A hybrid reptile search algorithm and Levenberg-Marquardt algorithm based Haar wavelets to solve regular and singular boundary value problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F23%3A10253450" target="_blank" >RIV/61989100:27240/23:10253450 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s12597-023-00661-0" target="_blank" >https://link.springer.com/article/10.1007/s12597-023-00661-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s12597-023-00661-0" target="_blank" >10.1007/s12597-023-00661-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A hybrid reptile search algorithm and Levenberg-Marquardt algorithm based Haar wavelets to solve regular and singular boundary value problems

Popis výsledku v původním jazyce

Various engineering applications lead to the appearance of partial differential equations resulting in boundary value problems (BVPs). Orthogonal collocation method based Haar wavelets has gained significant attention in solving these problems. The Haar wavelets have several properties like vanishing moment, compact effect, and orthogonality. These properties prioritize being used as base functions for solving BVPs. However, the approximation leads to a relatively high number of unknown coefficients, which needs an efficient and reliable nonlinear solver to reach their values. The Levenberg-Marquardt algorithm (LM) is one of the most efficient nonlinear solvers. However, it may diverge in case of too far initial guesses, especially in many unknowns. The reptile search algorithm (RSA) is a recent reliable, nature-inspired optimization technique that has a noticeable capability in dealing with high-dimensional issues. Therefore, this paper proposes a hybrid optimization algorithm that integrates the RSA and LM algorithms using Haar wavelets as bases, named RSA-LM-Haar algorithm, to solve regular and singular natures of the BVPs more efficiently. To evaluate the performance of the proposed RSA-LM-Haar algorithm, it is tested on twelve case studies of BVPs including the singular and regular problems. The results are compared with those based on the LM alone, named LM-Haar algorithm. Finally, the applicability of the proposed algorithm is verified using two practical chemical applications to prove its ability to solve real-time applications effectively. All the results affirmed the capability of the proposed algorithm in solving both regular and singular BVPs. All results and comparisons illustrated that the proposed hybridization algorithm provides remarkable performance.

Název v anglickém jazyce

A hybrid reptile search algorithm and Levenberg-Marquardt algorithm based Haar wavelets to solve regular and singular boundary value problems

Popis výsledku anglicky

Various engineering applications lead to the appearance of partial differential equations resulting in boundary value problems (BVPs). Orthogonal collocation method based Haar wavelets has gained significant attention in solving these problems. The Haar wavelets have several properties like vanishing moment, compact effect, and orthogonality. These properties prioritize being used as base functions for solving BVPs. However, the approximation leads to a relatively high number of unknown coefficients, which needs an efficient and reliable nonlinear solver to reach their values. The Levenberg-Marquardt algorithm (LM) is one of the most efficient nonlinear solvers. However, it may diverge in case of too far initial guesses, especially in many unknowns. The reptile search algorithm (RSA) is a recent reliable, nature-inspired optimization technique that has a noticeable capability in dealing with high-dimensional issues. Therefore, this paper proposes a hybrid optimization algorithm that integrates the RSA and LM algorithms using Haar wavelets as bases, named RSA-LM-Haar algorithm, to solve regular and singular natures of the BVPs more efficiently. To evaluate the performance of the proposed RSA-LM-Haar algorithm, it is tested on twelve case studies of BVPs including the singular and regular problems. The results are compared with those based on the LM alone, named LM-Haar algorithm. Finally, the applicability of the proposed algorithm is verified using two practical chemical applications to prove its ability to solve real-time applications effectively. All the results affirmed the capability of the proposed algorithm in solving both regular and singular BVPs. All results and comparisons illustrated that the proposed hybridization algorithm provides remarkable performance.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

OPSEARCH

ISSN

0030-3887

e-ISSN

0975-0320

Svazek periodika

60

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

IN - Indická republika

Počet stran výsledku

31

Strana od-do

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Kód UT WoS článku

001016466100001

EID výsledku v databázi Scopus

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