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Ha'erbin gongye daxue xuebao

Quantum genetic algorithm based on real encoding and gradient information of object function

Panchi Li

Published Jan 1, 2006• 29 citations
OpenAlex

Abstract

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.

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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.
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.
Due to the frequent decoding operations,the efficiency of optimization is severely reduced when the binary quantum genetic algorithm based on qubits measure is applied to the continuous space optimization.To solve this problem,a quantum genetic algorithm based on phase encoding is proposed.In this method,the chromosomes are encoded by the phase of qubits,evolved by quantum rotation gates,and mutated by quantum Pauli-Z gates.The optimization process is performed in[0,2π]~n,which has nothing to do with specific issues,therefore,the proposed method has good adaptability for a variety of optimization problems.In application of function extremum optimization,the simulation results show that the approach is superior to either common quantum genetic algorithm or simple genetic algorithm in both search capability and optimization efficiency.
Due to frequent decoding operations, the efficiency of optimization is severely reduced when the binary quantum genetic algorithm based on qubits measure is applied to the continuous space optimization.To solve this problem, a quantum genetic algorithm based on phase encoding is proposed.In this method, the chromosomes are encoded by the phase of qubits, evolved by quantum rotation gates, and mutated by quantum Pauli-Z gates.As the optimization process is performed in 0,2πn, which has nothing to do with specific issues, therefore, the proposed method has good adaptability for a variety of optimization problems.With application of function extremum optimization, the simulation results show that the approach is superior to common quantum genetic algorithm and simple genetic algorithm in both search capability and optimization efficiency.
Due to frequent decoding operations, the efficiency of optimization is severely reduced when the binary quantum genetic algorithm based on qubits measure is applied to the continuous space optimization. To solve this problem, a quantum genetic algorithm based on phase encoding is proposed in this paper. In this method, the chromosomes are encoded by the phase of qubits, evolved by quantum rotation gates, and mutated by quantum Pauli-Z gates. As the optimization process is performed in [0, 2π], which has nothing to do with specific issues, therefore, the proposed method has good adaptability for a variety of optimization problems. With application of function extremum optimization, the simulation results show that the approach is superior to common quantum genetic algorithm and simple genetic algorithm in both search capability and optimization efficiency.
In order to decrease the storage quantity and increase the search efficiency,a new quantum genetic algorithm called AC-QGA is proposed,in which the chromosome is encoded by the angle in based on the qubit's polar coordinate representation in the two-dimensional Hilbert space.Thus,the representation of the gene-bit is changed from the complex number pair to a real number,and the storage quantity is decreased greatly.Meanwhile,the updating process of the chromosome and the mutation process of the gene-bit are simplified from the matrix multiplied by the vector to the angle addition or subtraction.The process of observing the chromosome is changed from probability comparison to angle comparison.The above-mentioned measures make the storage quality and the search efficiency of AC-QGA be increased greatly.The experiments show AC-QGA is very effective.
In order to improve the efficiency of the quantum genetic algorithm,this paper proposed a quantum genetic algorithm based on a expanded multi-chain coding scheme.The algorithm took qubit as chromosome.Each chromosome generated multiple and parallel gene chains which were mapping to multiple optimized solutions by separating qubit into multiple and parallel genes.The expanded genes chains expanded the searching space effectively and increased evolutionary rate for quantum genetic algorithm.It introduced the dynamic adjusting rotation angle mechanism to quantum rotation gate to guide individual evolution and used quantum not-gate to prevent algorithm occurring premature convergence.The method further improved searching efficiency.In the simulation experiment,analysed the influence for the algorithm with different variation probability([0,0.1,…,0.9,1])and used different code schemes to optimize extremal function.The simulation experiment result shows that it can obviously improve the efficiency of quantum genetic algorithm by adding gene chain,and the quantum genetic algorithm based on a expanded multi-chain coding scheme is efficient.