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Computer Engineering and Science

An Angle-Coding Chromosome Quantum Genetic Algorithm

Shen Zhen-kang

Published Jan 1, 2009• 3 citations
OpenAlex

Abstract

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.

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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 make full use of the quantum characteristics of the quantum state in the algorithm,and improve the search efficiency,reduce storage space,a new quantum genetic algorithm called 3D-AQGA was proposed.The algorithm describes quantum bit as a pair of angles in 3D spherical coordinate,makes full use of the quantum space motion characteristics,and introduces a kind of adaptive scheme to calculate the rotation angle size and direction which not only makes the process of chromosome's update and variation simplified,but also improves quantum characteristics,storage properties and time performance of the algorithm greatly.The simulation results show that the efficiency of the algorithm and the search ability are superior to the simple genetic algorithm and common quantum genetic algorithm.
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.
The genetic algorithm is an efficient optimization tool for its independence of problems, intrinsic parallelism and inherent learning capacity; however, it has some disadvantages such as slow convergence and prematurity. In this paper, a novel algorithm, called the quantum genetic algorithm—QGA, is proposed based on the combination of the quantum theory with the evolutionary theory. By adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. The random observation simulating the quantum collapse can bring diverse individuals, and the evolution of quantum chromosome can also pilot the evolution. So it has better diversity than the classical genetic algorithm. Rapid convergence and good global search capacity characterize the performance of QGA. The paper not only proves the global convergence of the QGA, but also some simulation experiments are shown to prove its superiority over other algorithms.
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.
In this paper, we propose a novel genetic algorithm based on the quantum chromosome - QGA. We adopt quantum chromosome to represent a linear superposition of solutions, after the observation that simulates the quantum collapse. The algorithm has better diversity than its counterpart. In addition, the quantum evolutionary operator - quantum mutation is constructed, which is used to speed up the convergence. Rapid convergence and global search capacity characterize the performance of QGA. The paper also gives some simulation experiments to prove its superiority over the classical genetic algorithm.
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.