Formulations and Valid Inequalities for the Heterogeneous Vehicle Routing Problem

We consider the vehicle routing problem where one can choose among vehicles with different costs and capacities to serve the trips. We develop six different formulations: the first four based on Miller-Tucker-Zemlin constraints and the last two based on flows. We compare the linear programming bounds of these formulations. We derive valid inequalities and lift some of the constraints to improve the lower bounds. We generalize and strengthen subtour elimination and generalized large multistar inequalities.     

A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows

Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize the objectives of traveling distance and number of vehicles. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW. The proposed HMOEA is featured with specialized genetic operators and variable-length chromosome representation to accommodate the sequence-oriented optimization in VRPTW. Unlike existing VRPTW approaches that often aggregate multiple criteria and constraints into a compromise function, the proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace. The HMOEA is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, which yields 20 routing solutions better than or competitive as compared to the best solutions published in literature.     

基于三维矩阵重构争论有向图的域间路由振荡检测算法

边界网关协议(Border G atew ay P rotoco l,BGP)是当前In ternet域间路由协议的事实标准,基于策略的路由选择过程使它不再是严格意义上的距离矢量协议,也不再具有距离矢量协议的收敛性.V aradhan指出,自治系统各自为政的策略配置方式会导致全局策略冲突,引起永久性的路由振荡.针对该问题,G riffin利用稳定路径问题(S tab le Path P rob lem,SPP)模型形式化的抽象出BGP协议行为,并以此为基础提出了一种分布式的策略冲突检测算法,尽管该算法完全避免了传统方法的缺陷,但仍然存在泄漏策略信息和对BGP协议改动太大以及浪费网络资源的问题.本文提出了一种基于安全多方计算的检测路由策略冲突的方法,用于在怀疑BGP路由发生振荡时,动态的检测系统中是否存在策略冲突.该方法采纳了G riffin的理论基础,同时由于巧妙的运用了安全多方计算协议,可以完全解决G riffin算法的问题,具有很好的实用性.     

VRPTW的扰动恢复及其TABU SEARCH算法

本文对带时间窗的车辆路线安排扰动恢复问题进行了讨论,分析了各种可能的扰动:增加减少客户,时间窗、客户需求及路线可行性的扰动,构造了扰动模型.利用禁忌搜索算法对问题进行求解,同时通过对模型参数重新设置,得到了多个满足要求的不同的解,这样使解更具有实际可行性和有效性.     

A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem

The fleet size and mix vehicle routing problem consists of defining the type, the number of vehicles of each type, as well as the order in which to serve the customers with each vehicle when a company has to distribute goods to a set of customers geographically spread, with the objective of minimizing the total costs. In this paper, a heuristic algorithm based on tabu search is proposed and tested on several benchmark instances. The computational results show that the proposed algorithm produces high quality results within a reasonable computing time. Some new best solutions are reported for a set of test problems used in the literature.     

A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints

We present a metaheuristic methodology for the Capacitated Vehicle Routing Problem with two-dimensional loading constraints (2L-CVRP). 2L-CVRP is a generalisation of the Capacitated Vehicle Routing Problem, in which customer demand is formed by a set of two-dimensional, rectangular, weighted items. The purpose of this problem is to produce the minimum cost routes, starting and terminating at a central depot, to satisfy the customer demand. Furthermore, the transported items must be feasibly packed into the loading surfaces of the vehicles. We propose a metaheuristic algorithm which incorporates the rationale of Tabu Search and Guided Local Search. The loading aspects of the problem are tackled using a collection of packing heuristics. To accelerate the search process, we reduce the neighbourhoods explored, and employ a memory structure to record the loading feasibility information. Extensive experiments were conducted to calibrate the algorithmic parameters. The effectiveness of the proposed metaheuristic algorithm was tested on benchmark instances and led to several new best solutions.     

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%).     

An optimization approach for communal home meal delivery service: A case study

This paper is the first to discuss the communal home meal delivery problem. The problem can be modelled as a multiple travelling salesman problem with time windows, that is closely related to the well-studied vehicle routing problem with time windows. Experimental results are reported for a real-life case study from Central Finland over several alternative scenarios using the SPIDER commercial solver. The comparison with current practice reveals that a significant savings potential can be obtained using off-the-shelf optimization tools. As such, the potential for supporting real-life communal routing problems can be considered to be important for VRP practitioners.     

A note on “A LP-based heuristic for a time-constrained routing problem”

In their paper, Avella et al. (2006) investigate a time-constrained routing problem. The core of the proposed solution approach is a large-scale linear program that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate by using Lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination.     

An adaptive large neighborhood search heuristic for the Pollution-Routing Problem

The Pollution-Routing Problem (PRP) is a recently introduced extension of the classical Vehicle Routing Problem with Time Windows which consists of routing a number of vehicles to serve a set of customers, and determining their speed on each route segment so as to minimize a function comprising fuel, emission and driver costs. This paper presents an adaptive large neighborhood search for the PRP. Results of extensive computational experimentation confirm the efficiency of the algorithm.