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American journal of electrical and electronic engineering

Research on Particle Swarm Optimization Algorithm Based on Quantum Computing Technology

Guanghui Wang

Published Jan 5, 2020• 3 citations
Publisher

Abstract

In view of the shortcomings of particle swarm optimization such as premature convergence to local optimization, particle swarm optimization algorithm based on quantum gate and particle swarm optimization algorithm based on quantum behavior are studied in this paper. The first algorithm uses the random observation method of quantum bit coding particles to simulate quantum particle collapse for generating a population and uses the quantum rotating gate to generate a new population. The adaptive mutation operator is used for ensuring the diversity of the population, effectively reducing the impact of local optimization; therefore, the robustness of the algorithm is improved. The second algorithm uses the probability density function of quantum computation to make the particles jump out of the local extreme points and fulfils the global search, which is more suitable for continuous optimization. The results of computational experiments show that both the two particle swarm optimization algorithms based on quantum technology have a good global convergence.

DOI
10.12691/ajeee-8-1-3

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In view of the shortcomings of particle swarm optimization such as premature convergence to local optimization, particle swarm optimization algorithm based on quantum gate and particle swarm optimization algorithm based on quantum behavior are studied in this paper. The first algorithm uses the random observation method of quantum bit coding particles to simulate quantum particle collapse for generating a population and uses the quantum rotating gate to generate a new population. The adaptive mutation operator is used for ensuring the diversity of the population, effectively reducing the impact of local optimization; therefore, the robustness of the algorithm is improved. The second algorithm uses the probability density function of quantum computation to make the particles jump out of the local extreme points and fulfils the global search, which is more suitable for continuous optimization. The results of computational experiments show that both the two particle swarm optimization algorithms based on quantum technology have a good global convergence.
To improve search ability and optimization efficiency and to avoid premature con- vergence for particle swarms optimization,a novel quantum particle swarm optimization for continuous space optimization is proposed.The positions of particles are encoded by the prob- ability amplitudes of quantum bits,the movements of particles are performed by quantum rotation gates,which achieve particles searching.The mutations of particles are performed by quantum non-gate,which increase the diversity Of particles.As each quantum bit contains two probability amplitudes,each particle occupies two positions in space.Hence,the process of searching is accelerated.The experimental results show that the algorithm proposed is superior to the basic particle swarms optimization.
To improve the efficiency of Particle Swarm Optimization(PSO),a quantum particle swarm optimization algorithm combined with quantum theory on the basis of Bloch sphere was proposed.In Bloch spherical coordinates,the particle automatically updated rotation angle and particle position,without setting the rotation angle in the form of look-up table(or setting fixed value of the interval),making up for the deficiency of quantum evolutionary algorithm and quantum genetic algorithm on the basis of Bloch sphere,and the algorithm is more generalizable.Using quantum Hadamard gate to realize the variation of particle enhanced the diversity of population,and prompted particle jump out of local extreme value.The simulation results of the typical function optimization problem show that the algorithm is stable with high precision and fast convergence rate,and it is practical.
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.
To enhance optimization ability of quantum potential well-based particle swarm optimization algorithm,a quantum particle swarm optimization algorithm based on Bloch spherical search is proposed by analyzing the design of quantum potential well-based particle swarm optimization algorithms.Firstly,particles are expressed with qubits,axis of rotation is established with Pauli matrix,the angle of rotation is obtained with a model of Delta potential well,and search is realized with rotation of qubits in Bloch sphere.Then,to avoid premature convergence,mutation of particles is achieved with Hadamard gates.Such rotation makes current qubit approximates target qubit along with the biggest circle on Bloch sphere,which accelerates optimization process.It shows that the proposed algorithm is superior to the original one in optimization ability.
This paper proposes a new quantum particle swarm optimization algorithm with local attracting (LAQPSO), which is based on quantum-inspired evolutionary algorithm (QEA) and particle swarm optimization algorithm (PSO).In the proposed LAQPSO, a novel quantum bit expression mechanism called quantum angle is employed to encode the solution onto particle, and a new local attractor is proposed to determine the rotation angle of quantum rotation gate automatically.During the process of seeking the global solution, the magnitude of rotation angle is adjusted by an important parameter called contraction coefficient, which can quantitatively determine the tradeoff between exploration ability and exploitation ability.The simulation results for different contraction coefficients are helpful for selecting the key parameter.A set of benchmark functions are used to evaluate the performance of LAQPSO, QEA and QBPSO, and the results show that the proposed algorithm has a fast convergence rate and can effectively avoid premature convergence.
To improve the optimization performance of particle swarm, an adaptive quantum particle swarm optimization algorithm is proposed. In the algorithm, the spatial position of particles is described by the phase of quantum bits, and the position mutation of particles is achieved by Pauli-Z gates. An adaptive determination method of the global-factors is proposed by studying the relationship among inertia factors, self-factors and global-factors. The experimental results demonstrate that the proposed algorithm is much better than the standard particle swarm algorithm by solving the function extremum optimization problems.