基于蚁群算法求解带硬时间窗的VRPSDP

建立了描述带硬时间窗的同时送取货的车辆路径问题(VRPSDPTW)的混合整数规划模型,给出了求解该模型的基于蚁群算法的改进的启发式算法。最后,通过实例计算,验证了算法的可行性和有效性,结果表明改进的蚁群算法在求解小规模问题（20个客户点）时,其性能总体优于已有的同类问题算法。     

求解带容量和时间窗约束车辆路径问题的改进蝙蝠算法

带时间窗和容量约束的车辆路径问题是车辆路径问题重要的扩展之一,属于NP难题,精确算法的求解效率较低,且对于较大规模问题难以在有限时间内给出最优解.为了满足企业和客户快速有效的配送需求,使用智能优化算法可以在有限的时间内给出相对较优解.研究了求解带容量和时间窗约束车辆路径问题的改进离散蝙蝠算法,为增加扰动机制,提高搜索速度和精度,在对客户点按其所在位置进行聚类的基础上,在算法中引入了变步长搜索策略和两元素优化方法进行局部搜索.仿真实验结果表明,所设计算法具有较高寻优能力和较强的实用价值.     

多策略优化的蚁群算法求解带时间窗车辆路径问题

提出一种新的蚁群算法求解带时间窗的车辆路径问题.在状态转移规则中,引入了时间启发函数,修改Ant Cycle模型信息素增量公式,引入等待或延误时间对信息素增量的影响.为避免算法陷入早熟,通过混沌扰动适当减小随机选取的最优路径上的信息素,按照客户坐标和时间窗改变已有解的组合方式对最优解进行调整.通过对相关文献实验数据的测试并与其他启发式算法所得结果进行比较,获得了较好的效果.     

面向全局搜索的自适应领导者樽海鞘群算法

针对实际配送过程中客户需求、车辆服务时间随机可变,提出带软时间窗的随机需求和随机服务时间的车辆路径问题.以配送车辆行驶路径为研究对象,建立基于配送成本、时间惩罚成本、修正成本的配送车辆路径优化模型,并提出一种混合禁忌搜索算法.该算法将最近邻算法和禁忌搜索算法相结合,将时间窗宽度及距离作为最近邻算法中节点选择标准;并对禁忌搜索算法中禁忌长度等构成要素进行自适应调整,引入自适应惩罚系数.实验结果表明,改进后的混合禁忌搜索算法具有较强的寻优能力、较高的鲁棒性,同时算法所得车辆行驶路径受客户需求变动影响较小.     

求解带时间窗车辆路径问题的改进FPA

车辆路径规划问题广泛应用于物流行业,为解决这一NP难的组合优化问题,提出一种求解带时间窗车辆路径问题的改进花授粉算法。针对FPA存在寻优精度低和过早陷入局部最优等缺陷,在原始FPA中引入遗传算法的交叉和变异因子,设计基于精英父代的多点交叉算子和单亲多点基因变异换位算子;对FPA中的转换概率p进行自适应调整并重新定义全局授粉和局部授粉操作;采用国际通用标准测试集Solomon对算法进行测试,将求得结果与已知多个算法求得的结果进行对比分析。其结果表明,改进FPA求解带时间窗车辆路径问题是可行有效的。     

蚂蚁算法在带时间窗车辆路径问题中的应用及参数分析

带时间窗的车辆路径问题是一个典型的NP-Hard问题,本文将蚂蚁算法应用于带时间窗车辆路径问题,构造了该问题的表达方法,建立了相应的算法模型,对算法参数进行了分析并提出了相应的参数改进方案。仿真实验表明,改进后的算法可以快速、有效地求解带时间窗车辆路径问题,具有较好的可行性和适用性。     

求解车辆路径问题的一种混合方法

提出一种求解带软时间窗车辆路径问题的混合算法。采用蚁群系统算法产生阶段最优解,以此作为粒子模板,随机生成粒子群,利用粒子群算法在阶段最优解基础上进一步优化。且在蚁群系统算法中,当容量超过限制后,从剩余的客户里选择需求量最大的作为新的起点继续探索路径,直到所有客户都被访问一遍。实验表明,该混合算法是解决带软时间窗车辆路径问题的一个有效算法。     

改进蚁群算法求解有时间窗的物流配送路径问题

物流配送车辆路径优化问题已被证明是一个NP难题,很难得到最优解。应用蚁群算法对带时间窗的物流车辆路径优化问题进行了算法设计,建立了车辆路径优化问题的蚁群算法数学模型及解决方案。通过对蚁群算法的分析,提出了改进的蚁群算法,并结合实例对该算法进行测试和分析,检验其有效性,结果表明了改进蚁群算法的可行性,符合实际的需要。     

多目标多时间窗车辆路径问题的鸽群-水滴算法

针对智能水滴算法求解带时间窗车辆路径规划收敛速度慢、计算精度差的问题,根据带时间窗车辆路径问题的应用要求,利用整数线性规划方法,以配送车辆的最小运输总成本、最短运输距离和最少安排数量为目标,综合考虑了车辆出发点、服务点、装载量、行驶距离、服务时间窗等诸多约束条件,构建了多目标多时间窗车辆路径模型;为了精准快速求解多目标多时间窗车辆路径模型,提出一种鸽群-智能水滴互补改进优化算法,将河道水滴离散二进制变换后,采用地图罗盘算子和地标算子分别改进水滴的流动速度和方向,并利用自适应变邻域扰动策略干扰水滴携带的泥土量,提高水滴算法的开发和探索能力;利用理想点法和罚函数与多目标优化混合方法分别处理多目标函数与约束条件,并以两种经典的带时间窗车辆路径问题为实例,通过与遗传算法、智能水滴算法和鸽群-水滴算法的计算结果进行比较,结果表明：在相同的算法参数和经济指标下,鸽群-水滴算法相比于智能水滴算法求解模型中的运输路径缩短20 km左右、运输成本节约403元左右,且该算法的求解时间和迭代次数也明显优于其他两种人工智能算法。     

改进AHP-GA算法的多目标配送路径优化

为准确优化快递配送路径,建立了基于时间窗的快递配送路径优化的数学模型.提出改进AHP-GA算法对多目标配送车辆路径进行优化,利用中位数层次分析算法对多个子目标进行权重系数配比,避免了极端值的影响,从而将多目标优化问题转化为单目标优化问题.通过简单的自然数对车辆路径进行编码,避免了路径重复.考虑了客户对车辆到达时间窗要求,包括车辆在约定时间之前到达获得的机会成本、在约定时间之后到达的罚金成本.最后,本文以1个配送中心,20个服务客户为例,对构建的数学模型通过分别使用传统的GA算法和使用改进AHP-GA算法进行优化,仿真结果表明,利用改进AHP-GA算法进行多目标配送路径优化,可以更加高效地求得问题的最优解.     

A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery

Vehicle routing problem (VRP) is an important and well-known combinatorial optimization problem encountered in many transport logistics and distribution systems. The VRP has several variants depending on tasks performed and on some restrictions, such as time windows, multiple vehicles, backhauls, simultaneous delivery and pick-up, etc. In this paper, we consider vehicle routing problem with simultaneous pickup and delivery (VRPSPD). The VRPSPD deals with optimally integrating goods distribution and collection when there are no precedence restrictions on the order in which the operations must be performed. Since the VRPSPD is an NP-hard problem, we present a heuristic solution approach based on particle swarm optimization (PSO) in which a local search is performed by variable neighborhood descent algorithm (VND). Moreover, it implements an annealing-like strategy to preserve the swarm diversity. The effectiveness of the proposed PSO is investigated by an experiment conducted on benchmark problem instances available in the literature. The computational results indicate that the proposed algorithm competes with the heuristic approaches in the literature and improves several best known solutions.     

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.     

An adaptive guidance approach for the heuristic solution of a minimum multiple trip vehicle routing problem

One of the most important problems in combinatorial optimization is the well-known vehicle routing problem (VRP), which calls for the determination of the optimal routes to be performed by a fleet of vehicles to serve a given set of customers. Recently, there has been an increasing interest towards extensions of VRP arising from real-world applications. In this paper we consider a variant in which time windows for service at the customers are given, and vehicles may perform more than one route within a working shift. We call the resulting problem the minimum multiple trip VRP (MMTVRP), where a “multiple trip” is a sequence of routes corresponding to a working shift for a vehicle. The problem objective is to minimize the overall number of the multiple trips (hence the size of the required fleet), breaking ties in favor of the minimum routing cost.     

An improved model for vehicle routing problem with time constraint based on genetic algorithm

A vehicle routing problem (VRP) with time constraint is one of the important problems in distribution and transportation. Thus the generic VRP and its practical extensions are discussed in great detail in the literatures. In the VRP, the service of a customer must start and finish within a given time interval. The objective of this problem is to minimize the cost of servicing the set of customers without being tardy or exceeding the capacity or travel time of the vehicles. In this research we concentrated on developing a GA–TSP model by improving the genetic algorithm (GA) operators and the initial population. For the computational purpose, we developed a GUI (graphic user interface)-type computer program according to the proposed method. The computational results show that the proposed method is very effective on a set of standard test problems and it can be potentially useful in solving the VRPs.     

物流配送车辆路径问题的优化研究

物流中的车辆路径问题(VRP)是目前组合优化领域的研究热点问题,VRP为NP-hard问题。本文在对VRP分析的基础上,建立数学模型,提出了一种适合求解该问题的蚁群遗传融合优化算法。提出的优化算法首先采用蚁群算法在局部阶段产生最好解,然后利用遗传算法的优良基因在全局阶段对优化解进一步优化,以获取最好路径解。实验结果表明,提出的融合算法能高效解决VRP问题,且优化效果比单算法好。     

METAHEURISTIC APPROACH FOR THE MULTI-DEPOT VEHICLE ROUTING PROBLEM

Distribution logistics comprises all activities related to the provision of finished products and merchandise to a customer. The focal point of distribution logistics is the shipment of goods from the manufacturer to the consumer. The products can be delivered to a customer directly either from the production facility or from the trader's stock located close to the production site or, probably, via additional regional distribution warehouses. These kinds of distribution logistics are mathematically represented as a vehicle routing problem (VRP), a well-known nondeterministic polynomial time (NP)-hard problem of operations research. VRP is more suited for applications having one warehouse. In reality, however, many companies and industries possess more than one distribution warehouse. These kinds of problems can be solved with an extension of VRP called multi-depot VRP (MDVRP). MDVRP is an NP-hard and combinatorial optimization problem. MDVRP is an important and challenging problem in logistics management. It can be solved using a search algorithm or metaheuristic and can be viewed as searching for the best element in a set of discrete items. In this article, cluster first and route second methodology is adapted and metaheuristics genetic algorithms (GA) and particle swarm optimization (PSO) are used to solve MDVRP. A hybrid particle swarm optimization (HPSO) for solving MDVRP is also proposed. In HPSO, the initial particles are generated based on the k-means clustering and nearest neighbor heuristic (NNH). The particles are decoded into clusters and multiple routes are generated within the clusters. The 2-opt local search heuristic is used for optimizing the routes obtained; then the results are compared with GA and PSO for randomly generated problem instances. The home delivery pharmacy program and waste-collection problem are considered as case studies in this paper. The algorithm is implemented using MATLAB 7.0.1.     

A simple and effective evolutionary algorithm for the vehicle routing problem

The vehicle routing problem (VRP) plays a central role in the optimization of distribution networks. Since some classical instances with 75 nodes resist the best exact solution methods, most researchers concentrate on metaheuristics for solving real-life problems. Contrary to the VRP with time windows, no genetic algorithm (GA) can compete with the powerful tabu search (TS) methods designed for the VRP. This paper bridges the gap by presenting a relatively simple but effective hybrid GA. In terms of average solution cost, this algorithm outperforms most published TS heuristics on the 14 classical Christofides instances and becomes the best solution method for the 20 large-scale instances generated by Golden et al.Scope and purposeThe framework of this research is the development of effective metaheuristics for hard combinatorial optimization problems met in vehicle routing. It is surprising to notice in the literature the absence of effective genetic algorithms (GA) for the vehicle routing problem (VRP, the main capacitated node routing problem), contrary to node routing problems with time windows or arc routing problems. Earlier attempts were based on chromosomes with trip delimiters and needed a repair procedure to get feasible children after each crossover. Such procedures are known to weaken the genetic transmission of information from parents to children. This paper proposes a GA without trip delimiters, hybridized with a local search procedure. At any time, a chromosome can be converted into an optimal VRP solution (subject to chromosome sequence), thanks to a special splitting procedure. This design choice avoids repair procedures and enables the use of classical crossovers like OX. The resulting algorithm is flexible, relatively simple, and very effective when applied to two sets of standard benchmark instances ranging from 50 to 483 customers.     

A genetic and set partitioning two-phase approach for the vehicle routing problem with time windows

The Vehicle Routing Problem with Time Windows (VRPTW) is a well-known and complex combinatorial problem, which has received considerable attention in recent years. This problem has been addressed using many different techniques including both exact and heuristic methods. The VRPTW benchmark problems of Solomon [Algorithms for the vehicle routing and scheduling problems with time window constraints, Operations Research 1987; 35(2): 254–65] have been most commonly chosen to evaluate and compare all algorithms. Results from exact methods have been improved considerably because of parallel implementations and modern branch-and-cut techniques. However, 24 out of the 56 high order instances from Solomon's original test set still remain unsolved. Additionally, in many cases a prohibitive time is needed to find the exact solution. Many of the heuristic methods developed have proved to be efficient in identifying good solutions in reasonable amounts of time. Unfortunately, whilst the research efforts based on exact methods have been focused on the total travel distance, the focus of almost all heuristic attempts has been on the number of vehicles. Consequently, it is more difficult to compare and take advantage of the strong points from each approach. This paper proposes a robust heuristic approach for the VRPTW using travel distance as the main objective through an efficient genetic algorithm and a set partitioning formulation. The tests were produced using real numbers and truncated data type, allowing a direct comparison of its results against previously published heuristic and exact methods. Furthermore, computational results show that the proposed heuristic approach outperforms all previously known and published heuristic methods in terms of the minimal travel distance.     

基于分支定价算法的双层轿运车运输问题

整车物流中双层轿运车运输问题属于一类需要考虑乘用车装载(vehicle filling problem, VFP)及轿运车路径规划(vehicle routing problem, VRP)的组合优化问题,称此类问题为VFRP(vehicle filling and routing problem).由于VFP和VRP的问题复杂性均为NP完全问题(non-deterministic polynomial complete problem, NPC),且VFRP等组合优化问题模型的目标函数及约束往往具有非凸结构,使得该类问题的线性化处理、精确算法的设计及求解效率的提升一直是该领域的研究难点.对此,以轿运车使用成本最低为目标,构建双层轿运车的VFRP模型,在此基础上提出两种线性化方法并设计改进分支定价算法(branch-and-price algorithm)以求解:在分支定价算法的基础上,提出结合最为分数策略(most-infeasible-branching strategy)和强分支策略(strong-branching strategy)的分支策略,以及在分支过程中降低可行域维度的...     

The multi-shift vehicle routing problem with overtime

In this paper, we study a new variant of the vehicle routing problem (VRP) with time windows, multi-shift, and overtime. In this problem, a limited fleet of vehicles is used repeatedly to serve demand over a planning horizon of several days. The vehicles usually take long trips and there are significant demands near shift changes. The problem is inspired by a routing problem in healthcare, where the vehicles continuously operate in shifts, and overtime is allowed. We study whether the tradeoff between overtime and other operational costs such as travel cost, regular driver usage, and cost of unmet demands can lead to a more efficient solution. We develop a shift dependent (SD) heuristic that takes overtime into account when constructing routes. We show that the SD algorithm has significant savings in total cost as well as the number of vehicles over constructing the routes independently in each shift, in particular when demands are clustered or non-uniform. Lower bounds are obtained by solving the LP relaxation of the MIP model with specialized cuts. The solution of the SD algorithm on the test problems is within 1.09–1.82 times the optimal solution depending on the time window width, with the smaller time windows providing the tighter bounds.