Pure adaptive search in global optimization
Mathematical Programming: Series A and B
Drift analysis and average time complexity of evolutionary algorithms
Artificial Intelligence
Parameter Selection in Particle Swarm Optimization
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
The particle swarm optimization algorithm: convergence analysis and parameter selection
Information Processing Letters
Towards an analytic framework for analysing the computation time of evolutionary algorithms
Artificial Intelligence
Information Processing Letters
Population structure and particle swarm performance
CEC '02 Proceedings of the Evolutionary Computation on 2002. CEC '02. Proceedings of the 2002 Congress - Volume 02
Population structure and particle swarm performance
CEC '02 Proceedings of the Evolutionary Computation on 2002. CEC '02. Proceedings of the 2002 Congress - Volume 02
Multilevel Minimum Cross Entropy Threshold Selection Based on Quantum Particle Swarm Optimization
SNPD '07 Proceedings of the Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing - Volume 02
Toward a theory of evolution strategies: On the benefits of sex---the (μ/μ, λ) theory
Evolutionary Computation
Logarithmic convergence of random heuristic search
Evolutionary Computation
A new approach to estimating the expected first hitting time of evolutionary algorithms
Artificial Intelligence
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Neighborhood re-structuring in particle swarm optimization
AI'05 Proceedings of the 18th Australian Joint conference on Advances in Artificial Intelligence
Local convergence rates of simple evolutionary algorithms withCauchy mutations
IEEE Transactions on Evolutionary Computation
A new model of simulated evolutionary computation-convergenceanalysis and specifications
IEEE Transactions on Evolutionary Computation
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
The fully informed particle swarm: simpler, maybe better
IEEE Transactions on Evolutionary Computation
A Cooperative approach to particle swarm optimization
IEEE Transactions on Evolutionary Computation
Stability analysis of the particle dynamics in particle swarm optimizer
IEEE Transactions on Evolutionary Computation
Comprehensive learning particle swarm optimizer for global optimization of multimodal functions
IEEE Transactions on Evolutionary Computation
Locating and tracking multiple dynamic optima by a particle swarm model using speciation
IEEE Transactions on Evolutionary Computation
Stability analysis of social foraging swarms
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A hierarchical particle swarm optimizer and its adaptive variant
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Training ANFIS parameters with a quantum-behaved particle swarm optimization algorithm
ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part I
Tracking Multiple Optima in Dynamic Environments by Quantum-Behavior Particle Swarm Using Speciation
International Journal of Swarm Intelligence Research
Review: A parameter selection strategy for particle swarm optimization based on particle positions
Expert Systems with Applications: An International Journal
A parameter-free barebones particle swarm algorithm for unsupervised pattern classification
International Journal of Hybrid Intelligent Systems
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Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was proposed as a variant of PSO with better global search ability. Although it has been shown to perform well in finding optimal solutions for many optimization problems, there has so far been little theoretical analysis on its convergence and performance. This paper presents a convergence analysis and performance evaluation of the QPSO algorithm and it also proposes two variants of the QPSO algorithm. First, we investigate in detail the convergence of the QPSO algorithm on a probabilistic metric space and prove that the QPSO algorithm is a form of contraction mapping and can converge to the global optimum. This is the first time that the theory of probabilistic metric spaces has been employed to analyze a stochastic optimization algorithm. We provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values. With these definitions, the effectiveness of the QPSO is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm. Then, the QPSO with random mean best position (QPSO-RM) and the QPSO with ranking operator (QPSO-RO) are proposed as two improvements of the QPSO algorithm. Finally, some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between QPSO, QPSO-RM, QPSO-RO and other variants of PSO.