An optimization technique based on imperialist competition algorithm to measurement of error for solving initial and boundary value problems

K. Nemati, S. M. Shamsuddin, Maslina Darus

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Imperialist competitive algorithm (ICA) is proposed to solve initial and boundary value problems in this paper. A constrained problem is converted into an unconstrained problem through the use of a penalty method in other to define an appropriate fitness function that is optimized by means of the ICA method. The methodology adopted evaluates a large number of candidate solutions of the unconstrained problem with the ICA to minimize 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. The method is proficient approach to solve linear and nonlinear ODEs, systems of ordinary differential equations (SODEs), linear and nonlinear PDEs. Numerical experiments demonstrate the accuracy and efficiency of the proposed method. Thus, this method is a promising tool for solving higher-dimensional problems.

Original languageEnglish
Pages (from-to)96-108
Number of pages13
JournalMeasurement: Journal of the International Measurement Confederation
Volume48
Issue number1
DOIs
Publication statusPublished - 2014

Fingerprint

Initial value problems
Ordinary differential equations
boundary value problems
Optimization Techniques
Boundary value problems
Initial Value Problem
differential equations
Boundary Value Problem
partial differential equations
Partial differential equations
optimization
fitness
penalties
Linear Ordinary Differential Equations
Penalty Method
Linear partial differential equation
Number of Solutions
Nonlinear Ordinary Differential Equations
Fitness Function
System of Ordinary Differential Equations

Keywords

  • Evolutionary algorithm
  • Imperialist competitive algorithm
  • Initial and boundary value problems
  • Penalty method
  • Unconstrained optimization

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Applied Mathematics

Cite this

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N2 - Imperialist competitive algorithm (ICA) is proposed to solve initial and boundary value problems in this paper. A constrained problem is converted into an unconstrained problem through the use of a penalty method in other to define an appropriate fitness function that is optimized by means of the ICA method. The methodology adopted evaluates a large number of candidate solutions of the unconstrained problem with the ICA to minimize 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. The method is proficient approach to solve linear and nonlinear ODEs, systems of ordinary differential equations (SODEs), linear and nonlinear PDEs. Numerical experiments demonstrate the accuracy and efficiency of the proposed method. Thus, this method is a promising tool for solving higher-dimensional problems.

AB - Imperialist competitive algorithm (ICA) is proposed to solve initial and boundary value problems in this paper. A constrained problem is converted into an unconstrained problem through the use of a penalty method in other to define an appropriate fitness function that is optimized by means of the ICA method. The methodology adopted evaluates a large number of candidate solutions of the unconstrained problem with the ICA to minimize 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. The method is proficient approach to solve linear and nonlinear ODEs, systems of ordinary differential equations (SODEs), linear and nonlinear PDEs. Numerical experiments demonstrate the accuracy and efficiency of the proposed method. Thus, this method is a promising tool for solving higher-dimensional problems.

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