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Dianzi xuebao

A Novel Quantum Genetic Algorithm Based on Particle Swarm Optimization Method and Its Application

Ying Ding

Published Jan 1, 2006• 14 citations
OpenAlex

Abstract

This paper proposes a novel quantum genetic algorithm(QGA)——PSQGA,which uses particle swarm optimization method instead of quantum gate to update the state of quantum bit.It has the advantages of particle swarm optimization and quantum genetic algorithm.A variance function is introduced to estimate the stability of the algorithm.Though the experiments of four continuous functions and combination optimization problems,as well as its application to image sparse decomposition.Compared with the improved algorithm which involved quantum gate(IQGA),the ability of finding the best solution and the stability of PSQGA are greatly improved.PSQGA has better convergent property and ability of searching more extensive space.It is fit for the solution of complex optimization problems.

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This paper proposes a novel quantum genetic algorithm(QGA)——PSQGA,which uses particle swarm optimization method instead of quantum gate to update the state of quantum bit.It has the advantages of particle swarm optimization and quantum genetic algorithm.A variance function is introduced to estimate the stability of the algorithm.Though the experiments of four continuous functions and combination optimization problems,as well as its application to image sparse decomposition.Compared with the improved algorithm which involved quantum gate(IQGA),the ability of finding the best solution and the stability of PSQGA are greatly improved.PSQGA has better convergent property and ability of searching more extensive space.It is fit for the solution of complex optimization problems.
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.
Aiming at the disadvantages of the fixed rotation angle in quantum genetic algorithm (QGA), in this paper, the particle swarm optimization (PSO) was used to update the angle of quantum rotation gate in stead of the old one that locates the angle of quantum rotation gate by a designed query table. According to the experimental results, the novel quantum genetic algorithm (NQGA) with new updating method has got a higher global search capability than common QGA. The NQGA was used to the load distribution optimization of tandem cold rolling. The comparison data show that the NQGA is an effective method for load distribution optimization of tandem cold rolling.
Aiming at the problems of the classical algorithms for solving the nonlinear equations such as high sensitivity to the initial value、poor convergence,a hybrid quantum genetic algorithm for solving nonlinear equations is proposed.The positions of particles are encoded by the probability amplitudes of quantum bits.The movements and mutations of particles are performed by quantum rotation gate and quantum non-gate.The algorithm has the abilities of population search for quantum swarm particle and global convergence.The quasi-newton method is combined into the algorithm and increases local searching ability and the high accuracy.Numerical simulation experiments show that this algorithm has reliable convergence,fast convergence rate and high precision.
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.
The quantum genetic algorithm (QGA) is derived from the integration of quantum computation and genetic algorithm. It is characterized with advantages like strong global optimization ability, fast convergence speed and small population size. In this paper, the principle, method and basic flow of quantum genetic algorithm (QGA) are introduced, and the research progress of QGA in recent years is reviewed, including the coding extension of theoretical basis, the innovation of operators, the rotation angle of quantum gates, the optimization of complex high-dimensional functions, and hybrid algorithms, and then he application status of QGA is also discussed. Finally, the future development direction of QGA is put forward.
In order to save computation time and avoid falling into local optima in quantum genetic algorithm (QGA), this paper proposes a quantum genetic algorithm based on Boltzmann selection mechanism (B_QGA). The proposed algorithm has several novel characteristics. Firstly, Quantum bits are encoded by angle and introduce the constant factor, aiming at enhancing calculated amount. Secondly, a new dynamic rotation angle adjustment strategy is presented to achieve updated chromosome, and individuals directly evolve to the current optimal solution with linear increasing rate, which greatly improve the rate of convergence and the ability of global search. Thirdly, instead of roulette selection mode, Boltzmann selection mechanism is employed for avoiding the local optimal problem. Finally, for the selected offspring's individuals, Hadamard door is proposed to perform mutation operation to sustain stability and diversity of population. The experiment results on three complicated continuous functions show the proposed algorithm is able to find the best solution in very short time and has excellent global search ability comparing to quantum genetic algorithm (QGA) and genetic algorithm (GA).