改进蚁群算法优化周期性车辆路径问题

周期性车辆路径问题(PVRP)是标准车辆路径问题(VRP)的扩展,PVRP将配送期由单一配送期延伸到T(T＞1)期,因此,PVRP需要优化每个配送期的顾客组合和配送路径。由于PVRP是一个内嵌VRP的问题,其比标准VRP问题更加复杂,难于求解。本文采用蚁群算法对PVRP进行求解,并提出采用两种改进措施——多维信息素的运用和基于扫描法的局部优化方法来提高算法的性能。最后,通过9个经典PVRP算例对该算法进行了数据实验,结果表明本文提出的改进蚁群算法求解PVRP问题是可行有效的,同时也表明两种改进措施可以显著提高算法的性能。     

Requiem for the Miller–Tucker–Zemlin subtour elimination constraints?

The Miller–Tucker–Zemlin (MTZ) Subtour Elimination Constraints (SECs) and the improved version by Desrochers and Laporte (DL) have been and are still in regular use to model a variety of routing problems. This paper presents a systematic way of deriving inequalities that are more complicated than the MTZ and DL inequalities and that, in a certain way, “generalize” the underlying idea of the original inequalities. We present a polyhedral approach that studies and analyses the convex hull of feasible sets for small dimensions. This approach allows us to generate generalizations of the MTZ and DL inequalities, which are “good” in the sense that they define facets of these small polyhedra. It is well known that DL inequalities imply a subset of Dantzig–Fulkerson–Johnson (DFJ) SECs for two-node subsets. Through the approach presented, we describe a generalization of these inequalities which imply DFJ SECs for three-node subsets and show that generalizations for larger subsets are unlikely to exist. Our study presents a similar analysis with generalizations of MTZ inequalities and their relation with the lifted circuit inequalities for three node subsets.     

不确定性自私路由模型的理论和应用

为了更加准确地描述现实生活中的交通情况,以经典的自私路由模型为基础,在边的费用函数上引入不确定性,从而定义了具有不确定性的自私路由模型.对于不确定性自私路由模型,采用三种费用衡量标准,风险厌恶型（保守型）、风险折衷型（理智型）、风险偏好型（乐观型）,分别对应着不同人群在现实中的选择.进而定义了在不同衡量标准下所形成的稳定策略,即纳什均衡策略,并且证明了在任何一种衡量标准下,纳什均衡策略总是存在并且本质是唯一的.接着对三种费用衡量标准下的纳什均衡费用进行了比较,发现了一种反直观的现象：风险厌恶型（保守型）衡量标准下的纳什均衡费用可能严格低于风险偏好型（乐观型）衡量标准下的纳什均衡费用,即有可能会出现高风险低回报,低风险高回报的情况,这与经济学中高风险高回报,低风险低回报的原则是相违背的.以此为基础,进而提出了一种自私路由风险性悖论,并证明了这种自私路由风险回报悖论本质上是传统布雷斯悖论的推广.最后,刻画出了不会发生自私路由风险回报悖论的网络结构,证明了一个单对始终点网络不会发生自私路由风险回报悖论当且仅当它是序列-平行网络.     

Product form in networks of queues with batch arrivals and batch services

A product form equilibrium distribution is derived for a class of queueing networks in either discrete or continuous time, in which multiple customers arrive simultaneously and batches of customers complete service simultaneously.     

Implicit depot assignments and rotations in vehicle routing heuristics

Vehicle routing variants with multiple depots and mixed fleet present intricate combinatorial aspects related to sequencing choices, vehicle type choices, depot choices, and depots positioning. This paper introduces a dynamic programming methodology for efficiently evaluating compound neighborhoods combining sequence-based moves with an optimal choice of vehicle and depot, and an optimal determination of the first customer to be visited in the route, called rotation. The assignment choices, making the richness of the problem, are thus no more addressed in the solution structure, but implicitly determined during each move evaluation. Two meta-heuristics relying on these concepts, an iterated local search and a hybrid genetic algorithm, are presented. Extensive computational experiments demonstrate the remarkable performance of these methods on classic benchmark instances for multi-depot vehicle routing problems with and without fleet mix, as well as the notable contribution of the implicit depot choice and positioning methods to the search performance. New state-of-the-art results are obtained for multi-depot vehicle routing problems (MDVRP), and multi-depot vehicle fleet mix problems (MDVFMP) with unconstrained fleet size. The proposed concepts are fairly general, and widely applicable to many other vehicle routing variants.     

An iterated local search algorithm for the vehicle routing problem with backhauls

The Vehicle Routing Problem with Backhauls (VRPB) is an extension of the VRP that deals with two types of customers: the consumers (linehaul) that request goods from the depot and the suppliers (backhaul) that send goods to the depot. In this paper, we propose a simple yet effective iterated local search algorithm for the VRPB. Its main component is an oscillating local search heuristic that has two main features. First, it explores a broad neighborhood structure at each iteration. This is efficiently done using a data structure that stores information about the set of neighboring solutions. Second, the heuristic performs constant transitions between feasible and infeasible portions of the solution space. These transitions are regulated by a dynamic adjustment of the penalty applied to infeasible solutions. An extensive statistical analysis was carried out in order to identify the most important components of the algorithm and to properly tune the values of their parameters. The results of the computational experiments carried out show that this algorithm is very competitive in comparison to the best metaheuristic algorithms for the VRPB. Additionally, new best solutions have been found for two instances in one of the benchmark sets. These results show that the performance of existing metaheuristic algorithms can be considerably improved by carrying out a thorough statistical analysis of their components. In particular, it shows that by expanding the exploration area and improving the efficiency of the local search heuristic, it is possible to develop simpler and faster metaheuristic algorithms without compromising the quality of the solutions obtained.     

Intersecting a simple mixed integer set with a vertex packing set

We consider a mixed integer set that results from the intersection of a simple mixed integer set with a vertex packing set from a conflict graph. This set arises as a relaxation of the feasible set of mixed integer problems such as inventory routing problems. We derive families of strong valid inequalities that consider the structures of the simple mixed integer set and the vertex packing set simultaneously.     

基于非均匀分簇的无线传感器网络路由协议

在无线传感器网络中,分簇技术是一种有效延长网络生命周期的方法。但是这种多跳的网络模型,如果节点均匀分布并且簇的大小相等,则靠近基站的簇头由于要中继更多的数据,则会导致能量空洞现象。因此提出一种非均匀分簇方法来缓解能量空洞问题。首先,通过节点的剩余能量、到基站的距离以及邻居节点数量来选择簇头。簇一旦形成之后,通过单跳和多跳的混合机制将数据发送到基站。实验结果表明,此协议能有效的延长网络的生命周期,均衡网络能耗,有效延缓能量空洞的形成速度。     

An approximate dynamic programming approach for the vehicle routing problem with stochastic demands

This paper examines approximate dynamic programming algorithms for the single-vehicle routing problem with stochastic demands from a dynamic or reoptimization perspective. The methods extend the rollout algorithm by implementing different base sequences (i.e. a priori solutions), look-ahead policies, and pruning schemes. The paper also considers computing the cost-to-go with Monte Carlo simulation in addition to direct approaches. The best new method found is a two-step lookahead rollout started with a stochastic base sequence. The routing cost is about 4.8% less than the one-step rollout algorithm started with a deterministic sequence. Results also show that Monte Carlo cost-to-go estimation reduces computation time 65% in large instances with little or no loss in solution quality. Moreover, the paper compares results to the perfect information case from solving exact a posteriori solutions for sampled vehicle routing problems. The confidence interval for the overall mean difference is (3.56%, 4.11%).     

Analysis,modeling and solution of the concrete delivery problem

This paper describes a specific local search approach to solve a problem arising in logistics which we prove to be NP-hard. The problem is a complex scheduling or vehicle routing problem where we have to schedule the tours of concrete mixer vehicles over a working day from concrete-producing depots to concrete-demanding customers and vice versa. We give a general mixed integer programming model which is too hard to solve for state of the art mixed integer programming optimizers in the case of the usually huge problem instances coming from practice. Therefore we present a certain local search approach to be able to handle huge practical problem instances.