### 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 language | English |
---|---|

Pages (from-to) | 656-673 |

Number of pages | 18 |

Journal | Engineering Optimization |

Volume | 47 |

Issue number | 5 |

DOIs | |

Publication status | Published - 4 May 2015 |

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### 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

*Engineering Optimization*,

*47*(5), 656-673. https://doi.org/10.1080/0305215X.2014.914190

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

Research output: Contribution to journal › Article

*Engineering Optimization*, vol. 47, no. 5, pp. 656-673. https://doi.org/10.1080/0305215X.2014.914190

}

TY - JOUR

T1 - Solving initial and boundary value problems using learning automata particle swarm optimization

AU - Nemati, Kourosh

AU - Shamsuddin, Siti Mariyam

AU - Darus, Maslina

PY - 2015/5/4

Y1 - 2015/5/4

N2 - 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.

AB - 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.

KW - initial and boundary value problems

KW - learning automata

KW - particle swarm optimization

KW - penalty method

KW - unconstrained optimization

UR - http://www.scopus.com/inward/record.url?scp=84924087698&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924087698&partnerID=8YFLogxK

U2 - 10.1080/0305215X.2014.914190

DO - 10.1080/0305215X.2014.914190

M3 - Article

AN - SCOPUS:84924087698

VL - 47

SP - 656

EP - 673

JO - Engineering Optimization

JF - Engineering Optimization

SN - 0305-215X

IS - 5

ER -