TY - GEN
T1 - Metaheuristic optimization algorithms for approximate solutions to ordinary differential equations
AU - Sadollah, Ali
AU - Choi, Younghwan
AU - Kim, Joong Hoon
N1 - Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2013R1A2A1A01013886).
Publisher Copyright:
© 2015 IEEE.
PY - 2015/9/10
Y1 - 2015/9/10
N2 - 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.
AB - 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.
KW - Approximate solution
KW - Fourier series
KW - Linear/nonlinear differential equation
KW - Metaheuristics
KW - Particle swarm optimization
KW - Water cycle algorithm
KW - Weighted residual function
UR - http://www.scopus.com/inward/record.url?scp=84963591622&partnerID=8YFLogxK
U2 - 10.1109/CEC.2015.7256972
DO - 10.1109/CEC.2015.7256972
M3 - Conference contribution
AN - SCOPUS:84963591622
T3 - 2015 IEEE Congress on Evolutionary Computation, CEC 2015 - Proceedings
SP - 792
EP - 798
BT - 2015 IEEE Congress on Evolutionary Computation, CEC 2015 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - IEEE Congress on Evolutionary Computation, CEC 2015
Y2 - 25 May 2015 through 28 May 2015
ER -