Solving initial and boundary value problems using learning automata particle swarm optimization

Kourosh Nemati, Siti Mariyam Shamsuddin, Maslina Darus

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this article, the particle swarm optimization (PSO) algorithm is modified to use the learning automata (LA) technique for solving initial and boundary value problems. A constrained problem is converted into an unconstrained problem using a penalty method to define an appropriate fitness function, which is optimized using the LA-PSO method. This method analyses a large number of candidate solutions of the unconstrained problem with the LA-PSO algorithm to minimize an error measure, which quantifies how well a candidate solution satisfies the governing ordinary differential equations (ODEs) or partial differential equations (PDEs) and the boundary conditions. This approach is very capable of solving linear and nonlinear ODEs, systems of ordinary differential equations, and linear and nonlinear PDEs. The computational efficiency and accuracy of the PSO algorithm combined with the LA technique for solving initial and boundary value problems were improved. Numerical results demonstrate the high accuracy and efficiency of the proposed method.

Original languageEnglish
Pages (from-to)656-673
Number of pages18
JournalEngineering Optimization
Volume47
Issue number5
DOIs
Publication statusPublished - 4 May 2015

Fingerprint

Learning Automata
Initial value problems
Particle swarm optimization (PSO)
Boundary value problems
Particle Swarm Optimization
Initial Value Problem
Particle Swarm Optimization Algorithm
Boundary Value Problem
Ordinary differential equations
Partial differential equations
Linear Ordinary Differential Equations
Penalty Method
Linear partial differential equation
Number of Solutions
Nonlinear Ordinary Differential Equations
Fitness Function
Computational efficiency
System of Ordinary Differential Equations
Nonlinear Partial Differential Equations
Computational Efficiency

Keywords

  • initial and boundary value problems
  • learning automata
  • particle swarm optimization
  • penalty method
  • unconstrained optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Industrial and Manufacturing Engineering
  • Applied Mathematics
  • Computer Science Applications
  • Management Science and Operations Research

Cite this

Solving initial and boundary value problems using learning automata particle swarm optimization. / Nemati, Kourosh; Shamsuddin, Siti Mariyam; Darus, Maslina.

In: Engineering Optimization, Vol. 47, No. 5, 04.05.2015, p. 656-673.

Research output: Contribution to journalArticle

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