The maximum flow problem of uncertain network

Han, Song; Zhi-qiang, Peng; Wang, Shunqin

doi:10.1016/j.ins.2013.11.029

Cited by 85 publications

(38 citation statements)

References 26 publications

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“…For a random network, Fishman [9], Goldberg and Tarjan [10], and Nawathe and Rao [11] mainly used stochastic optimization to solve the maximum flow problem in a random network. For an uncertain network, Han et al [17] gave the inverse uncertain distribution of the maximum flow in an uncertain network. In this paper, according to chance theory, we will study the chance distribution, the maximum flow of an uncertain random network.…”

Section: Maximum Flow Problemmentioning

confidence: 99%

“…For the different capacities, obtain different but unique maximum flow f. In other words, the maximum flow f is a function of arc capacities. In paper [17], the author proved that the maximum flow f is a continuous and strictly increasing function with respect to C ij , where C ij denote the capacities of the (i, j) arcs. For a random network, the maximum flow f is a random variable function of arc capacities.…”

Section: Maximum Flow Problemmentioning

confidence: 99%

“…Gao [16] investigates solutions to the α-shortest path and the most shortest path in an uncertain network in 2011. Besides, the maximum flow problem was discussed by Han et al [17], the uncertain minimum cost flow problem was dealt with by Ding [18], and Chinese postman problem was explored by Zhang and Peng [19] for an uncertain network.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chance distribution of the maximum flow of uncertain random network

Sheng

Gao

2014

J. Uncertain. Anal. Appl.

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A network is called uncertain random network if some arc capacities of the network are uncertain variables and others are random variables. The main purpose of this paper is to study the maximum flow in an uncertain random network. Under the framework of chance theory, this paper obtains chance distribution of the maximum flow of an uncertain random network. At the same time, the expected value of maximum flow is given for an uncertain random network. A new method is derived to calculate chance distribution of the maximum flow for an uncertain random network.

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Section: Maximum Flow Problemmentioning

confidence: 99%

Section: Maximum Flow Problemmentioning

confidence: 99%

See 1 more Smart Citation

Chance distribution of the maximum flow of uncertain random network

Sheng

Gao

2014

J. Uncertain. Anal. Appl.

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“…Maximum flow problem of weighted graph, an important component of graph theory and artificial intelligence, has been widely used in many fields, such as computer network, data mining, image segmentation and ontology computation (see [1][2][3][4][5][6][7]). Hyper-graph is a subset system for limited set, which is the most general discrete structure, and it is the generalization of the common graph.…”

Section: Introductionmentioning

confidence: 99%

Algorithm for Fuzzy Maximum Flow Problem in Hyper-Network Setting

Zhu¹,

Min²,

Gao³

et al. 2015

TOCSJ

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Maximum flow problem on hypergraphs (hyper-networks) is an extension of maximum flow problem on normal graphs. In this paper, we consider a generalized fuzzy version of maximum flow problem in hyper-networks setting. Our algorithm is a class of genetic algorithms and based on genetic tricks. The crisp equivalents of fuzzy chance constraints in hyper-networks setting are defined, and the execution steps of encoding and decoding are presented. Finally, we manifest the implement procedure.

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“…Liu systematically studied mathematical programming problems in the uncertainty environment and developed the uncertain chance constrained programming model [9]. Many researchers also studied the problem of uncertain programming, and promote the development of the theory and application of uncertain programming [10][11][12]. This paper introduces uncertainty theory into TSP, assuming that the travel time of salesman visiting different cities is uncertain variables.…”

Section: Introductionmentioning

confidence: 99%

Travelling Salesman Problem in Uncertain Environments

Huiru¹,

Jia²,

Zhang³

et al. 2015

TOCSJ

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Abstract:In practice, due to the lack of information, imprecise variables which come from experts' empirical data usually appear. In order to deal with these imprecise variables, uncertainty theory is proposed and has been proved to be an efficient method. This paper introduces uncertainty theory into travelling salesman problem (TSP), in which the link travel times are assumed to be uncertain variables, and then a chance constrained programming model is proposed within the framework of uncertainty theory. The properties of the chance constrained programming model are investigated; furthermore, the uncertain model is proved to be equivalent to a deterministic model. To solve the problem, we design an algorithm based on genetic algorithm. Finally, a numerical example is given, the result of which verifies the effectiveness of the proposed chance constrained programming model and the algorithm.

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The maximum flow problem of uncertain network

Cited by 85 publications

References 26 publications

Chance distribution of the maximum flow of uncertain random network

Chance distribution of the maximum flow of uncertain random network

Algorithm for Fuzzy Maximum Flow Problem in Hyper-Network Setting

Travelling Salesman Problem in Uncertain Environments

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