Applications of new hybrid algorithm based on advanced cuckoo search and adaptive Gaussian quantum behaved particle swarm optimization in solving ordinary differential equations

•Transformation of ordinary differential equation to optimization problem.•Hybrid algorithm based on cuckoo search & advanced particle swarm optimization.•Testing of stability of the algorithm by convergence graph & statistical analysis.•Finding superiority of the algorithm by non-parametric...

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Vydané v:	Expert systems with applications Ročník 172; s. 114646
Hlavní autori:	Kumar, Nirmal, Shaikh, Ali Akbar, Mahato, Sanat Kumar, Bhunia, Asoke Kumar
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Elsevier Ltd 15.06.2021 Elsevier BV
Predmet:	Adaptive algorithms AGQPSO Algorithms Boundary conditions Boundary value problems Cuckoo search algorithm Differential equations Hybrid algorithm Mathematical analysis Optimization Ordinary differential equations Particle swarm optimization Search algorithms AGQPSO Cuckoo search algorithm Hybrid algorithm Differential equations
ISSN:	0957-4174, 1873-6793
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Abstract	•Transformation of ordinary differential equation to optimization problem.•Hybrid algorithm based on cuckoo search & advanced particle swarm optimization.•Testing of stability of the algorithm by convergence graph & statistical analysis.•Finding superiority of the algorithm by non-parametrical statistical test. This article solves first and second order differential equations with initial and/or boundary conditions by transforming these equations into unconstrained/bound constrained optimization problems. In order to solve these problems, a hybrid algorithm based on advanced cuckoo search (CS) algorithm and adaptive Gaussian quantum behaved particle swarm optimization (AGQPSO) is proposed. The CS algorithm is modified first by changing the step size in the simplified version. After that half of the total population is upgraded by this modified CS algorithm and another half is upgraded by AGQPSO algorithm. Then deletion strategy of CS algorithm is applied on the whole updated population. Next, to test the performance of the proposed hybrid algorithm, a number of benchmarks bound constrained optimization problems with different dimensions are considered and solved. Then this algorithm is applied fruitfully in first and second order initial value problems and boundary value problems by expressing the said problems in the form of bound constrained optimization problems.
AbstractList	This article solves first and second order differential equations with initial and/or boundary conditions by transforming these equations into unconstrained/bound constrained optimization problems. In order to solve these problems, a hybrid algorithm based on advanced cuckoo search (CS) algorithm and adaptive Gaussian quantum behaved particle swarm optimization (AGQPSO) is proposed. The CS algorithm is modified first by changing the step size in the simplified version. After that half of the total population is upgraded by this modified CS algorithm and another half is upgraded by AGQPSO algorithm. Then deletion strategy of CS algorithm is applied on the whole updated population. Next, to test the performance of the proposed hybrid algorithm, a number of benchmarks bound constrained optimization problems with different dimensions are considered and solved. Then this algorithm is applied fruitfully in first and second order initial value problems and boundary value problems by expressing the said problems in the form of bound constrained optimization problems. •Transformation of ordinary differential equation to optimization problem.•Hybrid algorithm based on cuckoo search & advanced particle swarm optimization.•Testing of stability of the algorithm by convergence graph & statistical analysis.•Finding superiority of the algorithm by non-parametrical statistical test. This article solves first and second order differential equations with initial and/or boundary conditions by transforming these equations into unconstrained/bound constrained optimization problems. In order to solve these problems, a hybrid algorithm based on advanced cuckoo search (CS) algorithm and adaptive Gaussian quantum behaved particle swarm optimization (AGQPSO) is proposed. The CS algorithm is modified first by changing the step size in the simplified version. After that half of the total population is upgraded by this modified CS algorithm and another half is upgraded by AGQPSO algorithm. Then deletion strategy of CS algorithm is applied on the whole updated population. Next, to test the performance of the proposed hybrid algorithm, a number of benchmarks bound constrained optimization problems with different dimensions are considered and solved. Then this algorithm is applied fruitfully in first and second order initial value problems and boundary value problems by expressing the said problems in the form of bound constrained optimization problems.
ArticleNumber	114646
Author	Kumar, Nirmal Shaikh, Ali Akbar Bhunia, Asoke Kumar Mahato, Sanat Kumar
Author_xml	– sequence: 1 givenname: Nirmal surname: Kumar fullname: Kumar, Nirmal email: kumarnirmal843@gmail.com organization: Department of Mathematics, The University of Burdwan, Purba Barddhaman 713104, WB, India – sequence: 2 givenname: Ali Akbar surname: Shaikh fullname: Shaikh, Ali Akbar email: aliashaikh@math.buruniv.ac.in organization: Department of Mathematics, The University of Burdwan, Purba Barddhaman 713104, WB, India – sequence: 3 givenname: Sanat Kumar surname: Mahato fullname: Mahato, Sanat Kumar email: sanatkmahato@gmail.com organization: Department of Mathematics, The University of Burdwan, Purba Barddhaman 713104, WB, India – sequence: 4 givenname: Asoke Kumar surname: Bhunia fullname: Bhunia, Asoke Kumar email: akbhunia@math.buruniv.ac.in organization: Department of Mathematics, The University of Burdwan, Purba Barddhaman 713104, WB, India
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Snippet	•Transformation of ordinary differential equation to optimization problem.•Hybrid algorithm based on cuckoo search & advanced particle swarm... This article solves first and second order differential equations with initial and/or boundary conditions by transforming these equations into...
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SubjectTerms	Adaptive algorithms AGQPSO Algorithms Boundary conditions Boundary value problems Cuckoo search algorithm Differential equations Hybrid algorithm Mathematical analysis Optimization Ordinary differential equations Particle swarm optimization Search algorithms
Title	Applications of new hybrid algorithm based on advanced cuckoo search and adaptive Gaussian quantum behaved particle swarm optimization in solving ordinary differential equations
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