Shortest Distance Matrix Research Articles

A new exact algorithm for the shortest path problem: An optimized shortest distance matrix

The growing amount of data generated from the increasingly sophisticated network connections requires greater accuracy and higher efficiency in pinpointing the shortest paths concerned. Therefore, the earlier classical exact algorithms are no longer 100 percent suitable for large-scale data processing, for their known great time complexity during calculation. In this paper, We present an updated shortest distance matrix (SDM) algorithm. Evidence to the operation's properties is provided and the properties are used in subsequent optimizations. Compared with Dijkstra's algorithm and Floyd's algorithm, the optimized SDM algorithm with parallel mode makes a great improvement in shortening the running time. The data test shows that the new algorithm improves the efficiency in processing a large amount of data.

Research on Resource Allocation Optimization of Smart City Based on Big Data

The resource allocation of charging stations is an important part of promoting the development of renewable energy in modern cities. It can promote the scientific and modern construction of urban resource allocation and promote the intelligent transformation of cities. In view of the existing problems in the resource allocation process of urban charging stations, such as a single planning method, considering the actual travel demand. Based on the smart city transportation network information, this article will consider the impact of charging station construction costs, user driving and waiting costs on the location of charging stations, construct a charging station configuration optimization model, and introduce charging convenience coefficients to modify the model. Secondly, this paper establishes a systematic clustering model based on principal component analysis, selecting factors such as per capita GDP, population, and civilian car ownership as indicators, clustering analysis of different regions and assigning different charging convenience coefficients. Finally, the shortest distance matrix between any two nodes is calculated by the Voronoi diagram to concentrate the regional charging load to the traffic node, and the Floyd algorithm is used to analyze and evaluate the effect of the established charging station configuration optimization model. This technology provides a basis for promoting the modernization of urban green transportation.

DECOMPOSITION OF THE ROUTING PROBLEM BASED ON THE CLARKE-WRIGHT HEURISTIC METHOD

For the English abstract and full text of the article please see the attached PDF-File (English version follows Russian version).ABSTRACT The article is devoted to decomposition of the task of transport routing based on heuristic estimates with the Clarke-Wright method. A procedure is proposed for designing an automobile transport system based on the criterion of minimizing the total mileage by various formalized decomposition methods, in particular, using the «benefit functions» algorithm and formation of zones (clusters, subsets) of vehicle maintenance. The advantages of the proposed method are clearly shown in comparison with the method of «the shortest distance matrix», at the example of delivery of ten cargo units from a supplier to ten consumers. The effect of reducing the total mileage on the designed routes was 9,45 %. Keywords: transport routing, Clarke-Wright method, «benefit function», cluster, decomposition method, heuristic estimation, the shortest distances matrix

Research on Model and Algorithm of Task Allocation and Path Planning for Multi-Robot

Based on the modeling of robot working environment, the shortest distance matrix between points is solved by Floyd algorithm. With the objective of minimizing the sum of the fixed cost of robot and the cost of robot operation, an integer programming model is established and a genetic algorithm for solving the model is designed. In order to make coordination to accomplish their respective tasks for each robot with high efficiency, this paper uses natural number encoding way. The objective function is based on penalty term constructed with the total number of collisions in the running path of robots. The fitness function is constructed by using the objective function with penalty term. Based on elitist retention strategy, a genetic algorithm with collision detection is designed. Using this algorithm for task allocation and path planning of multi-robot, it can effectively avoid or reduce the number of collisions in the process of multi-robot performing tasks. Finally, an example is used to validate the method.

Technical Note—Conditional Location Problems on Networks

In this paper, we describe an algorithm to solve conditional location problems (such as the conditional p-median problem or the conditional p-center problem) on networks, where demand points are served by the closest facility whether existing or new. This algorithm requires the one-time solution of a (p + 1)-unconditional corresponding location problem using an appropriate shortest distance matrix.

The Theory of Networks and Management Science. Part I

An expository treatment of three network models most often encountered in Management Science applications: (i) The Shortest Path Problems, (ii) Flow Networks, and (iii) Activity Networks. In the first problem are discussed the shortest path between two specified nodes; the shortest distance matrix; as well as the special case of directed acyclic networks. In the second problem, a brief exposition of the “labeling procedure” leads into multiterminal networks and the general minimal cost circulation problem and a discussion of the “out-of-kilter” method. In the third problem, the “classical” models of CPM and PERT are reviewed, together with a discussion of generalized activity networks and the viewing of GERT as a signal flow graph of a semi-Markov process. Illustrations of the application of each model are also given. The first two models appear in the September issue; and the third model in the October issue of Management Science.