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Quantum-behaved particle swarm optimization: analysis of individual particle behavior and parameter selection.

Jun Sun¹, Wei Fang, Xiaojun Wu

¹Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, Jiangsu 214122, China. sunjun_wx@hotmail.com

Evolutionary Computation

|September 13, 2011

Summary

This study analyzes the Quantum-behaved Particle Swarm Optimization (QPSO) algorithm. We establish theoretical bounds for its contraction-expansion coefficient to ensure particle convergence and improve performance on benchmark functions.

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Area of Science:

Computational Intelligence
Optimization Algorithms
Quantum-inspired Computing

Background:

Quantum-behaved Particle Swarm Optimization (QPSO) is a probabilistic algorithm combining quantum mechanics and Particle Swarm Optimization (PSO).
While effective, detailed analysis of QPSO's internal mechanisms and parameter influence is limited.

Purpose of the Study:

To provide a comprehensive theoretical and experimental analysis of the QPSO algorithm.
To determine the theoretical upper bound for the contraction-expansion (CE) coefficient to guarantee particle position convergence or boundedness.
To guide the selection and control of the CE coefficient for optimal performance in real-world applications.

Main Methods:

Theoretical analysis of single-particle behavior in QPSO using probability measures.
Stochastic simulations to validate theoretical findings on particle behavior.
Empirical studies on benchmark functions using derived CE coefficient bounds.

Main Results:

An upper bound for the CE coefficient was theoretically derived, ensuring particle convergence or boundedness.
The study demonstrates how to control and select the CE coefficient based on theoretical findings.
QPSO with proposed parameter control methods shows efficient performance compared to other PSO variants.

Conclusions:

The theoretical analysis provides crucial insights into QPSO's behavior and parameter sensitivity.
Effective control and selection of the CE coefficient enhance QPSO's applicability and performance.
This work contributes to a deeper understanding and practical implementation of QPSO for optimization problems.