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Calculation Method of Maximum Flow of Uncertain Network with Uncertain Loss

A technology of maximum flow rate and calculation method, which is applied in calculation, special data processing applications, instruments, etc., and can solve problems such as lack of observation data, inability to calculate the frequency of events, and inability to determine the probability distribution

Inactive Publication Date: 2017-09-19
DEZHOU UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Unfortunately, the problem we often face is precisely the lack of observational data, so that we can neither calculate the frequency of events nor determine the probability distribution

Method used

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  • Calculation Method of Maximum Flow of Uncertain Network with Uncertain Loss
  • Calculation Method of Maximum Flow of Uncertain Network with Uncertain Loss
  • Calculation Method of Maximum Flow of Uncertain Network with Uncertain Loss

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0066] Suppose G is a directed network with five arcs, such as figure 2 shown.

[0067] In an uncertain environment, we assume that the i-th node loss flow ξ i is a linear uncertain variable whose distribution is Φ i ,i=2,3.

[0068]

[0069]

[0070] We assume that the capacity of the (i,j) arc is a linear uncertainty variable η ij Its uncertain distribution is Ψ ij ,i≠j,i,j=1,2,3,4,5,

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] From Theorem 1, the following equivalent model (4) can be obtained

[0077]

[0078] Note that the expected value of the linearly uncertain variable L(a,b) is Its inverse uncertainty distribution is

[0079] Φ -1 (α)=(1-α)α+αb

[0080] Then the above model becomes

[0081]

[0082] The model is a typical linear programming problem, and its feasible region is a multifaceted convex set. The confidence level of the hypothesis is β i =0.5,γ ij =0.75. It can be obtained by the simplex method, figure 2 T...

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Abstract

The invention relates to a calculation method of the uncertain network maximum flow rate with uncertain loss. The method adopts models (1), (2) and (3), and a network, wherein the network comprises n nodes and m arcs and has single-source points and single-merging points, cij is used for expressing the arc volume from the node i to the node j, in addition, xij is used for expressing the flow rate from the node i to the node j, ui is used for expressing the flow rate lost by the flow at the node I, i,j=1, 2 to n, s indicates the source node, and t is the merging node. The method has the advantages that the novel processing method is provided for solving the problem of uncertain network maximum flow with the uncertain loss, and in addition, simplicity and high efficiency are realized.

Description

technical field [0001] The invention relates to a flow calculation method, in particular to a calculation method for the maximum flow of an uncertain network with an uncertain loss. Background technique [0002] It is well known that the maximum flow problem originated from the railway system of the former Soviet Union. Ford and Fulkerson mentioned the maximum flow problem by T.E.Harris: Consider a railway network connecting two cities through a certain number of intermediate cities. Each link in the network has a number representing its traffic capacity (called arc capacity). . Assuming a steady condition, find the maximum traffic from one city to another. [0003] The maximum flow problem is a classic network optimization problem, and has been widely used in various fields, such as electric power, transportation, communication systems, computer networks and logistics, etc. So it is very important to study this problem from the perspective of theory and practice. Over t...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F19/00
Inventor 王金婵高秀莲
Owner DEZHOU UNIV