Genetic algorithms + data structures = evolution programs (3rd ed.)
Genetic algorithms + data structures = evolution programs (3rd ed.)
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Evolutionary Optimization
The particle swarm optimization algorithm: convergence analysis and parameter selection
Information Processing Letters
On initial populations of a genetic algorithm for continuous optimization problems
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
A study of particle swarm optimization particle trajectories
Information Sciences: an International Journal
Evolutionary Computation for Modeling and Optimization
Evolutionary Computation for Modeling and Optimization
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
Stability of a one-dimensional discrete-time asynchronous swarm
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Incremental learning optimization on knowledge discovery in dynamic business intelligent systems
Journal of Global Optimization
Particle swarm optimization for solving engineering problems: A new constraint-handling mechanism
Engineering Applications of Artificial Intelligence
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In this paper we consider the evolutionary Particle Swarm Optimization (PSO) algorithm, for the minimization of a computationally costly nonlinear function, in global optimization frameworks. We study a reformulation of the standard iteration of PSO (Clerc and Kennedy in IEEE Trans Evol Comput 6(1) 2002), (Kennedy and Eberhart in IEEE Service Center, Piscataway, IV: 1942---1948, 1995) into a linear dynamic system. We carry out our analysis on a generalized PSO iteration, which includes the standard one proposed in the literature. We analyze three issues for the resulting generalized PSO: first, for any particle we give both theoretical and numerical evidence on an efficient choice of the starting point. Then, we study the cases in which either deterministic and uniformly randomly distributed coefficients are considered in the scheme. Finally, some convergence analysis is also provided, along with some necessary conditions to avoid diverging trajectories. The results proved in the paper can be immediately applied to the standard PSO iteration.