Metaheuristic optimization algorithms for approximate solutions to ordinary differential equations

Ali Sadollah, Younghwan Choi, Joong Hoon Kim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. In this paper, a general approach is suggested to solve a variety of linear and nonlinear ordinary differential equations (ODEs). With the aid of certain fundamental concepts of mathematics, Fourier series expansion and metaheuristic optimization methods, ODEs can be represented as an optimization problem. The aim is to minimize the weighted residual function (error function) of the ODEs. The boundary and initial values of ODEs are considered as constraints for the optimization model. Generational distance metric is used for evaluation and assessment of approximate solutions versus exact solutions. Two ODEs and one mechanical problem are approximately solved and compared with their exact solutions. The optimization task is carried out using different optimizers including the particle swarm optimization and the water cycle algorithm. The optimization results obtained show that the metaheuristic algorithms can be successfully applied for approximate solving of different types of ODEs.

Original languageEnglish
Title of host publication2015 IEEE Congress on Evolutionary Computation, CEC 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages792-798
Number of pages7
ISBN (Print)9781479974924
DOIs
Publication statusPublished - 2015 Sep 10
EventIEEE Congress on Evolutionary Computation, CEC 2015 - Sendai, Japan
Duration: 2015 May 252015 May 28

Other

OtherIEEE Congress on Evolutionary Computation, CEC 2015
CountryJapan
CitySendai
Period15/5/2515/5/28

Fingerprint

Metaheuristics
Ordinary differential equations
Optimization Algorithm
Ordinary differential equation
Approximate Solution
Exact Solution
Linear Ordinary Differential Equations
Optimization
Fourier Expansion
Distance Metric
Error function
Nonlinear Ordinary Differential Equations
Series Expansion
Optimization Model
Fourier series
Particle Swarm Optimization
Optimization Methods
Particle swarm optimization (PSO)
Physics
Economics

Keywords

  • Approximate solution
  • Fourier series
  • Linear/nonlinear differential equation
  • Metaheuristics
  • Particle swarm optimization
  • Water cycle algorithm
  • Weighted residual function

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mathematics

Cite this

Sadollah, A., Choi, Y., & Kim, J. H. (2015). Metaheuristic optimization algorithms for approximate solutions to ordinary differential equations. In 2015 IEEE Congress on Evolutionary Computation, CEC 2015 - Proceedings (pp. 792-798). [7256972] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CEC.2015.7256972

Metaheuristic optimization algorithms for approximate solutions to ordinary differential equations. / Sadollah, Ali; Choi, Younghwan; Kim, Joong Hoon.

2015 IEEE Congress on Evolutionary Computation, CEC 2015 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2015. p. 792-798 7256972.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sadollah, A, Choi, Y & Kim, JH 2015, Metaheuristic optimization algorithms for approximate solutions to ordinary differential equations. in 2015 IEEE Congress on Evolutionary Computation, CEC 2015 - Proceedings., 7256972, Institute of Electrical and Electronics Engineers Inc., pp. 792-798, IEEE Congress on Evolutionary Computation, CEC 2015, Sendai, Japan, 15/5/25. https://doi.org/10.1109/CEC.2015.7256972
Sadollah A, Choi Y, Kim JH. Metaheuristic optimization algorithms for approximate solutions to ordinary differential equations. In 2015 IEEE Congress on Evolutionary Computation, CEC 2015 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2015. p. 792-798. 7256972 https://doi.org/10.1109/CEC.2015.7256972
Sadollah, Ali ; Choi, Younghwan ; Kim, Joong Hoon. / Metaheuristic optimization algorithms for approximate solutions to ordinary differential equations. 2015 IEEE Congress on Evolutionary Computation, CEC 2015 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 792-798
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