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.     

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.     

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.     

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.     

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).     

A Branch-and-Cut method for the Capacitated Location-Routing Problem

Recent researches in the design of logistic networks have shown that the overall distribution cost may be excessive if routing decisions are ignored when locating depots. The Location-Routing Problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. The aim of this paper is to propose an exact approach based on a Branch-and-Cut algorithm for solving the LRP with capacity constraints on depots and vehicles. The proposed method is based on a zero-one linear model strengthened by new families of valid inequalities. The computational evaluation on three sets of instances (34 instances in total), with 5–10 potential depots and 20–88 customers, shows that 26 instances with five depots are solved to optimality, including all instances with up to 40 customers and three with 50 customers.     

基于节点位置和剩余能量的分簇路由改进算法

针对传统LEACH协议存在的随机选举簇头及网内节点能耗不均等问题,提出了一种能量均衡高效的分簇路由协议LEACH-EPN.在成簇阶段加入最优簇数约束,综合考虑节点位置和剩余能量等多种因素;引入距离因子、能量因子及节点密度因子改进阈值公式;通过改变簇的范围来改变成簇机制,使簇头选举更合理、能耗分布更均匀,提高了网络的能量...     

A List Based Threshold Accepting Algorithm for the Capacitated Vehicle Routing Problem

The aim of this study is to describe a new stochastic search meta-heuristic algorithm for solving the Capacitated Vehicle Routing Problem (CVRP), termed as the List Based Threshold Accepting (LBTA) algorithm. The main advantage of this algorithm over the majority of other meta-heuristics is that it produces quite satisfactory solutions in reasonable amount of time by tuning only one parameter of the algorithm. This property makes this algorithm a reliable and a practical tool for every decision support system designed for solving real life vehicle routing problems.     

基于节点位置和密度修正的自组网区域路由

自组网中区域路由协议主要由区域内路由和区域间路由组成。修正的区域路由算法利用节点位置信息,使得区域内的邻节点更新过程可以获得更有效的触发,从而减少了大量的不必要的广播报文开销。同时,根据节点密度调整了路径长度限制,使得区域间的路由查询和路由维护能够更快地收敛。仿真结果表明,修正后的区域路由算法与ZRP协议相比,在时延、吞吐量等方面有着较明显的性能提高。     

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASP×ELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASP×ELS approach outperforms all previously published methods.     

带有时间窗口的富网络配送问题研究及仿真

通过建立GIS富网络路网属性模型,并组合N阶最短近邻自适应聚类算法和遗传算法,来解决不确定车辆数目、较大规模网点和多层次交通网络的带时间窗口的联合配送问题。首先,为了解决传统带有时间窗口车辆线路调度模型中配送网点规模小(不超过20个网点)的问题,以及在建模时将各网点抽象为图的顶点的缺陷,建立基于实际道路数据的网络数据集,采用GIS技术精确计算各网点之间的距离,并建立距离OD矩阵;然后,为了降低对较大规模网点配送算法设计的复杂度,采用N阶最短近邻自适应算法确定聚类簇数,再通过聚类数划分配送网点。其次,为了确定配送车辆的种类、车辆数目以及时间窗口的限制,利用遗传算法对配送线路进行优化。最后,通过2个实例验证了所提方法的有效性。     

A constraint programming approach to the Chinese postman problem with time windows

The Chinese postman problem with time windows (CPPTW) is modelled as a constraint programme and results are reported for a set of test problems with up to 69 edges. Two different formulations are proposed. The first formulation approaches the problem directly and the second transforms the problem to an equivalent vehicle routing problem with time windows. The results demonstrate that optimal solutions can be obtained quickly when the time windows are tight. However, the results also show that as the time windows are made wider and the number of feasible solutions increases, these constraint programming formulations take significantly longer to find a provably optimal solution. The results also demonstrate how the size and density of the graph affects the computing time needed to find an optimal solution.     

Enhanced Simulated Annealing Technique for the Single-Row Routing Problem

This paper presents ESSR (Enhanced Simulated annealing for Single-row Routing) model for solving the single-row routing problem. The main objective in this problem is to produce a realization that minimizes both the street congestion and the number of doglegs. Simulated annealing (SA) is a stochastic, hill-climbing and gradient-descent technique based on the statistical properties of particles undergoing thermal annealing. By performing slow cooling, the nets in the single-row routing problem align themselves according to a configuration with the lowest energy. The model has been known to produce reasonably good solutions for many NP-complete optimization problems, such as the single-row routing problem. In ESSR, our strategy is to minimize both the street congestion and the number of interstreet crossings (doglegs) by expressing a single energy function as their collective properties. This objective is achieved by representing the energy as the absolute sum of the heights of the net segments. To speed up convergence, we pivot the street congestion value while having the energy drops directly proportional to the number of doglegs. This action has the effect of minimizing the number of doglegs as the energy stabilizes. Our simulation work on ESSR produces optimal results in most cases for both the street congestion and the number of doglegs. Our experimental results compare well against results obtained from our earlier model (SRR-7) and two other methods reported in the literature.     

易腐物品车辆路径问题的并行遗传算法

本文采用并行遗传算法研究了易腐物品的车辆路径问题。通过设计粗粒度并行遗传算法和交叉、变异等算子,提高了算法的计算效率和性能。最后,以计算示例验证了算法的有效性。     

Iterated local search heuristics for the Vehicle Routing Problem with Cross-Docking

This work addresses the Vehicle Routing Problem with Cross-Docking (VRPCD). The problem consists in defining a minimum cost set of routes for a fleet of vehicles that meets the demands of products for a set of suppliers and customers. The vehicles leave a single Cross-Dock (CD) towards the suppliers, pick up products and return to the CD, where products can be exchanged before being delivered to their customers. The vehicle routes must respect the vehicle capacity constraints, as well as the time window constraints. We adapted a constructive heuristic and six local search procedures from the literature of VRP, and made them efficient in the presence of the synchronization constraints of VRPCD. Besides, we propose three Iterated Local Search (Lourenço et al., 2010) heuristics for VRPCD. The first heuristic is a standard implementation of ILS, while the second extends the classic ILS framework by keeping a set of elite solutions, instead of a single current solution. The latter set is used in a restart procedure. As far as we can tell, this is the first ILS heuristic in the literature that keeps a population of current elite solutions. The third heuristic is an extension of the second that relies on an intensification procedure based on an Integer Programming formulation for the Set Partitioning problem. The latter allows a neighborhood with an exponential number of neighbors to be efficiently evaluated. We report computational results and comparisons with the best heuristics in the literature. Besides, we also present a new set with the largest instances in the literature of VRPCD, in order to demonstrate that the improvements we propose for the ILS metaheuristic are efficient even for large size instances. Results show that the best of our heuristics is competitive with the best heuristics in the literature of VRPCD. Besides, it improved the best solution known for half of the benchmark instances in the literature.