Afterword

In the previous chapters, we presented the fundamental concepts and variants of PSO, as along with a multitude of recent research results. The reported results suggest that PSO can be a very useful tool for solving optimization problems from different scientific and technological fields, especially in cases where classical optimization methods perform poorly or their application involves formidable technical difficulties due to the problem’s special structure or nature. PSO was capable of addressing continuous and integer optimization problems, handling noisy and multiobjective cases, and producing efficient hybrid schemes in combination with specialized techniques or other algorithms in order to detect multiple (local or global) minimizers or control its own parameters.

Applications in Multiobjective, Constrained and Minimax Problems

This chapter is devoted to the application of PSO and its variants on three very interesting problem types, namely (a) multiobjective, (b) constrained, and (c) minimax optimization problems. The biggest part of the chapter refers to the multiobjective case, since there is a huge bibliography with a rich assortment of PSO approaches developed to date. Different algorithm types are presented and briefly discussed, focusing on the most influential approaches.

Applications in Noisy and Dynamic Environments

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.

Applications in Bioinformatics and Medical Informatics

This chapter presents two interesting applications of PSO in bioinformatics and medical informatics. The first consists of the adaptation of probabilistic neural network models for medical classification tasks. The second application employs the unified PSO algorithm to tackle magnetoencephalography problems. Our main goal is to clarify crucial points where PSO interferes with the employed computational models and provide details on the formulation of the corresponding optimization problems and experimental settings. Indicative results are reported to illustrate the workings of the algorithms and provide representative samples of their performance.

Applications in Machine Learning

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.

Established and Recently Proposed Variants of Particle Swarm Optimization

In this chapter, we describe established and recently proposed variants of PSO. Due to the rich PSO literature, the choice among different variants proved to be very difficult. Thus, we were compelled to set some criteria and select those variants that best suit them. For this purpose, we considered the following criteria: 1. Sophisticated inspiration source. 2. Close relationship to the standard PSO. 3. Wide applicability in problems of different types. 4. Performance and theoretical properties. 5. Number of reported applications. 6. Potential for further development and improvements. Thus, we excluded variants based on complicated hybrid schemes that combine other algorithms, where it is not evident which algorithm triggers which effect, as well as over-specialized schemes that refer only to one problem type or instance. Under this prism, we selected the following methods: unified PSO, memetic PSO, composite PSO, vector evaluated PSO, guaranteed convergence PSO, cooperative PSO, niching PSO, TRIBES, and quantum PSO. Albeit possibly omitting an interesting approach, the aforementioned variants sketch a rough picture of the current status in PSO literature, exposing the main ideas and features that constitute the core of research nowadays.

Theoretical Derivations and Application Issues

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.

Particle Swarm Optimization

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.

Introduction

In this chapter, we provide brief introductions to the basic concepts of global optimization, evolutionary computation, and swarm intelligence. The necessity of solving optimization problems is outlined and various problem types are reported. A rough classification of established optimization algorithms is provided, followed by the historical development of evolutionary computation. The three fundamental evolutionary approaches are briefly presented, along with their basic features and operations. Finally, the reader is introduced to the field of swarm intelligence, and a strong theoretical result is concisely reported to justify the necessity for further development of global optimization algorithms.

Applications in Operations Research

This chapter is devoted to three representative applications of PSO in operations research. Similarly to the previous chapters, our attention is focused on the presentation of essential aspects rather than reviewing the existing literature. Thus, we present methodologies for formulation of the optimization problem, which is not always trivial, as well as for the efficient treatment of special problem requirements that cannot be handled directly by PSO. Under this prism, we report applications from the fields of scheduling, inventory optimization and game theory. Recent results are also reported per case to provide an idea of the efficiency of PSO.