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Advanced materials research

A Kind of Adaptive Quantum Particle Swarm Algorithm Based on Phase Encoding

Jun Hui Pan, Hui Wang, Pan Chi Li

Published Jul 1, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.4028/www.scientific.net/amr.548.612

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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.
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.
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.
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 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.
To enhance the optimization ability of particle swarm algorithm, a novel quantum-inspired particle swarm optimization algorithm is proposed. In this method, the particles are encoded by the probability amplitudes of the basic states of the multi-qubits system. The rotation angles of multi-qubits are determined based on the local optimum particle and the global optimal particle, and the multi-qubits rotation gates are employed to update the particles. At each of iteration, updating any qubit can lead to updating all probability amplitudes of the corresponding particle. The experimental results of some benchmark functions optimization show that, although its single step iteration consumes long time, the optimization ability of the proposed method is significantly higher than other similar algorithms.