Particle swarm optimization: An overview

Riccardo Poli · James Kennedy · Tim Blackwell
Swarm Intell (2007) 1: 33–57

Abstract
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.

Keywords: Particle swarms · Particle swarm optimization · PSO · Social networks · Swarm theory · Swarm dynamics · Real world applications

1 Introduction

The article is organized as follows.

• In Sect. 2, we explain what particle swarms are and
  we look at the rules that control their dynamics.
• In Sect. 3, we consider how different types of social networks influence the behavior of swarms.
• In Sect. 4, we review some interesting variants of particle swarm optimization.
• In Sect. 5, we summarize the main results of theoretical
  analyses of the particle swarm optimizers.
• Section 6 looks at areas where particle swarms have been successfully applied.
• Open problems in particle swarm optimization are listed and discussed in Sect. 7.
• We draw some conclusions in Sect. 8.

2 Population dynamics

2.1 The original version

The (original) process for implementing PSO is as in Algorithm 1.

PSO algorithm

2.2 Parameters

2.3 Inertia weight

the PSO’s update equations:

update equation

2.5 Fully informed particle swarm

3 Population topology

4 PSO variants and specializations

4.1 Binary particle swarms

4.2 Dynamic problems

4.3 Noisy functions

4.4 Hybrids and adaptive particle swarms

4.5 PSOs with diversity control

4.6 Bare-bones PSO

5 Theoretical analyses

current issue: a fully comprehensive mathematical model of particle swarm optimization is still not available

• Firstly, the PSO is made up of a large number of interacting elements (the particles).
• Secondly, the particles are provided with memory and
  the ability to decide when to update the memory.
• Thirdly, forces are stochastic. This prevents the use of standard mathematical tools used in the analysis of
  dynamical systems.
• Fourthly, the behavior of the PSO depends crucially on the structure of the fitness function.

5.1 Deterministic models

5.2 Modeling PSO’s randomness

5.3 Executable models

6 Applications

The main PSO application categories:

7 Open questions

7.1 Initialization and termination

7.2 Particle selection, movement, and evaluation

7.3 Memory selection and update

7.4 Adaptation

7.5 Theory

8 Conclusions