Cross Entropy Chance Distribution Model of Uncertain Random Shortest Path Problem

2021 ◽  
pp. 2150015
Author(s):  
Xin Gao ◽  
Yujie Jiao
Keyword(s):  
Shortest Path ◽  
Optimization Problems ◽  
Random Variables ◽  
Strain Analysis ◽  
Shortest Path Problem ◽  
Cross Entropy ◽  
Distribution Model ◽  
Transportation Engineering ◽  
Chance Distribution ◽  
Definition Of

The shortest path problem (SPP) is one of the most typical and basic optimization problems in network theory for decades, and it covers a series of practical application problems, such as urban planning, logistics transportation, engineering and power grid strain analysis, etc. The circumstance where the weight of arcs in a network contains both randomness and uncertainty is considered, and the case of the weights of arcs with uncertain random variables is focused on in this paper. Here, we introduced a new model of the SPP which is based on the new definition of uncertain random variables cross entropy, and the newly established model can be used to find the path with the closest chance distribution to the ideal SP. The efficiency of this model is also evaluated in the final part.

scholarly journals On the Sums of Compound Negative Binomial and Gamma Random Variables

2009 ◽  
Vol 46 (1) ◽  
pp. 272-283 ◽  
Author(s):  
P. Vellaisamy ◽  
N. S. Upadhye
Keyword(s):  
Graph Theory ◽  
Shortest Path ◽  
Negative Binomial ◽  
Random Variables ◽  
Random Parameter ◽  
Exact Expression ◽  
Shortest Path Problem ◽  
Binomial Distributions ◽  
Parameter Representation ◽  
Gamma Distributions

We study the convolution of compound negative binomial distributions with arbitrary parameters. The exact expression and also a random parameter representation are obtained. These results generalize some recent results in the literature. An application of these results to insurance mathematics is discussed. The sums of certain dependent compound Poisson variables are also studied. Using the connection between negative binomial and gamma distributions, we obtain a simple random parameter representation for the convolution of independent and weighted gamma variables with arbitrary parameters. Applications to the reliability of m-out-of-n:G systems and to the shortest path problem in graph theory are also discussed.

A new definition of cross entropy for uncertain random variables and its application

2018 ◽  
Vol 35 (1) ◽  
pp. 1193-1204 ◽  
Author(s):  
Lifen Jia ◽  
Xiangfeng Yang ◽  
Xin Gao
Keyword(s):  
Random Variables ◽  
Cross Entropy ◽  
Definition Of

DEVIATION ALGORITHMS FOR RANKING SHORTEST PATHS

1999 ◽  
Vol 10 (03) ◽  
pp. 247-261 ◽  
Author(s):  
ERNESTO DE QUEIRÓS VIEIRA MARTINS ◽  
MARTA MARGARIDA BRAZ PASCOAL ◽  
JOSÉ LUIS ESTEVES DOS SANTOS
Keyword(s):  
Shortest Path ◽  
Shortest Paths ◽  
Practical Interest ◽  
Shortest Path Problem ◽  
Optimality Principle ◽  
Network Problem ◽  
Different Types ◽  
Unconstrained Problem ◽  
Definition Of ◽  
New Algorithms

The shortest path problem is a classical network problem that has been extensively studied. The problem of determining not only the shortest path, but also listing the K shortest paths (for a given integer K>1) is also a classical one but has not been studied so intensively, despite its obvious practical interest. Two different types of problems are usually considered: the unconstrained and the constrained K shortest paths problem. While in the former no restriction in considered in the definition of a path, in the constrained K shortest paths problem all the paths have to satisfy some condition – for example, to be loopless. In this paper new algorithms are proposed for the uncontrained problem, which compute a super set of the K shortest paths. It is also shown that ranking loopless paths does not hold in general the Optimality Principle and how the proposed algorithms for the unconstrained problem can be adapted for ranking loopless paths.

The Shortest Path Problem Research Based on the Green Traffic

2015 ◽  
Vol 744-746 ◽  
pp. 2126-2130 ◽  
Author(s):  
Bao You Liu ◽  
Nan Xi Jin
Keyword(s):  
Shortest Path ◽  
Operational Research ◽  
Optimization Problems ◽  
Real Life ◽  
Shortest Path Problem ◽  
Practical Significance ◽  
Research Model ◽  
Low Carbon ◽  
Shortest Distance ◽  
Super League

"Advocate the low carbon travel and create the green traffic" is a hot topic in today's society. In order to explore the optimal travel route in 13 China football association super league cities, an operational research model based on the shortest path problem was put forward and resolved by Lingo 11.0 software. The study indicates that the shortest distance traveling each China football association super league city in order in ideal transportation conditions is 9596.000 km. While, considering the traffic restriction of Beijing-Shijiazhuang highway and Beijing-Tianjin highway, the optimized shortest distance is 9693.000 km. This study has a certain practical significance in solving transportation optimization problems in real life.

Tight Analysis of the (1+1)-EA for the Single Source Shortest Path Problem

2011 ◽  
Vol 19 (4) ◽  
pp. 673-691 ◽  
Author(s):  
Benjamin Doerr ◽  
Edda Happ ◽  
Christian Klein
Keyword(s):  
Evolutionary Algorithms ◽  
Shortest Path ◽  
High Probability ◽  
Shortest Paths ◽  
Type Inequality ◽  
Random Variables ◽  
Shortest Path Problem ◽  
Single Source ◽  
Coupon Collector ◽  
A New Technique

We conduct a rigorous analysis of the (1+1) evolutionary algorithm for the single source shortest path problem proposed by Scharnow, Tinnefeld, and Wegener (The analyses of evolutionary algorithms on sorting and shortest paths problems, 2004, Journal of Mathematical Modelling and Algorithms, 3(4):349–366). We prove that with high probability, the optimization time is O(n2 max{ℓ, log(n)}), where ℓ is the smallest integer such that any vertex can be reached from the source via a shortest path having at most ℓ edges. This bound is tight. For all values of n and ℓ we provide a graph with edge weights such that, with high probability, the optimization time is of order Ω(n2 max{ℓ, log(n)}). To obtain such sharp bounds, we develop a new technique that overcomes the coupon collector behavior of previously used arguments. Also, we exhibit a simple Chernoff type inequality for sums of independent geometrically distributed random variables, and one for sequences of random variables that are not independent, but show a desired behavior independent of the outcomes of the previous random variables. We are optimistic that these tools find further applications in the analysis of evolutionary algorithms.

scholarly journals On the Sums of Compound Negative Binomial and Gamma Random Variables

2009 ◽  
Vol 46 (01) ◽  
pp. 272-283 ◽  
Author(s):  
P. Vellaisamy ◽  
N. S. Upadhye
Keyword(s):  
Graph Theory ◽  
Shortest Path ◽  
Negative Binomial ◽  
Random Variables ◽  
Random Parameter ◽  
Exact Expression ◽  
Shortest Path Problem ◽  
Binomial Distributions ◽  
Parameter Representation ◽  
Gamma Distributions

We study the convolution of compound negative binomial distributions with arbitrary parameters. The exact expression and also a random parameter representation are obtained. These results generalize some recent results in the literature. An application of these results to insurance mathematics is discussed. The sums of certain dependent compound Poisson variables are also studied. Using the connection between negative binomial and gamma distributions, we obtain a simple random parameter representation for the convolution of independent and weighted gamma variables with arbitrary parameters. Applications to the reliability ofm-out-of-n:G systems and to the shortest path problem in graph theory are also discussed.

The Map-Based Shortest Route Selection by Using Ant Colony Optimization Algorithm

2018 ◽  
Vol 1 (1) ◽  
pp. 15
Author(s):  
Achmad Fanany Onnilita Gaffar ◽  
Agusma Wajiansyah ◽  
Supriadi Supriadi
Keyword(s):  
Ant Colony Optimization ◽  
Shortest Path ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Google Earth ◽  
Ant Colony ◽  
Food Sources ◽  
Shortest Route ◽  
Study Results ◽  
Destination Point

The shortest path problem is one of the optimization problems where the optimization value is a distance. In general, solving the problem of the shortest route search can be done using two methods, namely conventional methods and heuristic methods. The Ant Colony Optimization (ACO) is the one of the optimization algorithm based on heuristic method. ACO is adopted from the behavior of ant colonies which naturally able to find the shortest route on the way from the nest to the food sources. In this study, ACO is used to determine the shortest route from Bumi Senyiur Hotel (origin point) to East Kalimantan Governor's Office (destination point). The selection of the origin and destination points is based on a large number of possible major roads connecting the two points. The data source used is the base map of Samarinda City which is cropped on certain coordinates by using Google Earth app which covers the origin and destination points selected. The data pre-processing is performed on the base map image of the acquisition results to obtain its numerical data. ACO is implemented on the data to obtain the shortest path from the origin and destination point that has been determined. From the study results obtained that the number of ants that have been used has an effect on the increase of possible solutions to optimal. The number of tours effect on the number of pheromones that are left on each edge passed ant. With the global pheromone update on each tour then there is a possibility that the path that has passed the ant will run out of pheromone at the end of the tour. This causes the possibility of inconsistent results when using the number of ants smaller than the number of tours.

scholarly journals Topological measures for identifying and predicting the spread of complex contagions

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Douglas Guilbeault ◽  
Damon Centola
Keyword(s):  
Social Networks ◽  
Shortest Path ◽  
Empirical Data ◽  
Path Length ◽  
Centrality Measures ◽  
Social Phenomena ◽  
Node Centrality ◽  
Network Connectedness ◽  
Topological Measures ◽  
Definition Of

AbstractThe standard measure of distance in social networks – average shortest path length – assumes a model of “simple” contagion, in which people only need exposure to influence from one peer to adopt the contagion. However, many social phenomena are “complex” contagions, for which people need exposure to multiple peers before they adopt. Here, we show that the classical measure of path length fails to define network connectedness and node centrality for complex contagions. Centrality measures and seeding strategies based on the classical definition of path length frequently misidentify the network features that are most effective for spreading complex contagions. To address these issues, we derive measures of complex path length and complex centrality, which significantly improve the capacity to identify the network structures and central individuals best suited for spreading complex contagions. We validate our theory using empirical data on the spread of a microfinance program in 43 rural Indian villages.

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