Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm

The vehicle routing problem (VRP) is a well-known combinatorial optimisation problem and holds a central place in logistics management. Many exact, heuristic and metaheuristic approaches have been proposed to solve VRP. An important variant of the VRP arises when a ?eet of vehicles is fixed and characterised by different capacities for distribution activities. The problem is known as the heterogeneous fixed fleet VRP (HFFVRP). The HFFVRP is a natural generalisation of the VRP with several vehicle types, each type being defined by a capacity, a fixed cost and a cost per distance unit, and can cover more practical situations in transportation. This problem consists of determining a set of vehicle trips of minimum total length in which a set of customers is to be satisfied in the demand constraints using identical vehicles with limited capacity. If open routes instead of closed ones are considered in the HFFVRP, the problem becomes a heterogeneous fixed fleet Open VRP (HFFOVRP) which has numerous applications in industrial and service problems. In this paper, a bone route algorithm which uses the tabu search as an improved procedure is utilised to solve the HFFOVRP. The proposed algorithm was tested empirically on a 24 of generated VRPs, and compared with elite ant system and ant colony system. In all cases, the proposed algorithm finds the best-known solutions within a reasonable time.     

面向快递同城运输的车辆路径问题研究

为降低运输成本,研究了快递同城运输中的车辆路径问题。建立多车型,含时间窗约束、容量约束、车辆限行约束,并考虑错峰交货的,以最小化运输成本为目标的混合整数规划模型。提出以点到点集的距离之和作为邻域搜索优先指标的构造性启发式算法,设计了基于“路径−车型对”的列生成算法,初始列由启发式算法求得。实验结果显示,对于120个点的大规模问题,列生成算法只需175秒就能得到近似最优解,验证了该算法的有效性及对一定规模内快递同城运输问题的适用性。     

Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows

In this paper, we study a production scheduling and vehicle routing problem with job splitting and delivery time windows in a company working in the metal packaging industry. In this problem, a set of jobs has to be processed on unrelated parallel machines with job splitting and sequence-dependent setup time (cost). Then the finished products are delivered in batches to several customers with heterogeneous vehicles, subject to delivery time windows. The objective of production is to minimize the total setup cost and the objective of distribution is to minimize the transportation cost. We propose mathematical models for decentralized scheduling problems, where a production schedule and a distribution plan are built consecutively. We develop a two-phase iterative heuristic to solve the integrated scheduling problem. We evaluate the benefits of coordination through numerical experiments.     

带时间窗的时变多目标危险化学品道路运输路径优化

研究了危险化学品道路运输路径优化（VRP）问题,考虑了该问题的3个方面：1）路径选择涉及运输时间与运输风险两个目标;2）运输时间与风险具有时变特性;3）道路节点的服务时间窗限制。本文以运输时间和风险为多目标,综合考虑以上约束,建立了该问题的数学模型并设计了蚁群算法进行求解。求解结果表明该算法可以有效计算帕累托最优路径,决策者可结合实际问题和决策偏好作出最合适的决策,同时运输企业可依据不同时刻的运输结果制定车辆的出发时刻表,监管部门可通过合理规划各路径的服务时间窗及允许停留等待的节点来调节各路径运输时间及风险。     

A review on the electric vehicle routing problems: Variants and algorithms

Over the past decade, electric vehicles (EVs) have been considered in a growing number of models and methods for vehicle routing problems (VRPs). This study presents a comprehensive survey of EV routing problems and their many variants. We only consider the problems in which each vehicle may visit multiple vertices and be recharged during the trip. The related literature can be roughly divided into nine classes: Electric traveling salesman problem, green VRP, electric VRP, mixed electric VRP, electric location routing problem, hybrid electric VRP, electric dial-a-ride problem, electric two-echelon VRP, and electric pickup and delivery problem. For each of these nine classes, we focus on reviewing the settings of problem variants and the algorithms used to obtain their solutions.     

考虑道路坡度影响的多约束冷链配送问题研究

目的 为改进传统冷链VRP将配送区域默认为二维平面，使得实际调度与理想状态产生差异而造成配送成本增加的问题，本文对相关问题进行深入研究，旨在合理规划资源配置，提升企业经济效益。方法 通过引入坡度函数对油耗成本和碳排放成本进行计算，综合考虑三维空间位置、多车型、载质量变化、客户取送货需求和时间窗要求等多种现实约束，并提出一种基于K–means多维时空聚类的改进遗传算法进行求解。结果 求解结果表明，若最初将道路坡度考虑在成本计算内，可有效降低9.58%的配送成本。同时，应避免大型车辆在重载时突然发生海拔变化。当发生海拔变化时，大型车辆可在卸载一部分货物后改变至更高的高度。结论 本文研究的模型更加贴近实际路网，具有更高的适用性，特别是对有明显道路坡度城市的冷链品的配送具有现实的借鉴意义。     

A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. Our computational results on benchmark instances and on families of clustered instances show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most pronounced for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We compare the robust optimization model with classic stochastic VRP models for this problem to illustrate the differences and similarities between them. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles.     

Optimisation of the multi-depots pick-up and delivery problems with time windows and multi-vehicles using PSO algorithm

Many sectors in the transport industry are concerned about the vehicle routing problem (VRP), hence the growing interest of researchers for this type of problem and its variants. This is due essentially to its many real applications in logistics for the transport of goods. The originality and contribution of our work is that we have dealt a problem that combines several variants: multiple vehicles (m), multiple depots (MD), pickup and delivery problem (PDP) with time windows (TW). Hence the notation of our problem: m-MDPDPTW. In this paper, we present the m-MDPDPTW, which is an optimisation problem belonging to the category of NP Hard problems. This problem must meet requests for transport between customers and suppliers satisfying precedence, capacity and time constraints. The goal is to find the best solution, which is the best route minimising the total travelled distance. To solve and optimise our m-MDPDPTW, we have developed a new algorithm based on the particle swarm optimisation (PSO) method. The performance of this new approach is tested on data set instances of Li and Lim's benchmark problems in which we have added multiple depot locations. Comparing with prior works, our proposed approach gave better results by decreasing the distance for several studied instances.     

A hybrid genetic algorithm for the multi-depot open vehicle routing problem

This paper studies the multi-depot open vehicle routing problem (MDOVRP), a variant of the vehicle routing problem (VRP), in which vehicles start from several depots and are not required to return to the depot. Despite the vast amount of literature about VRPs, the MDOVRP has received very little attention from researchers. In this paper, a new hybrid genetic algorithm is presented for finding the routes that minimize the traveling cost of the vehicles. Computational results on a number of test instances indicate the proposed algorithm dominates the CPLEX solver and the existing approach in the literature. Meanwhile, experiments are conducted on multi-depot VRP benchmarks, and the results are compared with a sophisticated tabu search approach and an exact method.     

共享电动车电池配送问题研究

共享电动车电池的配送方案关系到用户的切身体验和企业利益。为制定最优配送方案，真正打通人们出行的“最后一公里”，本文考虑企业对成本的要求和用户对时效性的要求，以总配送成本最小以及用户满意度最高为目标建立了一个带软时间窗的车辆路径问题模型，利用扫描法和基于最佳路径成本的交叉算子改进了传统遗传算法，用算例验证了模型与改进算法的有效性，并通过数值实验找出了种群大小、迭代次数与最优解之间的相关关系。     

Research on Vehicle Routing Problem with Soft Time Windows Based on Hybrid Tabu Search and Scatter Search Algorithm

With the expansion of the application scope of social computing problems, many path problems in real life have evolved from pure path optimization problems to social computing problems that take into account various social attributes, cultures, and the emotional needs of customers. The actual soft time window vehicle routing problem, speeding up the response of customer needs, improving distribution efficiency, and reducing operating costs is the focus of current social computing problems. Therefore, designing fast and effective algorithms to solve this problem has certain theoretical and practical significance. In this paper, considering the time delay problem of customer demand, the compensation problem is given, and the mathematical model of vehicle path problem with soft time window is given. This paper proposes a hybrid tabu search (TS) & scatter search (SS) algorithm for vehicle routing problem with soft time windows (VRPSTW), which mainly embeds the TS dynamic tabu mechanism into the SS algorithm framework. TS uses the scattering of SS to avoid the dependence on the quality of the initial solution, and SS uses the climbing ability of TS improves the ability of optimizing, so that the quality of search for the optimal solution can be significantly improved. The hybrid algorithm is still based on the basic framework of SS. In particular, TS is mainly used for solution improvement and combination to generate new solutions. In the solution process, both the quality and the dispersion of the solution are considered. A simulation experiments verify the influence of the number of vehicles and maximum value of tabu length on solution, parameters’ control over the degree of convergence, and the influence of the number of diverse solutions on algorithm performance. Based on the determined parameters, simulation experiment is carried out in this paper to further prove the algorithm feasibility and effectiveness. The results of this paper provide further ideas for solving vehicle routing problems with time windows and improving the efficiency of vehicle routing problems and have strong applicability.     

Virtual flow paths for free-ranging automated guided vehicle systems

Recent technological development in vehicle design allow vehicles to operate without physical guide paths, i.e. free-ranging automated guided vehicles. This paper addresses the problem of defining flow paths for these vehicles. A model is presented whereby the number of allowable flow paths and the flow directions between nodes (representing pickup/delivery stations and aisle intersections) of the layout network are determined. Examples are presented to demonstrate the approach.     

A branch and cut algorithm for the VRP with satellite facilities

An important aspect of the vehicle routing problem (VRP) that has been largely overlooked is the use of satellite facilities to replenish vehicles during a route. When possible, satellite replenishment allows the drivers to continue making deliveries until the close of their shift without necessarily returning to the central depot. This situation arises primarily in the distribution of fuels and certain retail items. When demand is random, optimizing customer routes a priori may result in significant additional costs for a particular realization of demand. Satellite facilities are one way of safeguarding against unexpected demand. This paper presents a branch and cut methodology for solving the VRP with satellite facilities subject to capacity and route time constraints. We begin with a mixed-integer linear programming formulation and then describe a series of valid inequalities that can be used to cut off solutions to the linear programming relaxation. Several separation heuristics are then outlined that are used to generate the cuts. Embedded in the methodology is a VRP heuristic for finding good feasible solutions at each stage of the computations. Results are presented for a set of problems derived from our experience with a leading propane distributor.     

公交车调度问题的研究

本题为带软时间窗的单线路单车型的公交调度问题,针对其多目标、多变量的动态特点,我们为满足不同的实际需求建立两个多目标规划模型:双车场模型和单车场模型.双车场模型的主要目标是使运客能力与运输需求(实际客运量)达到最优匹配,单车场模型的主要目标是使乘客的平均不方便程度和公交公司的成本达最小,其目的都是为了兼顾乘客与公司双方的利益.两个模型的主体都是采用时间步长法,模拟实际的运营过程,从而得出符合实际要求的调度方案:静态调度和动态调度方案.     

Frenet坐标框架下的自适应避障算法

目的 解决包装车间无人运输车辆在沿全局路径行驶过程中,难以同时保证跟随轨迹平滑及规避障碍物的问题。方法 构建Frenet坐标框架,描述车辆位姿与全局路径的相对关系,利用五次多项式生成多条待选局部路径;采用障碍物势场法模糊处理包装车间障碍的外形轮廓,并设置膨胀区间;结合待选路径采样点经过障碍物膨胀区间得到的碰撞值,以及采样点与全局规划路径的偏差值,综合评估路径的避障能力,筛选出最优的避障路径。结果 该算法能根据障碍物的大小,动态解算出与全局路径偏移量小且运动连贯的局部避障路径。结论 所提算法使得车辆完成运输任务时的效果更好,且效率更高。     

考虑碳排放及时间窗的LIRP模型与算法研究

随着城市内车辆的不断增加,汽车尾气的排放对环境的影响越来越大,但传统的LIRP研究很少考虑节能减排的因素。本文在传统的LIRP基础上,针对考虑碳排放成本和时间窗惩罚成本的城市车辆配送问题,将选址、库存和路径集成化进行研究,建立以经济成本最小化为目标的LIRP模型,采用差分进化算法对该问题进行求解。通过实验,验证设计的差分进化算法在求解该问题时的有效性。     

无人配送车模块化功能设计研究

目的 基于无人配送车模块化设计应用研究,探索无人配送车功能的设计优化和造型升级,提高其灵活性和可扩展性,使其适应不同的场景和需求。方法 通过模块化理论分析和无人配送车应用场景、技术结构的功能分析,将其整车系统划分为基型模块、改型模块,以及附加模块。按需更换功能模块,覆盖更广的无人配送领域,以应对配送的多场景化,并以团队无人配送车设计实践应用进行验证,证明基于功能配置下无人配送车模块化设计方法的有效性。结果 模块化设计实现了无人配送车的“一车多能”、快速的组装和拆卸、方便的维护和升级,同时减少无用的组装和调试时间,提高了工作效率,增强了对市场变化和用户需求的快速反应能力。结论 通过模块化功能设计研究和多场景设计实践,证明无人配送车模块化设计的性能和可靠性,满足用户需求和产品结构的多样化,以适应日益复杂的使用环境。     

动态蚁群算法在带时间窗车辆路径问题中的应用

蚁群算法是近年来新出现的一种随机型搜索寻优算法。自从在旅行商等著名问题中得到富有成效的应用之后，已引起人们越来越多的关注和重视。将这种新型的生物优化思想扩展到物流管理中的带时间窗车辆路径问题，设计了一种动态蚁群算法，从数值计算上探索了这种新型蚁群算法的优化能力，获得了满意的效果。     

带软时间窗的同时取送货车辆路径问题研究

考虑软时间窗下的车辆路径问题,客户点常伴有同时取送货的双重需求。针对此类问题,通过对软时间窗、车辆在途前后时间关系及二者融合问题进行刻画,同时将车辆行驶距离、车辆使用数、违反软时间窗总时间、客户满意度等纳入综合考量,构建相应混合整数非线性规划(mixed integer nonlinear programming, MINLP)模型。设计相应多目标优化求解算法,运用理想点法对目标函数进行转化,将多目标优化问题转化为单目标优化问题。结合相应算例集,运用LINGO 17.0全局求解程序求得每组算例的全局最优解。结果表明,针对带软时间窗的同时取送货车辆路径问题(vehicle routing problem with simultaneous pick-up and delivery and soft time windows, VRPSPDSTW),所建模型及算法是有效且可行的。     

A coordinated algorithm for integrated production scheduling and vehicle routing problem

In this paper, the integrated production scheduling and vehicle routing problem is considered for a Make-to-Order manufacturer, who has a single machine for production and limited vehicles with capacity constraints for transportation. The objective is to determine production scheduling and vehicle routing, which are two interacted decisions, to minimise the maximum order delivery time. A property on optimal production sequence is proposed first, based on which backward and forward batching methods are developed and are embedded into a proposed genetic algorithm. The proposed genetic algorithm is capable of providing high-quality solutions by determining the two decisions simultaneously. For comparison purpose, a two-stage algorithm is developed, which decomposes the overall problem into two successively solved sub-problems. The experiments show that the proposed genetic algorithm can provide higher quality solutions than the proposed two-stage algorithm and two published algorithms studying related problems.