A parallel shortest path algorithm

A new algorithm to find the shortest path between a pair of nodes is presented. In one hand this algorithm expands the search from origin and destination simultaneously, on the other hand it uses a lower bound for the shortest path to guide this search. Computational comparisons with existing algorithms show its efficiency. The implementation on a parallel computer is also discussed.     

A numerical method for solving shortest path problems

Chebyshev pseudo-spectral method is one of the most efficient methods for solving continuous-time optimization problems. In this paper, we utilize this method to solve the general form of shortest path problem. Here, the main problem is converted into a nonlinear programming problem and by solving of which, we obtain an approximate shortest path. The feasibility of the nonlinear programming problem and the convergence of the method are given. Finally, some numerical examples are considered to show the efficiency of the presented method over the other methods.     

A shortest path routing algorithm for incomplete WK-recursivenetworks

The WK-recursive networks own two structural advantages: expansibility and equal degree. A network is expansible if no changes to node configuration and link connection are necessary when it is expanded, and of equal degree if its nodes have the same degree no matter what the size is. However, the number of nodes contained in a WK-recursive network is restricted to d^t, where d>1 is the size of the basic building block and t⩾1 is the level of expansion. The incomplete WK-recursive networks, which were proposed to relieve this restriction, are allowed to contain an arbitrary number of basic building blocks, while presenting the advantages of the WK-recursive networks. Designing shortest-path routing algorithms for incomplete networks is in general more difficult than for complete networks. The reason is that most incomplete networks lack a unified representation. One of the contributions of this paper is to demonstrate a useful representation, i.e., the multistage graph representation, for the incomplete WK-recursive networks. On the basis of it, a shortest-path routing algorithm is then proposed. With O(d·t) time preprocessing, this algorithm takes O(t) time for each intermediate node to determine the next node along the shortest path     

Massively parallel augmenting path algorithms for the assignment problem

In this paper we describe how to apply fine grain parallelism to augmenting path algorithms for the dense linear assignment problem. We prove by doing that the technique we suggest, can be efficiently implemented on commercial available, massively parallel computers. Using n processors, our method reduces the computational complexity from the sequentialO(n ³) to the parallel complexity ofO(n ²). Exhaustive experiments are performed on a Maspar MP-2 in order to determine which of the algorithmic flavors that fits best onto this kind of architecture.     

A population-based algorithm for solving linear assignment problems with two objectives

The paper presents a population-based algorithm for computing approximations of the efficient solution set for the linear assignment problem with two objectives. This is a multiobjective metaheuristic based on the intensive use of three operators – a local search, a crossover and a path-relinking – performed on a population composed only of elite solutions. The initial population is a set of feasible solutions, where each solution is one optimal assignment for an appropriate weighted sum of two objectives. Genetic information is derived from the elite solutions, providing a useful genetic heritage to be exploited by crossover operators. An upper bound set, defined in the objective space, provides one acceptable limit for performing a local search. Results reported using referenced data sets have shown that the heuristic is able to quickly find a very good approximation of the efficient frontier, even in situation of heterogeneity of objective functions. In addition, this heuristic has two main advantages. It is based on simple easy-to-implement principles, and it does not need a parameter tuning phase.     

求解最短路径的遗传算法中若干问题的讨论

针对道路交通网络中的最短路径问题,讨论了遗传算法中遗传算子的设计及运行参数的选择,提出一种新的交叉算子,提高了种群多样性.通过计算机仿真实验,比较了多种遗传算子设计方案的优劣及不同运行参数对算法效果的影响,为实际应用提供了参考.采用VC语言实现该遗传算法,并应用于实际的电子地图中,结果表明了算法的有效性和实用性.     

A biologically inspired solution for fuzzy shortest path problems

By considering the uncertainty that exists in the edge weights of the network, fuzzy shortest path problems, as one of the derivative problems of shortest path problems, emerge from various practical applications in different areas. A path finding model, inspired by an amoeboid organism, Physarum polycephalum, has been shown as an effective approach for deterministic shortest path problems. In this paper, a biologically inspired algorithm called Fuzzy Physarum Algorithm (FPA) is proposed for fuzzy shortest path problems. FPA is developed based on the path finding model, while utilizing fuzzy arithmetic and fuzzy distance to deal with fuzzy issues. As a result, FPA can represent and handle the fuzzy shortest path problem flexibly and effectively. Distinct from many existing methods, no order relation has been assumed in the proposed FPA. Several examples, including a tourist problem, are given to illustrate the effectiveness and flexibility of the proposed method and the results are compared with existing methods.     

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.     

A Routing Algorithm with Candidate Shortest Path

An improved algorithm based on the next node routing principle is proposed in this paper.In this algorithm there is a column added to the classical routing table, in which the candidateshortest distance to the destination node is the entry. When a link fails, the new shortest path inthe nodes connected directly with the failure link can be found immediately (it is just thecandidate shortest path before failure). For all other nodes in which routing tables should bechanged, the required number of control messages and time for convergence are also less thanTajibnapis' algorithm and Predecessor algorithm. The message looping problem does not existin duplex loop networks and is radically improved in mesh networks. These statements areproved by the analysis and simulation in this paper. From the simulation results of a 30-nodemesh network, when one link goes down, the total number of control messages generatedduring convergence with this algorithm on the average is about 30% of Tajibnapis' algorithm.The iterations required is 50% of Tajibnapis' algorithm. The memory space required andcomputation complexity in nodes are almost the same as the two algorithms mentioned aboveand the algorithm implementation is as easy as well.     

A distributed shortest path algorithm for a planar network

An algorithm is presented for finding a single source shortest path tree in a planar undirected distributed network with nonnegative edge costs. The number of messages used by the algorithm is O(n^5/3) on an n-node network. Distributed algorithms are also presented for finding a breath-first spanning tree in general network, for finding a shortest path tree in a general network, for finding a separator of a planar network, and for finding a division of a planar network.     

Reduction approaches for robust shortest path problems

We investigate the uncertain versions of two classical combinatorial optimization problems, namely the Single-Pair Shortest Path Problem (SP-SPP) and the Single-Source Shortest Path Problem (SS-SPP). The former consists of finding a path of minimum length connecting two specific nodes in a finite directed graph G; the latter consists of finding the shortest paths from a fixed node to the remaining nodes of G. When considering the uncertain versions of both problems we assume that cycles may occur in G and that arc lengths are (possibly degenerating) nonnegative intervals. We provide sufficient conditions for a node and an arc to be always or never in an optimal solution of the Minimax regret Single-Pair Shortest Path Problem (MSP-SPP). Similarly, we provide sufficient conditions for an arc to be always or never in an optimal solution of the Minimax regret Single-Source Shortest Path Problem (MSS-SPP). We exploit such results to develop pegging tests useful to reduce the overall running time necessary to exactly solve both problems.     

一种求受顶点数限制的最短路径的新算法

提出了一种基于逆邻接表求受顶点数限制的最短路径的新算法,其时间复杂度为O(m-2)^*w)(m是受限制的顶点数,w是有向图中弧的条数),优于同类算法。采用逆邻接表作为图的存储结构,该算法很容易实现。     

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.     

用于求解路径交通流量的改进Frank-Wolfe算法

Frank-Wolfe算法是用于求解交通流量分配问题的经典算法,但该算法是基于路段（Link-Based）的交通流量分配算法,无法用于求解路径交通流量。针对此问题,提出一种用于求解路径交通量的改进Frank-Wolfe算法。通过在Frank-Wolfe原算法中增加求解路径交通流量的计算步骤,根据原算法中“全有全无”加载方法获得的步长,更新源-目的（OD）间所有已配流的路径的交通流量,在原算法迭代计算路段流量的同时,同步计算路径流量。通过算例表明,改进算法是一个有效的算法,在Frank-Wolfe原算法的基础上增加少量的时间和空间成本即可求解路径交通流量,避免穷举交通网络中的所有路径,可以很好地用于用户均衡交通流量分配中。     

Parallel algorithms for shortest path problems in polygons

Given ann-vertex simple polygon we address the following problems: (i) find the shortest path between two pointss andd insideP, and (ii) compute the shortestpath tree between a single points and each vertex ofP (which implicitly represents all the shortest paths). We show how to solve the first problem inO(logn) time usingO(n) processors, and the more general second problem inO(log² n) time usingO(n) processors, and the more general second problem inO(log² n) time usingO(n) processors for any simple polygonP. We assume the CREW RAM shared memory model of computation in which concurrent reads are allowed, but no two processors should attempt to simultaneously write in the same memory location. The algorithms are based on the divide-and-conquer paradigm and are quite different from the known sequential algorithmsResearch supported by the Faculty of Graduate Studies and Research (McGill University) grant 276-07     

Multi-objective and multi-constrained non-additive shortest path problems

Shortest path problems appear as subproblems in numerous optimization problems. In most papers concerning multiple objective shortest path problems, additivity of the objective is a de-facto assumption, but in many real-life situations objectives and criteria, can be non-additive. The purpose of this paper is to give a general framework for dominance tests for problems involving a number of non-additive criteria. These dominance tests can help to eliminate paths in a dynamic programming framework when using multiple objectives. Results on real-life multi-objective problems containing non-additive criteria are reported. We show that in many cases the framework can be used to efficiently reduce the number of generated paths.     

一种快速求解最短路径巡游问题的涟漪扩散算法

针对最短路径巡游问题（SPTP）,提出了基于涟漪扩散算法（RSA）特征的SPTP分解方法。RSA通过模拟水面上涟漪传播的现象,在SPTP子问题间建立联系,相较于其他基于问题分解的算法减少了计算冗余度。进一步改进RSA,使其在维持时间复杂度不变的情况下求解多起点—多终点SPTP。在多种拓扑结构的网络中进行对比实验,结果表明,RSA在保证最优性的同时运算效率最高。RSA对于多起点—多终点SPTP的高效求解,可为多种现实问题快速提供解决方案,具有很高的应用价值。     

闭合螺线阵列的最短路径算法

介绍了闭合螺线阵列的概念;利用动态规划法中的Floyd算法思想对求解闭合螺线阵列最短路径的问题进行了描述,并给出了具体算法;给出了利用二维数组算法求解闭合螺线阵列最短路径的过程.对于以上两种算法的优缺点进行了比较.这两种算法可以用于解决大多数路径问题.     

A systolic algorithm for solving dense linear systems

For an arbitrary n × n matrix A and an n × 1 column vector b, we present a systolic algorithm to solve the dense linear equations Ax = b. An important consideration is that the pivot row can be changed during the execution of our systolic algorithm. The computational model consists of n linear systolic arrays. For 1 ≤ i ≤ n, the i^th linear array is responsible to eliminate the i^th unknown variable x_i of x. This algorithm requires 4n time steps to solve the linear system. The elapsed time unit within a time step is independent of the problem size n. Since the structure of a PE is simple and the same type PE executes the identical instructions, it is very suitable for VLSI implementation. The design process and correctness proof are considered in detail. Moreover, this algorithm can detect whether A is singular or not.