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International Workshop on Education Technology and Computer Science

Double Chains Quantum Genetic Algorithm with Application in Training of Process Neural Networks

Maojun Cao, Fuhua Shang

Published Jan 1, 2010• 9 citations
Publisher

Abstract

To address training of process neural networks based on the orthogonal basis expansion, a double chains quantum genetic algorithm based on the probability amplitudes of quantum bits is proposed. In this method, the probability amplitudes of each qubit are regarded as two paratactic genes, each chromosome contains two gene chains, and each of gene chains represents an optimization solution. The number of genes is determined by the number of weight parameters. Taking each qubit in the optimal chromosome as the goal, individuals are updated by quantum rotation gates, and mutated by quantum non-gates to increase the diversity of population. Taking the pattern classification of two groups of two-dimensional trigonometric functions as an example, the simulation results show that the proposed method is effective and efficient.

DOI
10.1109/etcs.2010.88

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To address training of process neural networks based on the orthogonal basis expansion, a double chains quantum genetic algorithm based on the probability amplitudes of quantum bits is proposed. In this method, the probability amplitudes of each qubit are regarded as two paratactic genes, each chromosome contains two gene chains, and each of gene chains represents an optimization solution. The number of genes is determined by the number of weight parameters. Taking each qubit in the optimal chromosome as the goal, individuals are updated by quantum rotation gates, and mutated by quantum non-gates to increase the diversity of population. Taking the pattern classification of two groups of two-dimensional trigonometric functions as an example, the simulation results show that the proposed method is effective and efficient.
A quantum genetic algorithm based on real number encoding and gradient of fitness function is proposed in this paper.Chromosomes comprised of quantum bits are updated by quantum rotating gates,and are mutated by quantum non-gate.A convenient method to choose the direction of rotation angle of quantum rotation gate is proposed.The computation formula of the rotation angle value is constructed by the gradients of fitness function.In this method,two probability amplitude of each quantum bit are regarded as two coordinate genes;each chromosome contains two chains of genes;and each chain of genes represents an optimization result.This method can accelerate convergence process and increase successful probability with the same number of chromosomes.Its application to fuzzy controller parameters optimization illustrates that the approach is superior to common quantum genetic algorithm in searching ability.
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A quantum genetic algorithm based on real number encoding and gradient of object function is presented. In this study, chromosomes are comprised of quantum bits encoded by real number. Chromosomes are renovated by quantum rotating gates and mutated by quantum non - gate. For direction of rotating angle of rotating gate, a convenient method is shown. The gradients of object function are utilized in choosing the value of rotating angle. In this method each quantum bit is regarded as two coordinate genes, each chromosome contains two chain of genes, each chain of genes represents a optimization result. Therefore, a double searching space is acquired for the same number of chromosomes. Finally the availability of the approach is illustrated by two application examples of function extremum and weighting optimization of neural networks.
Quantum genetic coding method plays an important role in improving the efficiency of optimization algorithm. The existing quantum genetic algorithm has some defects, that quantum encoding scheme is tend to reduce the stability, so that the algorithm is prone to premature convergence and falls into local minima. Therefore, the chain of multiple genes encoding scheme is used to extend in the multi-dimensional space for improving this algorithm. By function extremum and simulation of neural network weights optimization, according to the characteristics of qubits and the normalization condition, double and triple chain binding coding schemes are proposed. By experiments on multiple genes encoding scheme chain, the performance of the algorithm is tested. It shows that the algorithm can get better results by increasing the higher accuracy of solution chain genes. It is an effective strategy to improve the performance of genetic coding.
The double chains quantum genetic algorithm based on real coded and gradient of objective function increases the diversity of population,expands the search field about space,accelerates the algorithm evolutionary process,avoids the premature convergence phenomenon,is an effective optimization algorithm,but does prove theoretically convergence.This paper gives the corresponding theorem on the basis of previous work,theoretically proves the convergence of the algorithm by the theorem,and discusses the effects of the quantum coding and quantum rotation gate in terms of the algorithm convergence and optimization efficiency by simulation example.Results show that his research enriches and improves the double chains quantum genetic theory.
Aiming at the problems that the Quantum Genetic Algorithm(QGA) easily falls into local extremum,an improved QGA algorithm of quantum revolving gate is proposed.In order to achieve the goal of optimization solving,quantum bit probability amplitude is applied to the chromosome encoding,and quantum rotation gate is used to chromosome updating.The theoretical derivation proves that the proposed algorithm converges with probability 1,and the algorithm converges strongly to 1?e.Comparing with double QGA,simulation results show that the algorithm increases complexity,the average time extension,but convergence times increase,convergence times of the function 1 increases from 3 to 7,and convergence times of the function 2 increases from 8 to 9.