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Neural network for solving optimization problem

A neural network and optimization problem technology, applied in the field of neural network and its realization for solving optimization problems, can solve the problems of the initial conditions of the neural network affecting the calculation results, the slow convergence speed, and the low probability of converging to the global optimal solution, etc.

Inactive Publication Date: 2013-04-03
CIVIL AVIATION UNIV OF CHINA
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0003] The purpose of the present invention is to solve the problem that when the neural network is used to solve the optimization problem, the initial condition of the neural network seriously affects the calculation result, the convergence speed is slow, and the probability of converging to the global optimal solution is low, and a neural network for solving the optimization problem is provided and its method to achieve optimal solution

Method used

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  • Neural network for solving optimization problem
  • Neural network for solving optimization problem
  • Neural network for solving optimization problem

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Effect test

Embodiment 1

[0030] Embodiment 1, neural network

[0031] Such as figure 1 The neural network for solving optimization problems provided by the present invention includes neurons (1), fixed connection weights (2), variable connection weights (3) and neuron output (4);

[0032] The neuron S is realized by a continuous and monotonically increasing neuron activation function, and the dynamic equation of the neural network is

[0033] d y i dt = - k y i + α Σ j = 1 n W ij ...

Embodiment 2

[0047]Embodiment 2, using the neural network to realize the optimal solution example

[0048] The specific steps of using the above neural network to solve the optimization problem to realize the optimization solution are as follows: figure 2 shown.

[0049] When this neural network is used to solve the minimum value of the nonlinear optimization objective function of formula (1), the solution process is as follows:

[0050] E(x 1 ,x 2 )=(x 1 -1) 2 [(x 2 -0.9) 2 +0.01]+(x 2 -1) 2 [(x 1 -0.9) 2 +0.02] (1)

[0051] First, an energy function E is established for the optimization problem to be solved. Optimize the variable x of the objective function 1 and x 2 Set as the neuron output of the neural network, the optimization objective function at this time is the energy function E to be mapped to the neural network. Therefore there are

[0052] ∂ E ...

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Abstract

The invention discloses a neural network for solving an optimization problem and a method for implementing optimization solution. The neural network comprises neurons (1), constant link weights (2), variable link weights (3) and neuron outputs (4), wherein the neurons are realized by a continuous and monotone increasing neuron activation function, and the initial value of each neuron is a random number in a continuous range of [-1, 1]; each neuron is linked with other neurons through the link weights; and the neural network consists of the neurons, and each neuron is provided with a main processing unit with a function mapping function. The neural network is not required to be trained, and can directly solve the optimization problem.

Description

technical field [0001] The invention belongs to the application technical field of neural network, and relates to a neural network for solving optimization problems and its implementation method. The neural network can be realized by software or hardware, and the initial conditions of the neural network have little influence on the calculation results, and the convergence speed is very fast , the probability of converging to the global optimal solution is relatively high. Background technique [0002] Since the advent of the neural network, it has been one of the research hotspots in the scientific community, and has been widely used in the fields of solving optimization problems, associative memory, pattern recognition, and image processing. Especially in the field of optimization, neural networks have shown their talents. It has been successfully applied to optimization problems such as function optimal value solving, TSP (Traveling Salesman Problem), bin packing problem,...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06N3/02G06F17/12
Inventor 费春国陈维兴张积洪
Owner CIVIL AVIATION UNIV OF CHINA
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