New lower bound for the Capacitated Arc Routing Problem

We present a new lower bound, the Multiple Cuts Node Duplication Lower Bound, for the undirected Capacitated Arc Routing Problem. We prove that this new bound dominates the existing bounds for the problem. Computational results are also provided.     

An optimization-based heuristic for the Multi-objective Undirected Capacitated Arc Routing Problem

The Multi-objective Undirected Capacitated Arc Routing Problem (MUCARP) is the optimization problem aimed at finding the best strategy for servicing a subset of clients localized along the links of a logistic network, by using a fleet of vehicles and optimizing more than one objective. In general, the first goal consists in minimizing the total transportation cost, and in this case the problem brings back to the well-known Undirected Capacitated Arc Routing Problem (UCARP). The motivation behind the study of the MUCARP lies in the study of real situations where companies working in the logistic distribution field deal with complex operational strategies, in which different actors (trucks, drivers, customers) have to be allocated within an unified framework by taking into account opposite needs and different employment contracts. All the previous considerations lead to the MUCARP as a benchmark optimization problem for modeling practical situations. In this paper, the MUCARP is heuristically tackled. In particular, three competitive objectives are minimized at the same time: the total transportation cost, the longest route cost (makespan) and the number of vehicles (i.e., the total number of routes). An approximation of the optimal Pareto front is determined through an optimization-based heuristic procedure, whose performances are tested and analyzed on classical benchmark instances.     

约束法蚁群算法在多目标VRP中的研究

多目标车辆路径问题(MVRP)在物流研究领域具有重要的理论和现实意义,但由于各目标之间的相互联系和制约使得建模和求解具有很大的难度.在众多求解方法中,蚁群算法对解决类似组合优化问题具有明显的优势,蚁群算法已成功应用于一系列单目标优化问题,但对多目标问题的研究还处于起步阶段.侧重结合目标约束法与蚁群算法来研究多目标车辆路径问题,使各优化目标之间形成既彼此独立,又相互联系和制约的机制,最终求得多目标优化意义下的一种平衡解.仿真结果证明该算法具有良好的收敛性和运行效率,对于物流运输的实际运作具有重要的现实意义.     

A template-based Tabu Search algorithm for the Consistent Vehicle Routing Problem

This paper presents a generic template-based solution framework and its application to the so-called Consistent Vehicle Routing Problem (ConVRP). The ConVRP is an NP-hard combinatorial optimization problem and involves the design of a set of minimum cost vehicle routes to service a set of customers with known demands over multiple days. Customers may receive service either once or with a predefined frequency; however frequent customers must receive consistent service, i.e., must be visited by the same driver over approximately the same time throughout the planning period. The proposed solution framework adopts a two-level master-slave decomposition scheme. Initially, a master template route schedule is constructed in an effort to determine the service sequence and assignment of frequent customers to vehicles. On return, the master template is used as the basis to design the actual vehicle routes and service schedules for both frequent and non-frequent customers over multiple days. To this end, a Tabu Search improvement method is employed that operates on a dual mode basis and modifies both the template routes and the actual daily schedules in a sequential fashion. Computational experiments on benchmark data sets illustrate the competitiveness of the proposed approach compared to existing results.     

NoC节点编码及路由算法的研究

NoC的设计和实现受到芯片的面积、功耗、深亚微米效应的限制.将拓扑结构和节点编码相结合,提出一种基于约翰逊码的二维平面编码.该编码隐含了Torus网络拓扑结构以及网络节点之间的连接关系并且有很好的扩展性,能够简化Torus拓扑结构上路由算法的实现和降低硬件成本.基于此编码和利用X-Y路由的路由确定性特点,提出改进X-Y路由,在中间节点只需要3或5个逻辑运算,降低路由的计算复杂性和硬件成本.最后,进行了节点结构设计.提出的编码不仅用于NoC的路由方面而且在NoC任务映射方面有重要应用.     

Constructive heuristics for the Mixed Capacity Arc Routing Problem under Time Restrictions with Intermediate Facilities

The Mixed Capacity Arc Routing Problem under Time Restrictions with Intermediate Facilities (MCARPTIF) is an extension of the Arc Routing Problem under Capacity and Length Restrictions with Intermediate Facilities (CLARPIF) with application in municipal waste collection. This paper evaluates four constructive heuristics capable of computing feasible solutions for the MCARPTIF with a primary objective to either minimise total cost or to minimise the fleet size. The heuristics were adapted from Path-Scanning and Improved-Merge for the Mixed Capacitated Arc Routing Problem, and compared against two Route-First-Cluster-Second heuristics for the MCARPTIF. The objective was to identify the best performing heuristic for application purposes. In practice, the CARP is often solved for real-time or near real-time decision support. Computational time required by the heuristics was thus also evaluated. Identifying the best heuristic proved difficult due to a lack of realistic MCARPTIF benchmark sets, with the two CLARPIF sets predominantly solved in the literature not resembling actual waste collection instances. Route-First-Cluster-Second heuristics, linked with a new vehicle reduction heuristic performed the worst on the two CLARPIF sets, yet performed the best on new waste collection sets taken from the literature and introduced in this paper. Improved-Merge performed the best on two existing CLARPIF sets and on a realistic set with Intermediate-Facilities incident with the vehicle depot, but struggled on all other sets and in minimising fleet size. Path-Scanning was the most robust heuristic, performing reasonably well on all benchmark sets and both objectives. Results further show that due to the high computational time of one of the Route-First-Cluster-Second heuristics, which was only exposed on realistically sized sets, the slightly worse version is the best alternative when real-time support is required for waste collection applications.     

求解VRP的蚁群算法研究

车辆路径问题是物流配送中一个至关重要的问题。由于它是一个NP-Hard问题,启发式算法成为求解VRP的主要方法。蚁群算法是近年来发展起来的一种可以用来求解VRP的启发式算法。实验证明,该方法能够很好地解决车辆路径问题。本文详细阐述了蚁群算法的基本原理和求解VRP的蚁群算法过程。     

多车场洒水车路径问题的双层遗传算法

论文提出了一种新的遗传算法对有多个加水点的洒水车服务路线问题进行优化求解,给出了一种多车场车辆弧路径问题的数学模型,并对传统遗传算法的染色体编码机制和种群结构进行了改进,设计了一种解决多车场车辆弧路径问题的双层遗传算法,可以表示出各车场出动的车辆及路径,与人工安排的方案进行比较,安排效率高,总行驶路程缩短15％以上,车辆行驶路线更为合理,有效地实现多车场车辆弧路径问题的优化。     

基于改进蚁群算法的物流配送问题研究

对带时间窗的物流配送车辆路径优化调度问题进行了描述,给出了数学模型,在最大～最小蚁群算法的基础之上,提出了一种改进的蚁群算法,在物流配送路径优化问题初始解的构造、路径优化、转移规则、信息素更新方式、算法终止判断等进行了改进,并通过引入信息熵的概念,利用与算法运行过程有关的信息熵的值表示选择过程中的不确定性,来控制路径选择和局部随机变异扰动的概率,以实现算法的自适应调节,同时结合局部优化方法对解进行二次优化,通过这些改进,提高了算法的搜索效率,实验仿真整明了该改进算法的有效性.     

A tabu search approach for the livestock collection problem

We present a problem dealing with transportation of live animals to slaughterhouses. The problem is taken from the Norwegian meat industry, and may be viewed as a vehicle routing problem extended with inventory constraints to ensure a smooth production flow at the slaughterhouse. In addition, several constraints to ensure animal welfare have to be met. These include duration limits for how long animals can stay on the vehicle as well as rules for mixing different animal categories. In this paper, we show that this real-world problem can be solved heuristically, even if it is large both in size and complexity. A tabu search based solution method for the problem is presented, and results from computational testing are given, including comparisons with manual solutions from today's planning system.     

用于求解混合车辆路径问题的混合进化算法

文中研究了具有NP难度的混合车辆路径问题(Mixed Capacitated General Routing Problem,MCGRP),其是在基本车辆路径问题(Vehicle Routing Problem,VRP)的基础上通过添加限载容量约束及弧上的用户需求而衍生的。给定一列车辆数不限的车队,使车辆从站点出发向用户提供服务,服务完用户需求后仍返回站点;规定每辆车的总载重不能超过其载重量,且每个需求只能被一辆车服务且仅服务一次。MCGRP旨在求解每辆车的服务路线,使得在满足以上约束条件的情况下所有车辆的旅行消耗之和最小。混合车辆路径问题具有较高的理论价值和实际应用价值,针对该问题提出了一种高效的混合进化算法。该算法采用基于5种邻域算符的变邻域禁忌搜索来提高解的质量,并通过一种基于路径的交叉算符来继承解的优异性,从而有效地加速算法的收敛。在一组共计23个经典算例上的实验结果表明,该混合进化算法在求解混合车辆路径问题时是非常高效的。     

混合粒子群算法求解交通路网中的车辆调度问题

为使路网中的车辆调度问题更加符合实际交通状况．提出了改进的车辆调度模型;针对这个模型,将粒子群算法和模拟退火算法相结合,设计了混合粒子群算法求其有效近似解;最后结合西安市实际交通调查数据．编程实现混合粒子群算法对模型进行计算与仿真,仿真结果表明了此方法的有效性．     

商业区快递车辆路径优化及仿真

在快递车辆路径优化问题的研究中,网点作为快递最末端的服务空间设施,在快递网络中主要承担快件的收取及迅速送达到牧件人的功能.由于收派的快件量很大,对时效性要求也较高,因此对商业区快递车辆路径进行优化以提高快递企业服务水平、提升竞争力.为此考虑了影响快递企业在商业区竞争力的重要因素,提出移动仓库milk-run派送模式、用蚁群算法进行路径优化,最后以顺丰速运中关村分部为例,对所提出的模型和算法进行了仿真分析.结果表明,上述算法为快递企业在商业区的派送模式、路径规划提供了方法,通过合理优化降低了快递派送的成本,提高了快递企业的竞争力.     

多目标动态车辆路径问题建模及优化

针对物流配送中动态车辆路径优化问题,综合考虑动态需求、路网影响、车辆共享、时间窗以及客户满意度,建立了多目标动态数学规划模型,该模型能更好地描述现代物流配送问题.同时,提出一种两阶段求解策略,第一阶段采用多目标混合粒子群优化算法获取预优化阶段Pareto最优解,采用改进的粒子状态更新策略并融合模拟退火操作提升粒子群搜索性能,采用自适应网格技术保持解的分布性;第二阶段对客户的需求变化采用贪婪插入和变邻域搜索进行实时路径调整.实验表明,该算法在解空间中有更好的探寻能力,并能快速收敛到全局最优,满足动态路径优化实时性要求.     

配送中多车场多任务多车型车辆调度研究

多车场多车型多任务的车辆调度优化是城市配送中的典型问题。针对该问题从空驶成本、运输成本和时间成本三个维度构建了一个VRP的数学模型,并采用自适应多态蚁群算法对模型加以求解。通过实例仿真,将仿真优化结果与未优化的随机结果进行了比较。结果发现优化后的成本比未优化的成本低,并且证明了对多车场多车型多任务的VRP模型进行优化非常必要。     

A constructive heuristic for the Undirected Rural Postman Problem

This paper describes a constructive heuristic for the well-known Undirected Rural Postman Problem. At each iteration, the procedure inserts a connected component of the required edges and performs a local postoptimization. Computational results on a set of benchmark instances with up to 350 vertices show that the proposed procedure is competitive with the classical Frederickson procedure. Its use is recommended when a high-quality solution is needed in a short amount of time (e.g., in laser plotter applications).     

求解带时间窗车辆路径问题的改进粒子群算法

通过分析已有粒子群算法对有时间窗约束的车辆路径问题求解质量不高的原因,提出了一种基于粒子交换原理的整数粒子更新方法。采用构造的双层粒子进化算法分别对8个和20个任务点的有时间窗约束的车辆路径问题求解,数值实验结果表明算法的求解精度和耗时均优于已有算法。     

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.     

An Overview and Experimental Study of Learning-Based Optimization Algorithms for the Vehicle Routing Problem

The vehicle routing problem(VRP) is a typical discrete combinatorial optimization problem, and many models and algorithms have been proposed to solve the VRP and its variants. Although existing approaches have contributed significantly to the development of this field, these approaches either are limited in problem size or need manual intervention in choosing parameters. To solve these difficulties, many studies have considered learning-based optimization(LBO) algorithms to solve the VRP. This p...     

运输任务分配与路径选择的组合优化模型

针对运输任务分配与路径选择的组合优化问题,提出基于二维染色体结构的改进遗传求解算法。采用自然数编码,设计选择、交叉、变异、检查算子,以及算法的控制参数和算法终止条件,给出遗传算法的求解模型。开发基于C#的实验平台进行验证,结果证明,该算法具有较好的求解性能。