Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems
Many problems in life are composed of conflicting and influencing multiple objectives, and people often encounter the optimization problem of simultaneously optimizing multiple objectives in each area, which is called multiobjective optimization problem. Therefore, solving such problems has importan...
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| Format: | Article |
| Language: | English English |
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UniSE Press
2024
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| Online Access: | https://eprints.ums.edu.my/id/eprint/40753/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/40753/2/FULL%20TEXT.pdf |
| _version_ | 1811136509537943552 |
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| author | Peng Cheng Jumat Sulaiman Khadizah Ghazali |
| author_facet | Peng Cheng Jumat Sulaiman Khadizah Ghazali |
| author_sort | Peng Cheng |
| collection | UMS |
| description | Many problems in life are composed of conflicting and influencing multiple objectives, and people often encounter the optimization problem of simultaneously optimizing multiple objectives in each area, which is called multiobjective optimization problem. Therefore, solving such problems has important scientific research value and practical significance. This paper proposes a Newton Gauss-Seidel iteration method for solving multi-objective constrained optimization problems by constructing Newton directions and introducing Gauss-Seidel (GS) iterative method for solving linear equations. The solution of this combination between Newton, Gauss-seidel and Lagrange multiplier method involves two stages: objective function and constraint condition processing stage. In the first stage, the original multi-objective function is scalarized, and only the decision-maker needs to give each objective function a weight, by transforming it into a single objective constrained optimization problem. Then the Lagrange multiplier method was used to transform the constrained optimization problem into an unconstrained optimization problem. The second stage is to use the NewtonGauss-Seidel (NGS) iterative method to solve the transformed constrained optimization problem. Finally, numerical experiments showed that our proposed algorithm can achieve good results. |
| first_indexed | 2024-09-24T00:51:37Z |
| format | Article |
| id | ums.eprints-40753 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-09-24T00:51:37Z |
| publishDate | 2024 |
| publisher | UniSE Press |
| record_format | dspace |
| spelling | ums.eprints-407532024-08-21T08:37:02Z https://eprints.ums.edu.my/id/eprint/40753/ Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems Peng Cheng Jumat Sulaiman Khadizah Ghazali QA1-43 General QA299.6-433 Analysis Many problems in life are composed of conflicting and influencing multiple objectives, and people often encounter the optimization problem of simultaneously optimizing multiple objectives in each area, which is called multiobjective optimization problem. Therefore, solving such problems has important scientific research value and practical significance. This paper proposes a Newton Gauss-Seidel iteration method for solving multi-objective constrained optimization problems by constructing Newton directions and introducing Gauss-Seidel (GS) iterative method for solving linear equations. The solution of this combination between Newton, Gauss-seidel and Lagrange multiplier method involves two stages: objective function and constraint condition processing stage. In the first stage, the original multi-objective function is scalarized, and only the decision-maker needs to give each objective function a weight, by transforming it into a single objective constrained optimization problem. Then the Lagrange multiplier method was used to transform the constrained optimization problem into an unconstrained optimization problem. The second stage is to use the NewtonGauss-Seidel (NGS) iterative method to solve the transformed constrained optimization problem. Finally, numerical experiments showed that our proposed algorithm can achieve good results. UniSE Press 2024 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/40753/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/40753/2/FULL%20TEXT.pdf Peng Cheng and Jumat Sulaiman and Khadizah Ghazali (2024) Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems. Transactions on Science and Technology, 11. pp. 43-50. |
| spellingShingle | QA1-43 General QA299.6-433 Analysis Peng Cheng Jumat Sulaiman Khadizah Ghazali Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems |
| title | Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems |
| title_full | Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems |
| title_fullStr | Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems |
| title_full_unstemmed | Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems |
| title_short | Application of Newton-Gauss-Seidel method for solving multi-objective constrained optimization problems |
| title_sort | application of newton gauss seidel method for solving multi objective constrained optimization problems |
| topic | QA1-43 General QA299.6-433 Analysis |
| url | https://eprints.ums.edu.my/id/eprint/40753/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/40753/2/FULL%20TEXT.pdf |
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