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Journal of Computer Applications

Quantum model of particle swarm optimization

Qin Yong-bo

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

As for the weak theoretical foundation of the Particle Swarm Optimization(PSO) algorithm and its analysis of the nature of the problem having not yet formed system,a new quantum model was established,which was based on quantum mechanics from the microscopic point of view.This model defined the search process as quantum state transition that in infinitely deep potential well.Through the model,the internal mechanism of executing process interpreted,and the experimental results show that the proposed algorithm has the optimization of quantum nature.

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As for the weak theoretical foundation of the Particle Swarm Optimization(PSO) algorithm and its analysis of the nature of the problem having not yet formed system,a new quantum model was established,which was based on quantum mechanics from the microscopic point of view.This model defined the search process as quantum state transition that in infinitely deep potential well.Through the model,the internal mechanism of executing process interpreted,and the experimental results show that the proposed algorithm has the optimization of quantum nature.
To improve the efficiency of particle swarm optimization, a quantum particle swarm optimization algorithm is proposed on the basis of analyzing the search process of particle swarm optimization algorithm. In the proposed algorithm, particles are endoded by qubits described on the Bloch sphere, each particle occupy three locations of the search space, and each location represents a optimization solution. By employing the search method of general PSO to adjust the two parameters of qubit, the qubits rotation are performed on the Bloch sphere, which can simultaneously update three locations occupied by a qubit and quickly approach the global optimal solution. The experimental results of standard test function extreme optimization and fuzzy controller parameters optimization show that the proposed algorithm is superior to other similar algorithm in optimization ability and optimization efficiency.
The article explored and delved into the advanced computational strategies of Particle Swarm Optimization (PSO) by contrasting classical and quantum computing paradigms. The advantages of quantum computing lie in its potential to solve computationally complex problems exponentially faster than classical computers. One of the advantages of Particle Swarm Optimization is its ability to find optimal solutions in complex search spaces. The research centers around the performance of PSO algorithms, as a part of the biological swarm optimization algorithms, when applied to a set of single-objective optimization functions, namely the Sphere, Rosenbrock, Booth, and Himmelblau functions. Utilizing a controlled setup of 100 particles, iterating 100 times across various dimensions tailored to each function, our study reveals that quantum Particle Swarm Optimization, implemented via Q# programming language and tested in Azure Quantum Workspace, consistently surpasses classical PSO in precision and convergence to global minima, despite the increased computational demands and error sensitivity inherent to quantum computations. The classical approach facilitated through Python programming language and leveraging deterministic pseudorandom number generators demonstrates robustness and lower computational costs but does not achieve the quantum's level of accuracy. The paper highlights the potential of quantum PSO to achieve superior optimization results in scenarios with smaller datasets and less complex problem spaces, paving the way for future applications where quantum advantages can be fully realized. The analysis goes further to discuss the implications of these findings for the future of optimization in various industries, including logistics, engineering, and finance, where optimization plays a critical role. The potential of quantum Particle Swarm Optimization to achieve superior optimization results in scenarios with smaller datasets and less complex problem spaces is particularly notable. It suggests that quantum computing could soon transform the landscape of computational optimization, providing solutions that are not only quicker but also more accurate.
To improve the efficiency of particle swarm optimization,a quantum particle swarm optimization algorithm is proposed on the basis of analyzing the search process of particle swarm optimization algorithm.In the proposed algorithm,particles are endoded by qubits described on the Bloch sphere,each particle occupy three locations of the search space,and each location represents a optimization solution.By employing the search method of general PSO to adjust the two parameters of qubit,the qubits rotation are performed on the Bloch sphere,which can simultaneously update three loations occupied by a qubit and quickly approach the global optimal solution.The experimental results of standard test function extreme optimization and fuzzy controller parameters optimization show that the proposed algorithm is superior to other similar algorithm in optimization ability and optimization efficiency.
This paper discusses how particle swarm optimization (PSO) can be used to generate quantum circuits to solve an instance of the MaxOne problem. It then analyzes previous studies on evolutionary algorithms for circuit synthesis. With a brief introduction to PSO, including its parameters and algorithm flow, the paper focuses on a method of quantum circuit encoding and representation as PSO parameters. The fitness evaluation used in this paper is the MaxOne problem. The paper presents experimental results that compare different learning abilities and inertia weight variations in the PSO algorithm. A comparison is further made between the PSO algorithm and a genetic algorithm for quantum circuit synthesis. The results suggest PSO converges more quickly to the optimal solution.
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.