This chapter is devoted to particle swarm optimization (PSO), from early precursors to contemporary standard variants. The presentation begins with the main inspiration source behind its development, followed by early variants and discussion on their parameters. Severe deficiencies of early variants are also pointed out and their solutions are reported in a relative historical order, bringing the reader to contemporary developments, considered as the state-of-the-art PSO variants today.
This chapter presents the fundamental concepts regarding the application of PSO on machine learning problems. The main objective in such problems is the training of computational models for performing classification and simulation tasks. It is not our intention to provide a literature review of the numerous relative applications. Instead, we aim at providing guidelines for the application and adaptation of PSO on this problem type. To achieve this, we focus on two representative cases, namely the training of artificial neural networks, and learning in fuzzy cognitive maps. In each case, the problem is first defined in a general framework, and then an illustrative example is provided to familiarize readers with the main procedures and possible obstacles that may arise during the optimization process.
This chapter discusses the workings of PSO in two research fields with special importance in real-world applications, namely noisy and dynamic environments. Noise simulation schemes are presented and experimental results on benchmark problems are reported. In addition, we present the application of PSO on a simulated real world problem, namely the particle identification by light scattering. Moreover, a hybrid scheme that incorporates PSO in particle filtering methods to estimate system states online is analyzed, and representative experimental results are reported. Finally, the combination of noisy and continuously changing environments is shortly discussed, providing illustrative graphical representations of performance for different PSO variants. The text focuses on providing the basic concepts and problem formulations, and suggesting experimental settings reported in literature, rather than on the bibliographical presentation of the (prohibitively extensive) literature.
This chapter is devoted to the application of PSO in dynamical systems. The core subject of the chapter is the problem of detecting periodic orbits of nonlinear mappings. This problem is very interesting and significant, as the study of periodic orbits can reveal several crucial properties of a dynamical system. Traditional root-finding algorithms, such as the Newton-family methods, are widely applied on such problems. However, obstacles arise as soon as non-differentiable or discontinuous mappings come under investigation. In such cases, PSO has been shown to be a very useful and efficient alternative. The chapter aims at presenting fundamental ideas and specific application issues. We thoroughly discuss the transformation of the original problem to a corresponding global optimization task. The application of the deflection technique, presented in Chapter Five, for computing several periodic orbits is analyzed and the algorithm is illustrated on well known benchmark problems. Finally, we present and discuss a very significant application, i.e., the detection of periodic orbits in 3-dimensional galactic potentials.
This chapter deals with fundamental theoretical investigations and application issues of PSO. We are mostly interested in developments that offer new insight in configuring and tuning the parameters of the method. For this purpose, the chapter opens with a discussion on initialization techniques, followed by brief presentations of investigations on particle trajectories and the stability analysis of PSO. A useful technique based on computational statistics is also presented for the optimal tuning of the algorithm on specific problems. The chapter closes with a short discussion on termination conditions.
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