A direct method for solving calculus of variations problems using the whale optimization algorithm

Seyed Hamed Hashemi Mehne; Seyedali Mirjalili

doi:10.1007/s12065-019-00275-w

A direct method for solving calculus of variations problems using the whale optimization algorithm

Seyed Hamed Hashemi Mehne
, Seyedali Mirjalili

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

A numerical algorithm for solving problems of calculus of variations is proposed and analyzed in the present paper. The method is based on direct minimizing the functional in its discrete form with finite dimension. To solve the resulting optimization problem , the recently proposed whale optimization algorithms is used and adopted. The method proposed in this work is capable of solving constrained and unconstrained problems with fixed or free endpoint conditions. Numerical examples are given to check the validity and accuracy of the proposed method in practice. The results show the superior accuracy and efficiency of the proposed technique as compared to other numerical methods.

Original language	English
Journal	Evolutionary Intelligence
DOIs	https://doi.org/10.1007/s12065-019-00275-w
Publication status	Published - 1 Jan 2019
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being
SDG 7 Affordable and Clean Energy
SDG 9 Industry, Innovation, and Infrastructure
SDG 11 Sustainable Cities and Communities
SDG 12 Responsible Consumption and Production
SDG 13 Climate Action
SDG 17 Partnerships for the Goals

Keywords

Calculus of variations
Finite difference
Numerical solution
Whale optimization algorithm

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10.1007/s12065-019-00275-w

Cite this

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title = "A direct method for solving calculus of variations problems using the whale optimization algorithm",

abstract = "A numerical algorithm for solving problems of calculus of variations is proposed and analyzed in the present paper. The method is based on direct minimizing the functional in its discrete form with finite dimension. To solve the resulting optimization problem , the recently proposed whale optimization algorithms is used and adopted. The method proposed in this work is capable of solving constrained and unconstrained problems with fixed or free endpoint conditions. Numerical examples are given to check the validity and accuracy of the proposed method in practice. The results show the superior accuracy and efficiency of the proposed technique as compared to other numerical methods.",

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AU - Mirjalili, Seyedali

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N2 - A numerical algorithm for solving problems of calculus of variations is proposed and analyzed in the present paper. The method is based on direct minimizing the functional in its discrete form with finite dimension. To solve the resulting optimization problem , the recently proposed whale optimization algorithms is used and adopted. The method proposed in this work is capable of solving constrained and unconstrained problems with fixed or free endpoint conditions. Numerical examples are given to check the validity and accuracy of the proposed method in practice. The results show the superior accuracy and efficiency of the proposed technique as compared to other numerical methods.

AB - A numerical algorithm for solving problems of calculus of variations is proposed and analyzed in the present paper. The method is based on direct minimizing the functional in its discrete form with finite dimension. To solve the resulting optimization problem , the recently proposed whale optimization algorithms is used and adopted. The method proposed in this work is capable of solving constrained and unconstrained problems with fixed or free endpoint conditions. Numerical examples are given to check the validity and accuracy of the proposed method in practice. The results show the superior accuracy and efficiency of the proposed technique as compared to other numerical methods.

KW - Calculus of variations

KW - Finite difference

KW - Numerical solution

KW - Whale optimization algorithm

UR - https://www.scopus.com/pages/publications/85070809370

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SN - 1864-5909

JO - Evolutionary Intelligence

JF - Evolutionary Intelligence

ER -

A direct method for solving calculus of variations problems using the whale optimization algorithm

Abstract

UN SDGs

Keywords

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