A Note on Particle Swarm Optimization: An integrated and theoretical approach

Abstract

In this paper, a general and integrated form is predefined goal. In the selective breeding or crossover proposed for the different kinds of particle swarm process, fit individuals are chosen to produce more optimization. Also, some related theoretical results are given, offspring than less fit individuals, which tends to including a convergence theorem for the random selection homogenize the population and improves the average result case and a lemma on probability percentile. To compare as the algorithm progresses. Subsequent mutations of the different PSO algorithms in effectiveness and efficiency, we offspring add diversity to the population and explore new propose three comparison indexes of universal standard.areas of the parameter search space. On a different side, the Particle Swarm Optimization I INTRODUCTION (PSO), introduced by Kennedy and Eberhart [9], [10], is a stochastic optimization technique that can be likened to theIn contrast to the traditional adaptive stochastic search behavior of a flock of birds or the sociological behavior of algorithms, evolutionary computation (EC) techniques a group of people. The PSO is a population based exploit a set of potential solutions, named a population, and optimization technique, where the population is called a detect the optimal solution through cooperation and swarm. A simple explanation of the PSO's operation is as competition among the individuals of the population. These follows. Each particle represents a possible solution to the techniques often detect optima in difficult optimization optimization task at hand. During iterations, each particle problems faster than traditional optimization methods. The accelerates in the direction of its own personal best solution most frequently encountered population-based EC found so far, as well as in the direction of the global best techniques, such as evolutionary programming [1], position discovered so far by any of the particles in the evolution strategies (ES) [2], [3], [4], genetic algorithms swarm. This means that if a particle discovers a promising (GAs) [5], [6], and genetic programming [7], [8], are new solution, all the other particles will move closer to it, inspired from the evolutionary mechanisms of nature. exploring the region more thoroughly in the process. The Among others, GAs are a family of computational PSO has been used to solve a range of optimization models inspired by the concept about natural evolution, problems, including neural network training [1 1] ,[12] , [13] Motivated by Darwin's theories of evolution and the and function minimization [14], [15].concept of "survival of the fittest,"' GAs use processes analogous to genetic recombination and mutation to II INTEGRATED PSO ALGORITHM promote the evolution of a population that best satisfies a

Constructing a Markov Chain on Particle Swarm Optimizer

“…Theorem 1 and Lemma 1 are from Chou etc. [24]. Theorem 1 gives the result that the non-cooperative i.i.d.…”

Markov Chain and Adaptive Parameter Selection on Particle Swarm Optimizer

“…Theorem 2.1 and Lemma 2.1 are from Chou etc. [5]. Theorem 2.1 gives the result that even the non-cooperative independent and identically distributed (i.i.d.)…”