Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions
This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel tec...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2920 |
| _version_ | 1797591303814381568 |
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| author | Linas Stripinis Remigijus Paulavičius |
| author_facet | Linas Stripinis Remigijus Paulavičius |
| author_sort | Linas Stripinis |
| collection | DOAJ |
| description | This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential optimal hyper-rectangles. A key contribution lies in applying a new mapping technique to eliminate the infeasible region efficiently. This allows calculations to be performed only within the feasible region defined by linear constraints. We perform extensive tests using a diverse set of benchmark problems to evaluate the effectiveness and performance of the proposed algorithm compared to existing DIRECT solvers. Statistical analyses using Friedman and Wilcoxon tests demonstrate the superiority of a new algorithm in solving such problems. |
| first_indexed | 2024-03-11T01:35:30Z |
| format | Article |
| id | doaj.art-b7a18968e989408d8421c9eaf6394da6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:35:30Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b7a18968e989408d8421c9eaf6394da62023-11-18T17:03:15ZengMDPI AGMathematics2227-73902023-06-011113292010.3390/math11132920Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz FunctionsLinas Stripinis0Remigijus Paulavičius1Institute of Data Science and Digital Technologies, Vilnius University, Akademijos 4, LT-08663 Vilnius, LithuaniaInstitute of Data Science and Digital Technologies, Vilnius University, Akademijos 4, LT-08663 Vilnius, LithuaniaThis paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential optimal hyper-rectangles. A key contribution lies in applying a new mapping technique to eliminate the infeasible region efficiently. This allows calculations to be performed only within the feasible region defined by linear constraints. We perform extensive tests using a diverse set of benchmark problems to evaluate the effectiveness and performance of the proposed algorithm compared to existing DIRECT solvers. Statistical analyses using Friedman and Wilcoxon tests demonstrate the superiority of a new algorithm in solving such problems.https://www.mdpi.com/2227-7390/11/13/2920global optimizationderivative-free optimizationpartitioningDIRECT-type algorithmslinear constraintsconstraint handling techniques |
| spellingShingle | Linas Stripinis Remigijus Paulavičius Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions Mathematics global optimization derivative-free optimization partitioning DIRECT-type algorithms linear constraints constraint handling techniques |
| title | Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions |
| title_full | Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions |
| title_fullStr | Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions |
| title_full_unstemmed | Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions |
| title_short | Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions |
| title_sort | novel algorithm for linearly constrained derivative free global optimization of lipschitz functions |
| topic | global optimization derivative-free optimization partitioning DIRECT-type algorithms linear constraints constraint handling techniques |
| url | https://www.mdpi.com/2227-7390/11/13/2920 |
| work_keys_str_mv | AT linasstripinis novelalgorithmforlinearlyconstrainedderivativefreeglobaloptimizationoflipschitzfunctions AT remigijuspaulavicius novelalgorithmforlinearlyconstrainedderivativefreeglobaloptimizationoflipschitzfunctions |