基于实时信息的车辆导航路由算法

讨论了在动态随机网基于实时信息的车辆导航问题。交通网中的每一路段的旅行时间建模为随机变量,可以在车辆进入路段前根据实时信息估计其旅行时间。与经典最短路径算法不同的是,不需要在车辆行驶前就确定一条从起始点到终点的完整固定的路径,只需要在车辆到达结点时,根据实时信息估算出从当前位置到终点的预计旅行时间,选择下一路段。这样在车辆行驶过程中就能根据提供的实时信息选择更好的路径,达到优化路径的目的。     

有时间窗车辆路径问题的捕食搜索算法

有时间窗车辆路径问题是当前物流配送系统研究中的热点问题,该问题具有NP难性质。难以求得最优解或满意解,在建立有时间窗车辆路径问题数学模型的基础上。设计了一种模仿动物捕食策略的捕食搜索算法．该算法利用控制搜索空间的限制大小来实现算法的局域搜索和全局搜索,具有良好的局部集中搜索和跳出局部最优的能力．通过实例计算,并与相关启发式算法比较．取得了满意的结果．     

Decremental state space relaxation strategies and initialization heuristics for solving the Orienteering Problem with Time Windows with dynamic programming

We present an exact optimization algorithm for the Orienteering Problem with Time Windows (OPTW). The algorithm is based on bi-directional and bounded dynamic programming with decremental state space relaxation. We compare different strategies proposed in the literature to guide decremental state space relaxation: our experiments on instances derived from the literature show that there is no dominance between these strategies. We also propose a new heuristic technique to initialize the critical vertex set and we provide experimental evidence of its effectiveness.     

A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem

In the heterogeneous fleet vehicle routing problem (HVRP), several different types of vehicles can be used to service the customers. The types of vehicles differ with respect to capacity, fixed cost, and variable cost. We assume that the number of vehicles of each type is fixed and equal to a constant. We must decide how to make the best use of the fixed fleet of heterogeneous vehicles.     

基于多点协作的团队出行路径优化算法

针对团队出行过程中因信息孤岛导致出行路径非优化和延时等待等问题,提出了一种以团队成员信息共享为基础,以集中式计算为手段的协作式路径优化算法。该算法统筹考虑成员间会合的便捷性、路径/时间最短化等多种因素基础上,通过引入团队会合优先度因子对路径计算进行加权处理,从而实现整个团队出行路径的最优化。理论分析表明,协作式路径优化算法的计算复杂度随团队成员的数量线性增长,与传统的最短路径算法计算复杂度基本相当。仿真结果表明,会合优先度因子值的高低,将会影响会合点及出行路径的选择,因此,可根据实际需求设置会合优先度因子,实现团队会合和路径最短化的动态均衡。最后,以协作式路径优化算法的一个具体的工程应用,阐述团队成员间如何提供支持和帮助,从而安全、高效和有序地到达目的地。     

Time-dependent routing problems: A review

Time-dependent routing amounts to design “best” routes in a graph in which arc traversal times may vary over the planning horizon. In the last decade, a number of technological advances have stimulated an increased interest in this field. We survey the research in the area and present a comprehensive review of travel time modelling, applications and solution methods. In particular, we make a first classification in point-to-point and multiple-point problems. A second major classification is then performed with respect to the quality and evolution of information. Other criteria included: (i) node, arc or general routing; (ii) the possibility to choose the vehicle speed.     

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) provides an excellent algorithmic framework for solving multi-objective optimization problems. It decomposes a target problem into a set of scalar sub-problems and optimizes them simultaneously. Due to its simplicity and outstanding performance, MOEA/D has been widely studied and applied. However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions. It is well-known that MO-VRPTW is a challenging problem and has very few Pareto optimal solutions. To address this problem, a novel selection operator is designed in this work to enhance the original MOEA/D for dealing with MO-VRPTW. Moreover, three local search methods are introduced into the enhanced algorithm. Experimental results indicate that the proposed algorithm can obtain highly competitive results on Solomon׳s benchmark problems. Especially for instances with long time windows, the proposed algorithm can obtain more diverse set of non-dominated solutions than the other algorithms. The effectiveness of the proposed selection operator is also demonstrated by further analysis.     

A hill-jump algorithm of Hopfield neural network for shortest path problem in communication network

In this paper, we present a hill-jump algorithm of the Hopfield neural network for the shortest path problem in communication networks, where the goal is to find the shortest path from a starting node to an ending node. The method is intended to provide a near-optimum parallel algorithm for solving the shortest path problem. To do this, first the method uses the Hopfield neural network to get a path. Because the neural network always falls into a local minimum, the found path is usually not a shortest path. To search the shortest path, the method then helps the neural network jump from local minima of energy function by using another neural network built from a part of energy function of the problem. The method is tested through simulating some randomly generated communication networks, with the simulation results showing that the solution found by the proposed method is superior to that of the best existing neural network based algorithm.     

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

The vehicle routing problem with time windows is a complex combinatorial problem with many real-world applications in transportation and distribution logistics. Its main objective is to find the lowest distance set of routes to deliver goods, using a fleet of identical vehicles with restricted capacity, to customers with service time windows. However, there are other objectives, and having a range of solutions representing the trade-offs between objectives is crucial for many applications. Although previous research has used evolutionary methods for solving this problem, it has rarely concentrated on the optimization of more than one objective, and hardly ever explicitly considered the diversity of solutions. This paper proposes and analyzes a novel multi-objective evolutionary algorithm, which incorporates methods for measuring the similarity of solutions, to solve the multi-objective problem. The algorithm is applied to a standard benchmark problem set, showing that when the similarity measure is used appropriately, the diversity and quality of solutions is higher than when it is not used, and the algorithm achieves highly competitive results compared with previously published studies and those from a popular evolutionary multi-objective optimizer.     

New dominance criteria for the generalized permanent labelling algorithm for the shortest path problem with time windows on dense graphs

This paper describes state-dominance criteria for the Generalized Permanent Labelling Algorithm (GPLA) for solving the Shortest Path Problem with Time Windows on dense graphs, which occurs as a subproblem of a vehicle routing problem. These criteria markedly improve its performance. One of the criteria we propose is based on a backward-looking test at the destination node. The other is a dominance test for the label being treated, which avoids the generation of successor states from dominated labels. Both are possible due to a new order of storing the labels for a given node within each bucket: the generated temporary labels are stored and later treated in decreasing service time order and increasing cost order. This order of label treatment, allied with the suggested dominance criteria, results in a significant time execution performance improvement with respect to the basic dense-graph GPLA.     

Vehicle routing problem with uncertain demands: An advanced particle swarm algorithm

The Vehicle Routing Problem (VRP) has been thoroughly studied in the last decades. However, the main focus has been on the deterministic version where customer demands are fixed and known in advance. Uncertainty in demand has not received enough consideration. When demands are uncertain, several problems arise in the VRP. For example, there might be unmet customers’ demands, which eventually lead to profit loss. A reliable plan and set of routes, after solving the VRP, can significantly reduce the unmet demand costs, helping in obtaining customer satisfaction. This paper investigates a variant of an uncertain VRP in which the customers’ demands are supposed to be uncertain with unknown distributions. An advanced Particle Swarm Optimization (PSO) algorithm has been proposed to solve such a VRP. A novel decoding scheme has also been developed to increase the PSO efficiency. Comprehensive computational experiments, along with comparisons with other existing algorithms, have been provided to validate the proposed algorithms.     

An efficient fault-containing self-stabilizing algorithm for the shortest path problem

Shortest path finding has a variety of applications in transportation and communication. In this paper, we propose a fault-containing self-stabilizing algorithm for the shortest path problem in a distributed system. The improvement made by the proposed algorithm in stabilization times for single-fault situations can demonstrate the desirability of an efficient fault-containing self-stabilizing algorithm. For single-fault situations, the worst-case stabilization time of the proposed algorithm is O(Δ), where Δ is the maximum node degree in the system, and the contamination number of the proposed algorithm is 1.     

行驶时间随机的分批配送车辆路径问题模型与算法

为研究分批配送和等待时间对行驶时间随机的车辆路径问题（VRP）的影响,针对行驶时间随机的分批配送车辆路径问题,在软时间窗下考虑等待时间,建立带修正的随机规划模型;同时设计改进的粒子群优化（PSO）算法进行求解：使用需求点可多次出现的整数编码,设计改进的相对位置索引算法进行解码以解决粒子中出现分批需求点问题;将自适应选择用于速度更新以解决各向量长度不同的问题;将路径重连算法用于位置更新过程以解决粒子在离散空间和连续空间转换时信息丢失的问题,适应允许分批配送的特点。通过对调整的Solomon算例测试,考虑等待时间将造成总费用平均增加约3%,且更倾向于分批配送。分批配送能有效降低总费用（2%）和减少使用的车辆数（0.6）;在部分算例,特别是R2类算例中,分批配送能有效降低等待时间,平均降低0.78%。     

Hybrid shortest path algorithm for vehicle navigation

Vehicle navigation is one of the important applications of the single-source single-target shortest path algorithm. This application frequently involves large scale networks with limited computing power and memory space. In this study, several heuristic concepts, including hierarchical, bidirectional, and A^*, are combined and used to develop hybrid algorithms that reduce searching space, improve searching speed, and provide the shortest path that closely resembles the behavior of most road users. The proposed algorithms are demonstrated on a real network consisting 374,520 nodes and 502,485 links. The network is preprocessed and separated into two connected subnetworks. The upper layer of network is constructed with high mobility links, while the lower layer comprises high accessibility links. The proposed hybrid algorithms are implemented on both PC and hand-held platforms. Experiments show a significant acceleration compared to the Dijkstra and A^* algorithm. Memory consumption of the hybrid algorithm is also considerably less than traditional algorithms. Results of this study showed the hybrid algorithms have an advantage over the traditional algorithm for vehicle navigation systems.     

An adaptive local search algorithm for vehicle routing problem with simultaneous and mixed pickups and deliveries

The Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) is an extension to the classical Vehicle Routing Problem (VRP), where customers may both receive and send goods simultaneously. The Vehicle Routing Problem with Mixed Pickup and Delivery (VRPMPD) differs from the VRPSPD in that the customers may have either pickup or delivery demand. However, the solution approaches proposed for the VRPSPD can be directly applied to the VRPMPD. In this study, an adaptive local search solution approach is developed for both the VRPSPD and the VRPMPD, which hybridizes a Simulated Annealing inspired algorithm with Variable Neighborhood Descent. The algorithm uses an adaptive threshold function that makes the algorithm self-tuning. The proposed approach is tested on well-known VRPSPD and VRPMPD benchmark instances derived from the literature. The computational results indicate that the proposed algorithm is effective in solving the problems in reasonable computation time.     

An oriented spanning tree based genetic algorithm for multi-criteria shortest path problems

This paper investigates an oriented spanning tree (OST) based genetic algorithm (GA) for the multi-criteria shortest path problem (MSPP) as well as the multi-criteria constrained shortest path problem (MCSPP). By encoding a path as an OST, in contrast with the existing evolutionary algorithms (EA) for shortest path problem (SPP), the designed GA provides a “search from a paths set to another paths set” mutation mechanism such that both of its local search and global search capabilities are greatly improved. Because the possibility to find a feasible path in a paths set is usually larger than that of only one path is feasible, the designed GA has more predominance for solving MCSPPs. Some computational tests are presented and the test results are compared with those obtained by a recent EA of which the encoding approach and the ideas of evolution operators such as mutation and crossover are adopted in most of the existing EAs for shortest path problems. The test results indicate that the new algorithm is available for both of MSPP and MCSPP.     

蜂群优化算法在车辆路径问题中的应用

车辆路径问题（VRP）是组合优化中典型的NP难题。根据车辆路径问题的实际情况,考察车辆数和总行程两个目标函数,给出了该问题的一种新的算法,蜂群算法。通过计算若干benchmark问题,并将结果与其他算法相比较与分析,验证了算法的有效性。蜂群算法是刚刚起步的智能优化算法,目前国内外关于蜂群算法的文献较少,故不仅是拓宽蜂群算法的应用范围的有效的尝试,同时也给车辆路径问题提供了一种新的解决方法。     

A model with a solution algorithm for the cash transportation vehicle routing and scheduling problem

Cash transportation vehicle routing and scheduling are essential for security carriers to minimize their operating costs and ensure safe cash conveyance. In real operations, to increase cash conveyance safety, there must be significant variation in daily cash transportation vehicle routes and schedules, making such vehicle routes and schedules difficult to formulate. However, for convenient planning purposes, security carriers normally plan such routes and schedules based on personal experience, without considering variations in routes and schedules from a system perspective. As a result, the obtained routes and schedules are neither safe nor efficient for transporting cash. In this study, a model is developed where the time–space network technique is utilized to formulate the potential movements of cash transportation vehicles among all demand points in the dimensions of time and space. This model incorporates a new concept of similarity of time and space for routing and scheduling, which is expected to help security carriers formulate more flexible routing and scheduling strategies. This is helpful to reduce the risk of robbery. Mathematically, the model is formulated as an integer multiple-commodity network flow problem. A solution algorithm, based on a problem decomposition/collapsing technique, coupled with the use of a mathematical programming software, is developed to efficiently solve the problem. The case study results show that our model and solution algorithm could be useful references for security carriers in actual practice.     

改进的自适应大规模邻域搜索算法求解动态需求的混合车辆路径问题

为了给物流企业在车辆配送方案制定上提供决策支持,针对电动物流车与燃油物流车混合配送的模式,研究了带时间窗的动态需求车辆路径问题,建立了以配送总成本最小化为目标的两阶段整数规划模型.针对模型特点,设计了改进的自适应大规模邻域搜索(improved adaptive large neighborhood search,IALNS)算法,提出新的删除、修复算子及动态阶段加速策略,分别针对大规模的静态算例与动态算例进行算法性能测试.结果表明,与无改进策略的IALNS(IALNS-ND)相比,静态问题中在相同的求解时间内75％的算例(12个算例中9个)IALNS得到的最小值和平均值优于IALNS-ND,动态问题中95％(60个算例中57个算例)的算例可以得到成本和时间均优于IALNS-ND的解;与三种算法——自适应大规模邻域搜索算法(ALNS)、大规模邻域搜索算法(LNS)以及变邻域搜索算法(VNS)相比,静态问题中所有算例IALNS获得的总成本的最小值和平均值均优于三个对比算法,动态问题中58％(60个算例中35个算例)的算例IALNS能够以少于三个对比算法1.5倍甚至10倍的时间获得更优的解.同时随着问题动态度的提高,IALNS的速度更快,质量更好,证明了该算法在求解时效性要求高的动态需求车辆路径问题的优越性.     

求解车辆路径问题的离散粒子群算法

考虑车辆行驶时间和顾客服务时间的不确定性,建立了以车辆配送总费用最小为目标的机会约束规划模型,将其进行清晰化处理,使之转化为一类确定性数学模型,并构造了求解该问题的一种离散粒子群算法。算法重新定义了粒子的运动方程及其相关离散量运算法则,并设计了排斥算子来维持群体的多样性。与标准遗传算法和粒子群算法比较,该算法能够有效避免算法陷入局部最优,取得了满意的结果。