Solution of Nonlinear Systems of Equations via Metaheuristics
A framework devoted to the solution of nonlinear systems of equations using grey wolf optimization algorithm (GWO) and a multi-objective particle swarm optimization algorithm (MOPSO) is presented in this work. Due to several numerical issues and very high computational complexity, it is hard to find...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Ram Arti Publishers
2019-10-01
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| Series: | International Journal of Mathematical, Engineering and Management Sciences |
| Subjects: | |
| Online Access: | https://www.ijmems.in/assets//88-IJMEMS-19-30-Vol.%204,%20No.%205,%201108%E2%80%931126,%202019.pdf |
| _version_ | 1819049566144561152 |
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| author | Sangeeta Pant Anuj Kumar Mangey Ram |
| author_facet | Sangeeta Pant Anuj Kumar Mangey Ram |
| author_sort | Sangeeta Pant |
| collection | DOAJ |
| description | A framework devoted to the solution of nonlinear systems of equations using grey wolf optimization algorithm (GWO) and a multi-objective particle swarm optimization algorithm (MOPSO) is presented in this work. Due to several numerical issues and very high computational complexity, it is hard to find the solution of such a complex nonlinear system of equations. It then explains that the problem of solution to a system of nonlinear equations can be simplified by viewing it as an optimization problem and solutions can be obtained by applying a nature inspired optimization technique. The results achieved are compared with classical as well as new techniques established in the literature. The proposed framework also seems to be very effective for the problems of system of non-linear equations arising in the various fields of science. For this purpose, the problem of neurophysiology application and the problem of combustion of hydrocarbons are considered for testing. Empirical results show that the presented framework is bright to deal with the high dimensional equations system. |
| first_indexed | 2024-12-21T11:34:11Z |
| format | Article |
| id | doaj.art-855a07ae54aa43d5a3dd84fc666dc4b9 |
| institution | Directory Open Access Journal |
| issn | 2455-7749 2455-7749 |
| language | English |
| last_indexed | 2024-12-21T11:34:11Z |
| publishDate | 2019-10-01 |
| publisher | Ram Arti Publishers |
| record_format | Article |
| series | International Journal of Mathematical, Engineering and Management Sciences |
| spelling | doaj.art-855a07ae54aa43d5a3dd84fc666dc4b92022-12-21T19:05:29ZengRam Arti PublishersInternational Journal of Mathematical, Engineering and Management Sciences2455-77492455-77492019-10-01451108112610.33889/IJMEMS.2019.4.5-088Solution of Nonlinear Systems of Equations via MetaheuristicsSangeeta Pant0Anuj Kumar1Mangey Ram2Department of Mathematics, University of Petroleum & Energy Studies, Dehradun, IndiaDepartment of Mathematics, University of Petroleum & Energy Studies, Dehradun, IndiaDepartment of Mathematics; Computer Science & Engineering, Graphic Era Deemed to be University, Dehradun, IndiaA framework devoted to the solution of nonlinear systems of equations using grey wolf optimization algorithm (GWO) and a multi-objective particle swarm optimization algorithm (MOPSO) is presented in this work. Due to several numerical issues and very high computational complexity, it is hard to find the solution of such a complex nonlinear system of equations. It then explains that the problem of solution to a system of nonlinear equations can be simplified by viewing it as an optimization problem and solutions can be obtained by applying a nature inspired optimization technique. The results achieved are compared with classical as well as new techniques established in the literature. The proposed framework also seems to be very effective for the problems of system of non-linear equations arising in the various fields of science. For this purpose, the problem of neurophysiology application and the problem of combustion of hydrocarbons are considered for testing. Empirical results show that the presented framework is bright to deal with the high dimensional equations system.https://www.ijmems.in/assets//88-IJMEMS-19-30-Vol.%204,%20No.%205,%201108%E2%80%931126,%202019.pdfOptimization; MetaheuristicGrey wolf optimizer algorithm (GWO)Particle swarm optimization (PSO)Nonlinear equation system |
| spellingShingle | Sangeeta Pant Anuj Kumar Mangey Ram Solution of Nonlinear Systems of Equations via Metaheuristics International Journal of Mathematical, Engineering and Management Sciences Optimization; Metaheuristic Grey wolf optimizer algorithm (GWO) Particle swarm optimization (PSO) Nonlinear equation system |
| title | Solution of Nonlinear Systems of Equations via Metaheuristics |
| title_full | Solution of Nonlinear Systems of Equations via Metaheuristics |
| title_fullStr | Solution of Nonlinear Systems of Equations via Metaheuristics |
| title_full_unstemmed | Solution of Nonlinear Systems of Equations via Metaheuristics |
| title_short | Solution of Nonlinear Systems of Equations via Metaheuristics |
| title_sort | solution of nonlinear systems of equations via metaheuristics |
| topic | Optimization; Metaheuristic Grey wolf optimizer algorithm (GWO) Particle swarm optimization (PSO) Nonlinear equation system |
| url | https://www.ijmems.in/assets//88-IJMEMS-19-30-Vol.%204,%20No.%205,%201108%E2%80%931126,%202019.pdf |
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