Particle swarm optimization stability analysis

Date of Award

2013

Degree Name

M.S. in Electrical Engineering

Department

Department of Electrical and Computer Engineering

Advisor/Chair

Advisor: Raúl Ordóñez

Abstract

Optimizing a multidimensional function -- uni-modal or multi-modal -- is a problem that regularly comes about in engineering and science. Evolutionary Computation techniques, including Evolutionary Algorithm and Swarm Intelligence (SI), are biological systems inspired search methods often used to solve optimization problems. In this thesis, the SI technique Particle Swarm Optimization (PSO) is studied. Convergence and stability of swarm optimizers have been subject of PSO research. Here, using discrete-time adaptive control tools found in literature, an adaptive particle swarm optimizer is developed. An error system is devised and a controller is designed to adaptively drive the error to zero. The controller features a function approximator, used here as a predictor to estimate future signals. Through Lyapunov's direct method, it is shown that the devised error system is ultimately uniformly bounded and the adaptive optimizer is stable. Moreover, through LaSalle-Yoshizawa theorem, it is also shown that the error system goes to zero as time evolves. Experiments are performed on a variety of benchmark functions and results for comparison purposes between the adaptive optimizer and other algorithms found in literature are provided.

Keywords

Swarm intelligence Mathematical models, Mathematical optimization, Electrical engineering; particle swarm optimization; discrete-time adaptive control; stability analysis; Lyapunov direct method; LaSalle-Yoshizawa theorem; function approximation

Rights Statement

Copyright © 2013, author

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