Optimizing Connections:Applied Shortest Path Algorithms for MANETs

This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks(MANETs)from dynamic topologies that pose great challenges because of the mobility of nodes.Themain objective was to delve into and refine the application of the Dijkstra’s algorithm in this context,a method conventionally esteemed for its efficiency in static networks.Thus,this paper has carried out a comparative theoretical analysis with the Bellman-Ford algorithm,considering adaptation to the dynamic network conditions that are typical for MANETs.This paper has shown through detailed algorithmic analysis that Dijkstra’s algorithm,when adapted for dynamic updates,yields a very workable solution to the problem of real-time routing in MANETs.The results indicate that with these changes,Dijkstra’s algorithm performs much better computationally and 30%better in routing optimization than Bellman-Ford when working with configurations of sparse networks.The theoretical framework adapted,with the adaptation of the Dijkstra’s algorithm for dynamically changing network topologies,is novel in this work and quite different from any traditional application.The adaptation should offer more efficient routing and less computational overhead,most apt in the limited resource environment of MANETs.Thus,from these findings,one may derive a conclusion that the proposed version of Dijkstra’s algorithm is the best and most feasible choice of the routing protocol for MANETs given all pertinent key performance and resource consumption indicators and further that the proposed method offers a marked improvement over traditional methods.This paper,therefore,operationalizes the theoretical model into practical scenarios and also further research with empirical simulations to understand more about its operational effectiveness.

Efficient Route Planning for Real-Time Demand-Responsive Transit

Demand Responsive Transit (DRT) responds to the dynamic users’ requests without any fixed routes and timetablesand determines the stop and the start according to the demands. This study explores the optimization of dynamicvehicle scheduling and real-time route planning in urban public transportation systems, with a focus on busservices. It addresses the limitations of current shared mobility routing algorithms, which are primarily designedfor simpler, single origin/destination scenarios, and do not meet the complex demands of bus transit systems. Theresearch introduces an route planning algorithm designed to dynamically accommodate passenger travel needsand enable real-time route modifications. Unlike traditional methods, this algorithm leverages a queue-based,multi-objective heuristic A∗ approach, offering a solution to the inflexibility and limited coverage of suburbanbus routes. Also, this study conducts a comparative analysis of the proposed algorithm with solutions based onGenetic Algorithm (GA) and Ant Colony Optimization Algorithm (ACO), focusing on calculation time, routelength, passenger waiting time, boarding time, and detour rate. The findings demonstrate that the proposedalgorithmsignificantly enhances route planning speed, achieving an 80–100-fold increase in efficiency over existingmodels, thereby supporting the real-time demands of Demand-Responsive Transportation (DRT) systems. Thestudy concludes that this algorithm not only optimizes route planning in bus transit but also presents a scalablesolution for improving urban mobility.

On-line real-time path planning of mobile robots in dynamic uncertain environment

A new path planning method for mobile robots in globally unknown environment with moving obstacles is pre- sented. With an autoregressive (AR) model to predict the future positions of moving obstacles, and the predicted position taken as the next position of moving obstacles, a motion path in dynamic uncertain environment is planned by means of an on-line real-time path planning technique based on polar coordinates in which the desirable direction angle is taken into consideration as an optimization index. The effectiveness, feasibility, high stability, perfect performance of obstacle avoidance, real-time and optimization capability are demonstrated by simulation examples.

Original optimal method to solve the all-pairs shortest path problem: Dhouib-matrix-ALL-SPP

The All-pairs shortest path problem(ALL-SPP)aims to find the shortest path joining all the vertices in a given graph.This study proposed a new optimal method,Dhouib-matrix-ALL-SPP(DM-ALL-SPP)to solve the ALL-SPP based on column-row navigation through the adjacency matrix.DM-ALL-SPP is designed to generate in a single execution the shortest path with details among all-pairs of vertices for a graph with positive and negative weighted edges.Even for graphs with a negative cycle,DM-ALL-SPP reported a negative cycle.In addition,DM-ALL-SPP continues to work for directed,undirected and mixed graphs.Furthermore,it is characterized by two phases:the first phase consists of adding by column repeated(n)iterations(where n is the number of vertices),and the second phase resides in adding by row executed in the worst case(n∗log(n))iterations.The first phase,focused on improving the elements of each column by adding their values to each row and modifying them with the smallest value.The second phase is emphasized by rows only for the elements modified in the first phase.Different instances from the literature were used to test the performance of the proposed DM-ALL-SPP method,which was developed using the Python programming language and the results were compared to those obtained by the Floyd-Warshall algorithm.

Real-time accurate hand path tracking and joint trajectory planning for industrial robots(Ⅰ)

Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Car-tesian space mainly through increasing the number of knots on the path and the number of the path′s segments, which results in the heavier online computational burden for the robot controller. Aiming at overcoming this drawback, the authors propose a new kind of real-time accurate hand path tracking and joint trajectory planning method. Through selecting some extra knots on the specified hand path by a certain rule and introducing a sinusoidal function to the joint displacement equation of each segment, this method can greatly raise the path tracking accuracy of robot′s hand and does not change the number of the path′s segments. It also does not increase markedly the computational burden of robot controller. The result of simulation indicates that this method is very effective, and has important value in increasing the application of industrial robots.

Real-time accurate hand path tracking and joint trajectory planning for industrial robots(Ⅱ)

Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Cartesian space mainly through increasing the number of knots on the path and the segments of the path. But, this method resulted in the heavier on line computational burden for the robot controller. In this paper, aiming at this drawback, the authors propose a new kind of real time accurate hand path tracking and joint trajectory planning method for robots. Through selecting some extra knots on the specified hand path by a certain rule, which enables the number of knots on each segment to increase from two to four, and through introducing a sinusoidal function and a cosinoidal function to the joint displacement equation of each segment, this method can raise the path tracking accuracy of robot′s hand greatly but does not increase the computational burden of robot controller markedly.

New Methods to Solve Fuzzy Shortest Path Problems

This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers (TFN). Because of the characteristic of TFNs, the length of any path p from s to t , which equals the extended sum of all arcs belonging to p , is also TFN. Therefore, the fuzzy shortest path problem (FSPP) becomes to select the smallest among all those TFNs corresponding to different paths from s to t (specifically, the smallest TFN represents the shortest path). Based on Adamo's method for ranking fuzzy number, the pessimistic method and its extensions - optimistic method and λ combination method, are presented, and the FSPP is finally converted into the crisp shortest path problems.

A STUDY ON THE ENSEMBLE FORECAST REAL-TIME CORRECTION METHOD

Using real-time correction technology for typhoons, this paper discusses real-time correction for forecasting the track of four typhoons during 2009 and 2010 in Japan, Beijing, Guangzhou, and Shanghai. It was determined that the short-time forecast effect was better than the original objective mode. By selecting four types of integration schemes after multiple mode path integration for those four objective modes, the forecast effect of the multi-mode path integration is better, on average, than any single model. Moreover, multi-mode ensemble forecasting has obvious advantages during the initial 36 h.

A genetic algorithm for the pareto optimal solution set of multi-objective shortest path problem

Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algo- rithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this pa- per. The encoding of the solution and the operators such as crossover, mutation and selection are developed. The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.

Distribution network planning based on shortest path

In order to form an algorithm for distribution network routing,an automatic routing method of distribution network planning was proposed based on the shortest path.The problem of automatic routing was divided into two steps in the method:the first step was that the shortest paths along streets between substation and load points were found by the basic ant colony algorithm to form a preliminary radial distribution network,and the second step was that the result of the shortest path was used to initialize pheromone concentration and pheromone updating rules to generate globally optimal distribution network.Cases studies show that the proposed method is effective and can meet the planning requirements.It is verified that the proposed method has better solution and utility than planning method based on the ant colony algorithm.

The Shortest Path Analysis Based on Road Network

Rational planning of agricultural product transport route from initial node to destination node can effectively reduce the cost price of agricultural products,and the calculation of shortest path between any two points also affects people’s daily travel.Taking Heze Railway Station to Heze College for example,with remote sensing image data as the base map,we conduct vectorization and topological analysis on roads in the target area.With Dijkstra as theoretical basis of shortest path algorithm,we use ArcG IS network analysis method to build road network,and calculate the planning program of the shortest distance path,the shortest path by driving and the shortest path by walking.

An efficient parallel algorithm for shortest pathsin planar layered digraphs

This paper presents an efficient parallel algorithm for the shortest path problem in planar layered digraphs that runs in O(log^3n) time with n processors. The algorithms uses a divide and conquer approach and is based on the novel idea of a one-way separator, which has the property that any directed path can be crossed only once.

Dynamic Shortest Path Algorithm in Stochastic Traffic Networks Using PSO Based on Fluid Neural Network

The shortest path planning issure is critical for dynamic traffic assignment and route guidance in intelligent transportation systems. In this paper, a Particle Swarm Optimization (PSO) algorithm with priority-based encoding scheme based on fluid neural network (FNN) to search for the shortest path in stochastic traffic networks is introduced. The proposed algorithm overcomes the weight coefficient symmetry restrictions of the traditional FNN and disadvantage of easily getting into a local optimum for PSO. Simulation experiments have been carried out on different traffic network topologies consisting of 15-65 nodes and the results showed that the proposed approach can find the optimal path and closer sub-optimal paths with good success ratio. At the same time, the algorithms greatly improve the convergence efficiency of fluid neuron network.

A~*算法在Shortest-Path方面的优化研究

在游戏和地理信息系统开发等领域中,专门针对最短路径搜索方面的优化研究较多,尤其是最短路径中启发式搜索算法中的A*算法的效率优化研究.本文将针对在人工智能或算法研究中的使用的地图大多数是基于任意图而不是网格图的状况,通过任意图与网格图及方向的相结合,提出了三种优化A*算法的启发式函数搜索策略,较好地减小了算法搜索的范围和规模,有效地提高了A*算法的运行效率.最后的实验结果显示,与传统的A*算法相比较,优化启发搜索策略后的A*算法寻径更快速,更准确,计算效率更高.

An Algorithm to Find K Shortest Path

In this figure, it finds a vertex to another vertex k shortest path algorithm. Provided there are n vertices and edges in the diagram. If the path loops, the time complexity of the algorithm is allowed O（w ＋ n log 2 n ＋ kw log 2 k）. If the request path does not contain the loop, the time complexity of the algorithm O（kn（w ＋ n log2 n）＋ kw log2 k）. The algorithm utilizes a simple extension of the Dijkstra algorithm determined the end of the length of the shortest path to the other vertices, and then, based on these data, branch and bound method to identify the required path. Experimental results show that the actual running time has relations with the structure of FIG.

An efficient shortest path approach for social networks based on community structure

Finding the shortest path （SP） in a large-scale network analysis between any two nodes is a tough but very significant task. The SP can help us to analyze the information spreading performance and research the latent relationship in the weighted social network, and so on. As the size of the social network increases, the traditional SP algorithms have poor performance and there is not a suitable algorithm for weighted social network. Some features of the network analysis are beneficial to solve this problem, and community structure ignored by the traditional methods is one of the most important features. In this paper, we propose a shortest path algorithm based on community detection （SPCD） by integrating community detection algorithm with traditional search methods. SPCD constructs a community graph by using community structure to narrow the searching scope. The algorithm presented improves the time efficiency and maintains the accuracy scale of the SR Experimental results on five real-world networks demonstrate the effectiveness of the proposed methods for the SP problem.

A self-organizing shortest path finding strategy on complex networks

The shortcomings of traditional methods to find the shortest path are revealed, and a strategy of finding the self- organizing shortest path based on thermal flux diffusion on complex networks is presented. In our method, the shortest paths between the source node and the other nodes are found to be self-organized by comparing node temperatures. The computation complexity of the method scales linearly with the number of edges on underlying networks. The effects of the method on several networks, including a regular network proposed by Ravasz and Barabasi which is called the RB network, a real network, a random network proposed by Ravasz and Barabasi which is called the ER network and a scale-free network, are also demonstrated. Analytic and simulation results show that the method has a higher accuracy and lower computational complexity than the conventional methods.

Shortest Path Routing Algorithm Based on Chaotic Neural Network

A shortest path routing algorithm based on transient chaotic neural network is proposed in this paper. Gam-pared with previous models adopting Hopfield neural network, this algorithm has a higher ability to overcome the local minimum, and achieves a better performance. By introducing a special post-processing technique for the output matrixes, our algorithm can obtain an optimal solution with a high probability even for the paths that need more hops in large-size networks.

The Algorithm of the Time-Dependent Shortest Path Problem with Time Windows

In this paper, we present a new algorithm of the time-dependent shortest path problem with time windows. Give a directed graph , where V is a set of nodes, E is a set of edges with a non-negative transit-time function . For each node , a time window ?within which the node may be visited and ?, is non-negative of the service and leaving time of the node. A source node s, a destination node d and a departure time?t0, the time-dependent shortest path problem with time windows asks to find an s, d-path that leaves a source node s at a departure time t0;and minimizes the total arrival time at a destination node d. This formulation generalizes the classical shortest path problem in which ce are constants. Our algorithm of the time windows gave the generalization of the ALT algorithm and A* algorithm for the classical problem according to Goldberg and Harrelson [1], Dreyfus [2] and Hart et al. [3].

Shortest Alternate Path Discovery through Recursive Bounding Box Pruning

Congestion is a dynamic phenomenon and hence efficiently computing alternate shortest route can only help expedite decongestion. This research is aimed to efficiently compute shortest path for road traffic network so that congestion can be eased resulting in reduced CO2 emission and improved economy. Congestion detection is achieved after evaluating road capacity and road occupancy. Congestion index, a ratio of road occupancy to road capacity is computed, congestion index higher than 0.6 necessitates computation of alternate shortest route. Various algorithms offer shortest alternate route. The paper discusses minimization of graph based by removing redundant nodes which don’t play a role in computation of shortest path. The proposal is based on continuous definition of a bounding box every time a next neighboring node is considered. This reduces maximum number of contentious nodes repeatedly and optimizes the network. The algorithm is deployed from both the ends sequentially to ensure zero error and validate the shortest path discovery. While discovering shortest path, the algorithm also offers an array of shortest path in ascending order of the path length. However, vehicular traffic exhibits network duality viz. static and dynamic network graphs. Shortest route for static distance graph is pre-computed and stored for look-up, alternate shortest path based on assignment of congestion levels to edge weights is triggered by congestion index. The research also supports directed graphs to address traffic rules for lanes having unidirectional and bidirectional traffic.