带软时间窗的多车场开放式车辆调度

带软时间窗的多车场开放式车辆调度问题是在开放式车辆路径问题的基础上,考虑了多车场和客户服务时间的约束,是一类典型的NP难解问题。针对该问题,提出了一种改进的蚁群算法求解方案,并建立了相应的数学模型。首先通过设置一个虚拟车场将多车场VRP转化为单车场VRP,然后利用参数控制的改进蚁群算法与2-opt算法结合来对模型求解。算法先利用K-means与细菌觅食算法相结合的聚类技术判断蚁群状态,进而动态调整算法参数,使其快速收敛到全局最优解附近,再依据混沌理论的特点来调整参数,使其跳出局部最优。最后,再利用2-opt算法对最优解进行优化。实验结果验证了该算法求解MDOVRPSTW问题的有效性。     

行驶时间随机的分批配送车辆路径问题模型与算法

为研究分批配送和等待时间对行驶时间随机的车辆路径问题（VRP）的影响,针对行驶时间随机的分批配送车辆路径问题,在软时间窗下考虑等待时间,建立带修正的随机规划模型;同时设计改进的粒子群优化（PSO）算法进行求解：使用需求点可多次出现的整数编码,设计改进的相对位置索引算法进行解码以解决粒子中出现分批需求点问题;将自适应选择用于速度更新以解决各向量长度不同的问题;将路径重连算法用于位置更新过程以解决粒子在离散空间和连续空间转换时信息丢失的问题,适应允许分批配送的特点。通过对调整的Solomon算例测试,考虑等待时间将造成总费用平均增加约3%,且更倾向于分批配送。分批配送能有效降低总费用（2%）和减少使用的车辆数（0.6）;在部分算例,特别是R2类算例中,分批配送能有效降低等待时间,平均降低0.78%。     

需求点随机的分批配送VRP模型与算法研究

针对城市配送中需求点不确定的现象, 在分批配送车辆路径问题中引入随机需求点进行研究.建立带修正的随机规划模型, 采用先验优化策略, 根据分批配送的特点, 在自适应大邻域搜索算法中引入改进的分割插入算子进行求解.在调整的Solomon算例上进行的测试表明, 允许分批配送在大部分算例中的费用低于不允许分批配送的情形.通过分析计算过程中各个算子权重变化, 确定性最差删除算子和随机删除算子在求解此类问题时表现较好; 贪婪插入算子、后悔插入算子表现较好; 而分割插入算子虽然权重较低, 但能对解产生质的影响.     

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.     

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.     

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.     

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.     

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.     

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.     

带时间窗的同时集散货物路线问题研究

研究了业务繁忙环境下带时间窗的同时集散货物路线问题．以车辆数、运输距离和完成运输任务的总 时间最小为目标建立了多目标模型,提出用基于路线集合划分的分解迭代算法求解该问题．该算法首先用两种策略 将问题的解分解为几个子集合,用记录更新法分别求解每个子集合,将子集合求得的最好路线反馈回来形成新的当 前解,再分解迭代,逐渐改善解的质量．最后数据实验表明该算法能有效解决带时间窗的单向车辆路线问题和集散 一体化的双向车辆路线问题．     

An open source Spreadsheet Solver for Vehicle Routing Problems

The Vehicle Routing Problem (VRP) is one of the most frequently encountered optimization problems in logistics, which aims to minimize the cost of transportation operations by a fleet of vehicles operating out of a base. This paper introduces VRP Spreadsheet Solver, an open source Excel based tool for solving many variants of the Vehicle Routing Problem (VRP). Case studies of two real-world applications of the solver from the healthcare and tourism sectors that demonstrate its use are presented. The solution algorithm for the solver, and computational results on benchmark instances from the literature are provided. The solver is found to be capable of solving Capacitated VRP and Distance-Constrained VRP instances with up to 200 customers within 1 h of CPU time.     

An evolutionary approach for multi-objective vehicle routing problems with backhauls

The vehicle routing problem (VRP) is an important aspect of transportation logistics with many variants. This paper studies the VRP with backhauls (VRPB) in which the set of customers is partitioned into two subsets: linehaul customers requiring a quantity of product to be delivered, and backhaul customers with a quantity to be picked up. The basic VRPB involves finding a collection of routes with minimum cost, such that all linehaul and backhaul customers are serviced. A common variant is the VRP with selective backhauls (VRPSB), where the collection from backhaul customers is optional. For most real world applications, the number of vehicles, the total travel cost, and the uncollected backhauls are all important objectives to be minimized, so the VRPB needs to be tackled as a multi-objective problem. In this paper, a similarity-based selection evolutionary algorithm approach is proposed for finding improved multi-objective solutions for VRPB, VRPSB, and two further generalizations of them, with fully multi-objective performance evaluation.     

Particle swarm optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows

Today, companies need to collect and to deliver goods from and to their depots and their customers. This problem is described as a Vehicle Routing Problem with Mixed Linehaul and Backhaul customers (VRPMB). The goods delivered from the depot to the customers can be alternated with the goods picked up. Other variants of VRP added to VRPMB are Heterogeneous fleet and Time Windows. This paper studies a complex VRP called HVRPMBTW which concerns a logistic/transport society, a problem rarely studied in literature. In this paper, we propose a Particle Swarm Optimization (PSO) with a local search. This approach has shown its effectiveness on several combinatorial problems. The adaptation of this approach to the problem studied is explained and tested on the benchmarks. The results are compared with our previous methods and they show that in several cases PSO improves the results.     

Arc routing in a node routing environment

We describe a special variant of the vehicle routing problem (VRP), where there are many customers per road segment. This class of VRPs arises in, e.g. mail delivery, and is a borderline case where both arc routing and node routing techniques may be applied for modeling and solving. In a real-world setting, the problem should be modeled so as to incorporate all important constraining factors. We use a simplified node routing model and aggregate customers into supernodes to reduce problem size. A tabu search metaheuristic for the standard node routing-based VRP is then applied to the aggregated version of the problem. Our method is tested both on test instances from the literature as well as on a portfolio of new test instances especially made to fit the problem at hand. Experimental results are reported, showing that aggregation of customers can lead to substantial improvements both in solution time and solution quality in this setting, especially for larger instances.     

A hybrid genetic algorithm for the electric vehicle routing problem with time windows

Driven by the newlegislation on greenhouse gas emissions, carriers began to use electric vehicles (EVs) for logistics transportation. This paper addresses an electric vehicle routing problem with time windows (EVRPTW). The electricity consumption of EVs is expressed by the battery state-of-charge (SoC). To make it more realistic, we take into account the terrain grades of roads, which affect the travel process of EVs. Within our work, the battery SoC dynamics of EVs are used to describe this situation. We aim to minimize the total electricity consumption while serving a set of customers. To tackle this problem, we formulate the problem as a mixed integer programming model. Furthermore, we develop a hybrid genetic algorithm (GA) that combines the 2-opt algorithm with GA. In simulation results, by the comparison of the simulated annealing (SA) algorithm and GA, the proposed approach indicates that it can provide better solutions in a short time.     

基于启发式带时间窗的车辆路径规划问题求解

车辆路径规划问题广泛地存在于现代物流行业中,该问题属于NP难的组合优化问题.随着客户需求的多样化、道路限行等因素的影响,该问题变得更加的复杂,采用传统的组合优化方法和运筹学方法往往难以求解.本文对一类常见的带时间窗的车辆路径规划问题进行了研究,根据时间窗参数来调整客户的优先级,以减少车辆的等待时间,由此改进了几个常见的启发式算法,并对56个常见的车辆路径规划问题进行了测试,实验结果表明,改进的节约算法在带容量约束的车辆路径问题中效果较好,改进的插入法则在带时间窗的车辆路径问题中具有优越性,另外,改进的启发式算法在4个测试用例上使用更多车辆时可使总路程优于已知最优值.     

A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows

This paper addresses the multiobjective vehicle routing problem with time windows (MOVRPTW). The objectives are to minimize the number of vehicles and the total distance simultaneously. Our approach is based on an evolutionary algorithm and aims to find the set of Pareto optimal solutions. We incorporate problem-specific knowledge into the genetic operators. The crossover operator exchanges one of the best routes, which has the shortest average distance, the relocation mutation operator relocates a large number of customers in non-decreasing order of the length of the time window, and the split mutation operator breaks the longest-distance link in the routes. Our algorithm is compared with 10 existing algorithms by standard 100-customer and 200-customer problem instances. It shows competitive performance and updates more than 1/3 of the net set of the non-dominated solutions.     

A planning model and solution algorithm for multi-trip split-delivery vehicle routing and scheduling problems with time windows

This study proposes a daily vehicle routing model for minimizing the total cost of replenishing inventory within a supply chain. The first major contribution of this research is to allow multiple use of vehicles in a split delivery vehicle routing problem with time windows (SDVRPTW), which is more realistic for various real-life applications. The multi-trip SDVRPTW (MTSDVRPTW) is formulated using the time–space network technique, which provides greater flexibility for formulating the complicated interactions between vehicles and products when multi-trip, split delivery, and delivery time windows are simultaneously considered. The resulting formulation of the MTSDVRPTW can be categorized as an integer multi-commodity network flow problem with side constraints. A two-step solution algorithm is proposed to solve this NP-hard problem, which is the second major contribution of this research. Finally, a real-world scale numerical example is performed to demonstrate and to test the methodology. The results indicate that these vehicle routing problems can be solved effectively and efficiently and that the proposed methodology has great potential for inventory replenishment scheduling where split deliveries and multiple trips for a single vehicle are allowed and time window constraints are imposed.     

基于实时交通信息的车辆路径问题研究

石油化工企业的物流配送越来越成为降低成本、提高效率的1个重要环节,而车辆路径问题是其中的基础性问题。面对各种不确定性,动态随机车辆路径问题越来越成为有价值的研究方向,其关键在于实时交通信息的利用。本文研究了基于实时交通信息的单配送中心、有时间窗口约束的车辆路径问题,建立了混合整数规划模型,提出了利用实时速度估计信息的动态调度策略,并设计了带插入规则的节约算法。通过对标准benchmark问题进行仿真,验证了策略和算法的有效性。     

多时间窗车辆路径问题的混合蚁群算法

研究了多时间窗车辆路径问题,建立了多时间窗车辆路径问题的数学模型,并基于蚁群算法设计了一种混合蚁群算法对问题进行了求解。该算法首先利用基本蚁群算法求解,然后采用2-opt算法和元胞自动算法对结果进行优化,同时加入变异算子。实验结果表明该算法可以有效地求解多时间窗车辆路径问题。