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International Conference on Genetic and Evolutionary Computing

An Improved Quantum Genetic Algorithm

Jian Bao Guo, Lijuan Sun, Ruchuan Wang, Zhonggen Yu

Published Oct 1, 2009• 22 citations
Publisher

Abstract

Quantum genetic algorithm (QGA) is the combination between genetic algorithm and quantum computing. In this paper, a chromosome of the standard QGA is seen as a node and the chromosome population is regarded as a network. Then the reasons for the prematurity and the stagnation of the standard QGA are analyzed from the perspective of network structure. To solve the two problems, an improved quantum genetic algorithm (IQGA) based on the small world theory is proposed. In IQGA, chromosomes encoded with qubits are divided into some sub-groups and the NW network model is introduced into the population structure. When updating chromosomes, an optimal chromosome in locality or in other sub-groups is chosen based on a certain probability as the evolution target for each chromosome. The new network structure of the chromosome population has a relatively moderate clustering coefficient and is favorable to the diversity of individual chromosomes. Tests of three classic functions prove the effectiveness and superiority of IQGA.

DOI
10.1109/wgec.2009.41

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Quantum genetic algorithm (QGA) is the combination between genetic algorithm and quantum computing. In this paper, a chromosome of the standard QGA is seen as a node and the chromosome population is regarded as a network. Then the reasons for the prematurity and the stagnation of the standard QGA are analyzed from the perspective of network structure. To solve the two problems, an improved quantum genetic algorithm (IQGA) based on the small world theory is proposed. In IQGA, chromosomes encoded with qubits are divided into some sub-groups and the NW network model is introduced into the population structure. When updating chromosomes, an optimal chromosome in locality or in other sub-groups is chosen based on a certain probability as the evolution target for each chromosome. The new network structure of the chromosome population has a relatively moderate clustering coefficient and is favorable to the diversity of individual chromosomes. Tests of three classic functions prove the effectiveness and superiority of IQGA.
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.
An improved quantum genetic algorithm(IQGA) was proposed to overcome the shortcoming of the quantum genetic algorithm(QGA),i.e. local optimization, when it is used for the optimization of continuous functions with many extreme values. In IQGA, the strategies of updating quantum gate using the best solution obtained and population catastrophe were adopted. The test results for two typical functions show that the convergence speed of IQGA is faster than that of QGA, and IQGA can converge in a global solution space, overcoming the shortcoming of QGA. The application results indicate that IQGA is better than QGA and other genetic algorithms.
Abstract With the in-depth study of quantum genetic algorithm (QGA), the defect of premature convergence limits its development more and more. In order to further improve QGA, we propose an improved QGA based on multi population (IQGA). In the process of population initialization in IQGA, we generate multiple populations to avoid a single population falling into a local optimal value. We also abandon the fixed angle used by the traditional quantum revolving gate, and design a strategy to adjust the angle adaptively according to the difference from the optimal solution. In addition, we introduce a population catastrophe strategy to deal with the premature convergence of each population. The populations are connected based on migration operation, and the optimal solution of each population obtained by each iteration is collected in the elite group. A series of simulation experiments show that our improvement strategies of IQGA are effective.
This paper suggests an improved quantum genetic algorithm(IQGA).In encoding,a kind of encoding method to determine the quantum chromosome gene length is advanced in terms of accurate dynamics of the problem to be found out.This encoding method takes the equilibrium relations between the calculation solution accuracy and seeking for efficiency into consideration.Also,this paper discusses the dynamic adjustment and tactics of quantum rotation angle,whereby making operator realize the combination of a kind of rough searching with the fine searching under the different cases.The combination of quantum mutation operation can render the postmutation to be able to carry out searching in a larger neighborhood range in such a way that the algorithm is ensured to search for a solution with high accuracy within a rational calculation cost.In the end,IQGA is used to test several selected standard base functions.The tested results indicate that IQGA can obtain the best solusion,the best average value and convergence algebra as against the existing algorithm data cited in literature,and with a certain advantage.
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.
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.