排放成本最小化为目标的共同配送车辆路径模型,用K-means聚类方法对客户节点进行分区聚类,确定各末端配送网点所服务的客户,并在此基础上利用基于节约里程算法的遗传算法对该模型进行求解.通过利用公共数据集实验验证设计的CW-GA算法的优越性,发现相较于传统GA,本文算法具有良好的求解性能.利用本文算法仿真分析共同配送前后相关成本的变化以及不同配送模式下的燃料消耗、行驶距离变化,结果表明共同配送能够有效降低物流总成本.

Approximation Algorithms for Multi-vehicle Stacker Crane Problems

We study a variety of multi-vehicle generalizations of the Stacker Crane Problem(SCP).The input consists of a mixed graph G=(V,E,A)with vertex set V,edge set E and arc set A,and a nonnegative integer cost function c on E∪A.We consider the following three problems:(1)k-depot SCP(k-DSCP).There is a depot set D⊆V containing k distinct depots.The goal is to determine a collection of k closed walks including all the arcs of A such that the total cost of the closed walks is minimized,where each closed walk corresponds to the route of one vehicle and has to start from a distinct depot and return to it.(2)k-SCP.There are no given depots,and each vehicle may start from any vertex and then go back to it.The objective is to find a collection of k closed walks including all the arcs of A such that the total cost of the closed walks is minimized.(3)k-depot Stacker Crane Path Problem(k-DSCPP).There is a depot set D⊆V containing k distinct depots.The aim is to find k(open)walks including all the arcs of A such that the total cost of the walks is minimized,where each(open)walk has to start from a distinct depot but may end at any vertex.We present the first constant-factor approximation algorithms for all the above three problems.To be specific,we give 3-approximation algorithms for the k-DSCP,the k-SCP and the k-DSCPP.If the costs of the arcs are symmetric,i.e.,for every arc there is a parallel edge of no greater cost,we develop better algorithms with approximation ratios max{9/5,2−1/2k+1},2,2,respectively.All the proposed algorithms have a time complexity of O(|V|3)except that the two 2-approximation algorithms run in O(|V|2log|V|)time.

考虑同时取送和时间窗的车辆路径及求解算法

针对带时间窗的同时取送货车辆路径问题(vehicle routing problem with simultaneous pickup-delivery and time windows,VRPSPDTW),构建了以车辆使用成本、车辆行驶距离成本总支出最小化的路径优化数学模型,提出自适应头脑风暴算法(adaptive brain storm optimization,ABSO)进行求解。全局搜索阶段,采用多项惩罚方式扩大搜索区域,并使用聚类及三种路径搜索策略进行全局搜索;局部搜索阶段,将六种破坏-修复算子作为备选集合,进而设计自适应动态选择邻域搜索机制,增强局部搜索效能。选取测试数据集和实际案例对算法性能进行测试,实验结果表明针对小规模标准算例,所提算法全部取得了当前已知最优解;对于大规模标准算例,通过与遗传算法、并行模拟退火算法、离散布谷鸟算法对比,所提算法实验计算结果有7.52%~12.03%的提升;对于实际案例,所提算法在收敛速度和寻优能力方面均展示出优越性,充分验证了所提算法对解决VRPSPDTW问题的有效性。

考虑软时间窗的同时送取货随机旅行时间车辆路径问题

考虑车辆总旅行时间约束和车辆载重限制以及客户对服务时间窗的要求,研究带有软时间窗的同时送取货随机旅行时间车辆路径问题(STT‒VRPSPD),建立机会约束规划模型。将禁忌搜索算法与分散搜索算法相结合,构建混合分散禁忌搜索(HSTS)算法,并采用C‒W节约算法生成初始解。基于经典的Dethloff算例和Solomon时间窗生成方法,分别生成包括50个客户、200个客户各20组算例,算例测试结果验证了混合分散禁忌搜索算法的有效性。

基于狼群算法的同时取送货模糊绿色车辆路径问题

文章提出了带模糊需求的同时取送货绿色车辆路径问题,并将碳排放作为优化目标,建立了相应的模糊规划模型。然后给出了解决问题的狼群算法,定义了人工狼的游走行为、召唤行为、围攻行为。最后通过仿真实验,验证了该算法的有效性,并将其与其他算法进行了对比,分析了决策者主观偏好值的变化对目标值的影响。

考虑需求可拆分的共享单车调度优化研究

研究考虑需求可拆分的共享单车调度优化问题为可拆分单商品取送货TSP问题,考虑一辆调度车,允许调度车多次访问各站点,每次满足站点的部分需求,即允许对站点的需求进行拆分。首先,考虑到调度车容量限制,统筹安排调度车行驶路径和调度车在每个站点的取车量、送车量,使得企业的运营成本达到最优。其次,提出了一种改进的变邻域搜索算法求解上述问题,使算法在陷入局部最优解时改变邻域结构,扩大搜索范围,以此提升算法跳出局部最优解的能力,加快收敛速度。最后,用数值实验验证了算法的有效性。研究结论拓展了可拆分单商品取送货问题的相关理论,并为共享单车企业的实际运营提供决策支持。