A new optimization method has been proposed by Kennedy et. al. in [7, 8], called Particle Swarm Optimization (PSO). This approach combines social psychology principles in socio-cognition of human (and artificial) agents and evolutionary computation. It has been successfully applied to nonlinear function optimization and neural network training. Preliminary formal analyses for a simple PSO system show that a particle in a simple PSO system follows a path defined by a sinusoidal wave, randomly deciding on both its amplitude and frequency [12]. This paper takes the next step, generalizing to obtain closed form equations for trajectories of particles in a multi-dimensional search space. 1 Introduction Evolutionary computation techniques are search methods based on natural systems. For example, Genetic Algorithms (GAs) use principles of genetics and natural selection [4]. "Particle Swarm Optimization" (PSO) [7, 8] is a recently proposed algorithm, motivated by the behavior of organisms s...

Particle swarm optimization (PSO) has undergone many changes since its introduction in 1995. As researchers have learned about the technique, they have derived new versions, developed new applications, and published theoretical studies of the effects of the various parameters and aspects of the algorithm. This paper comprises a snapshot of particle swarming from the authors’ perspective, including variations in the algorithm, current and ongoing research, applications and open problems.

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Several theoretical analyses of the dynamics of particle swarms have been offered in the literature over the last decade. Virtually all rely on substantial simplifications, including the assumption that the particles are deterministic. This has prevented the exact characterisation of the sampling distribution of the PSO. In this paper we introduce a novel method, which allows one to exactly determine all the characteristics of a PSO’s sampling distribution and explain how they change over any number of generations, in the presence stochasticity. The only assumption we make is stagnation, i.e., we study the sampling distribution produced by particles in search for a better personal best. We apply the analysis to the PSO with inertia weight, but the analysis is also valid for the PSO with constriction.

Several theoretical analyses of the dynamics of particle swarms have been offered in the literature over the last decade. Virtually all rely on substantial simplifications, often including the assumption that the particles are deterministic. This has prevented the exact characterisation of the sampling distribution of the PSO. In this paper we introduce a novel method that allows us to exactly determine all the characteristics of a PSO’s sampling distribution and explain how it changes over any number of generations, in the presence stochasticity. The only assumption we make is stagnation, i.e., we study the sampling distribution produced by particles in search for a better personal best. We apply the analysis to the PSO with inertia weight, but the analysis is also valid for the PSO with constriction and other forms of PSO. 1

This paper proposes the application of particle swarm optimization (PSO) to the problem of full model selection, FMS, for classification tasks. FMS is defined as follows: given a pool of preprocessing methods, feature selection and learning algorithms, to select the combination of these that obtains the lowest classification error for a given data set; the task also includes the selection of hyperparameters for the considered methods. This problem generates a vast search space to be explored, well suited for stochastic optimization techniques. FMS can be applied to any classification domain as it does not require domain knowledge. Different model types and a variety of algorithms can be considered under this formulation. Furthermore, competitive yet simple models can be obtained with FMS. We adopt PSO for the search because of its proven performance in different problems and because of its simplicity, since neither expensive computations nor complicated operations are needed. Interestingly, the way the search is guided allows PSO to avoid overfitting to some extend. Experimental results on benchmark data sets give evidence that the proposed approach is very effective, despite its simplicity. Furthermore, results obtained in the framework of a model selection challenge show the competitiveness of the models selected with PSO, compared to models selected with other techniques that focus on a single algorithm and that use domain knowledge.

Abstract — Several theoretical analyses of the dynamics of particle swarms have been offered in the literature over the last decade. Virtually all rely on substantial simplifications, often including the assumption that the particles are deterministic. This has prevented the exact characterization of the sampling distribution of the particle swarm optimizer (PSO). In this paper we introduce a novel method that allows us to exactly determine all the characteristics of a PSO sampling distribution and explain how it changes over any number of generations, in the presence stochasticity. The only assumption we make is stagnation, i.e., we study the sampling distribution produced by particles in search for a better personal best. We apply the analysis to the PSO with inertia weight, but the analysis is also valid for the PSO with constriction and other forms of PSO. Index Terms — Particle swarm optimization, PSO theory, sampling distribution, stagnation.

Institute of Information Management I-Shou University This thesis presents a new approach to the support vector learning for dynamic clustering based on particle swarm optimization. Support vector clustering requires solving a constrained quadratic optimization problem. This problem often involves a matrix with an extremely large number of entries, which make off-the-shelf optimization packages unsuitable. Several methods have been used to decompose the problem, of which many require numeric packages for solving the smaller sub-problems. Support vector clustering solves the unsupervised clustering problem by searching for a minimal sphere enclosing all data images in feature space. Data points are mapped

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Received in a revised form 12.06.2008 Purpose: Selection of machining parameters is an important step in process planning therefore a new evolutionary computation technique is developed to optimize machining process. This study has presented multi-objective optimization of milling process by using neural network modelling and Particle swarm optimization. Particle Swarm Optimization (PSO) is used to efficiently optimize machining parameters simultaneously in high-speed milling processes where multiple conflicting objectives are present. The goal of optimization is to determine the objective function maximum (predicted cutting force surface) by consideration of cutting constraints. Design/methodology/approach: First, an Artificial Neural Network (ANN) predictive model is used to predict cutting forces during machining and then PSO algorithm is used to obtain optimum cutting speed and feed rates. Findings: During optimization the particles ‘fly ’ intelligently in the solution space and search for optimal cutting conditions according to the strategies of the PSO algorithm. The simulation results show that compared with genetic algorithms (GA) and simulated annealing (SA), the proposed algorithm can improve the quality of the solution while speeding up the convergence process. Research limitations/implications: The experimental results show that the MRR is improved by 28%.