Particle Swarm Optimization: Fundamentals and Applications

By Fouad Sabry

What Is Particle Swarm Optimization

Particle swarm optimization, often known as PSO, is a computer method that was developed in the field of computational science. This method optimizes a problem by iteratively trying to improve a candidate solution with relation to a specific measure of quality. It solves a problem by having a population of potential solutions, which are referred to as particles here, and moving these particles around in the search space in accordance with a basic mathematical formula over the particle's position and velocity. This method is called particle-based search. The movement of each particle is led toward the best known positions in the search space, which are updated when better places are identified by other particles. However, the movement of each particle is also impacted by its best known position in its local region. It is anticipated that this will direct the hive toward the optimal options.

How You Will Benefit

(I) Insights, and validations about the following topics:

Chapter 1: Particle swarm optimization

Chapter 2: Particle filter

Chapter 3: Swarm intelligence

Chapter 4: Bees algorithm

Chapter 5: Fish School Search

Chapter 6: Artificial bee colony algorithm

Chapter 7: Derivative-free optimization

Chapter 8: Multi-swarm optimization

Chapter 9: Dispersive flies optimisation

Chapter 10: Metaheuristic

(II) Answering the public top questions about particle swarm optimization.

(III) Real world examples for the usage of particle swarm optimization in many fields.

(IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of particle swarm optimization' technologies.

Who This Book Is For

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of particle swarm optimization.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: Jul 1, 2023

Book preview

Chapter 1: Particle swarm optimization

Particle swarm optimization, often known as PSO, is a computer approach that was developed in the field of computational science. This method optimizes a problem by repeatedly attempting to improve a candidate solution with relation to a specific measure of quality. It solves a problem by having a population of candidate solutions, which are referred to as particles, and moving these particles around in the search space in accordance with a simple mathematical formula over the particle's position and velocity. Specifically, the problem is solved by having particles. The movement of each particle is led toward the best known locations in the search space, which are updated when better places are identified by other particles. However, the movement of each particle is also impacted by its best known position in its local region. It is anticipated that this would direct the horde in the direction of the optimal solutions.

The discovery of PSO was first credited to Kennedy, Eberhart, and Shi.

PSO is a metaheuristic because it searches extremely wide spaces for candidate solutions and makes few or no assumptions about the issue that is being optimized. In addition, PSO does not use the gradient of the problem that is being optimized. Since PSO does not use the gradient of the problem, it does not require that the optimization problem be differentiable. This is in contrast to traditional optimization methods such as gradient descent and quasi-newton methods, which do require that the optimization problem be differentiable. On the other hand, metaheuristics like PSO do not ensure that an optimum solution will ever be found.

There may be a connection between PSO and molecular dynamics.

A fundamental implementation of the PSO algorithm makes use of a population of potential solutions, which is referred to as a swarm (called particles). The search space is reorganized to accommodate the movement of these particles in accordance with a few simple formulas. The motions of the particles are directed by both the particles' best-known location in the search space and the best-known position of the swarm as a whole. When better places are identified, they will eventually come to be used to steer the motions of the swarm. The procedure is carried out several times, and it is hoped—though not guaranteed—that doing so would ultimately lead to the discovery of a solution that is adequate.

Formally, let f: ℝn → ℝ be the cost function which must be minimized.

The function accepts a candidate solution in the form of a vector of real numbers as its argument, and it generates a real number as its output, which represents the value of the objective function for the candidate solution that was