An Application of Infinite Programming on Desirability Functions
When assessing the quality of a system or product, it is necessary to take all responses into account and optimize them in a concurrent manner to find the factor levels that satisfy the overall system, process, or product properties to solve the robust design problem. This problem can be solved as a...
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| Format: | Article |
| Language: | English |
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Mahmut Akyigit
2023-12-01
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| Series: | Journal of Mathematical Sciences and Modelling |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2730569 |
| _version_ | 1827381405796007936 |
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| author | Başak Öztürk |
| author_facet | Başak Öztürk |
| author_sort | Başak Öztürk |
| collection | DOAJ |
| description | When assessing the quality of a system or product, it is necessary to take all responses into account and optimize them in a concurrent manner to find the factor levels that satisfy the overall system, process, or product properties to solve the robust design problem. This problem can be solved as a multi-response optimization problem. There are many methods suggested to solve this problem based on different disciplines like multi-objective optimization. In this study, we improve the theory of nondifferentiable desirability functions' optimization for which the so-called gradient-based methods are not useful. In this study, we propose an infinite programming approach for nondifferentiable desirability functions including more than one nondifferentiable point. We employed DNLP model of GAMS/BARON which is a nondifferentiable solver, however, the solution of more than one nondifferentiable point problem is resulted as infeasible. We also tested MATLAB/NOMAD which is a derivative-free solver for MINLP problems, however, MATLAB/NOMAD also did not succeed and could not solve this nondifferentiable problem. Lastly, we use a genetic algorithm that is implemented under MATLAB and it also cannot find a feasible solution. We use an example that is solved by different desirability functions approaches before and show that the desirability functions approach with more than one nondifferentiable point is a good alternative to the ones in the literature. We present the conclusion and future studies at the end of the paper. |
| first_indexed | 2024-03-08T13:54:47Z |
| format | Article |
| id | doaj.art-01fb52a3cfc04173a2fe1d6938c3f268 |
| institution | Directory Open Access Journal |
| issn | 2636-8692 |
| language | English |
| last_indexed | 2024-03-08T13:54:47Z |
| publishDate | 2023-12-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj.art-01fb52a3cfc04173a2fe1d6938c3f2682024-01-15T15:30:12ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922023-12-01639710410.33187/jmsm.11944871408An Application of Infinite Programming on Desirability FunctionsBaşak Öztürk0orta doğu teknik üniversitesi, endüstri müh.When assessing the quality of a system or product, it is necessary to take all responses into account and optimize them in a concurrent manner to find the factor levels that satisfy the overall system, process, or product properties to solve the robust design problem. This problem can be solved as a multi-response optimization problem. There are many methods suggested to solve this problem based on different disciplines like multi-objective optimization. In this study, we improve the theory of nondifferentiable desirability functions' optimization for which the so-called gradient-based methods are not useful. In this study, we propose an infinite programming approach for nondifferentiable desirability functions including more than one nondifferentiable point. We employed DNLP model of GAMS/BARON which is a nondifferentiable solver, however, the solution of more than one nondifferentiable point problem is resulted as infeasible. We also tested MATLAB/NOMAD which is a derivative-free solver for MINLP problems, however, MATLAB/NOMAD also did not succeed and could not solve this nondifferentiable problem. Lastly, we use a genetic algorithm that is implemented under MATLAB and it also cannot find a feasible solution. We use an example that is solved by different desirability functions approaches before and show that the desirability functions approach with more than one nondifferentiable point is a good alternative to the ones in the literature. We present the conclusion and future studies at the end of the paper.https://dergipark.org.tr/tr/download/article-file/2730569desirability functionsmatlabmulti-response optimization |
| spellingShingle | Başak Öztürk An Application of Infinite Programming on Desirability Functions Journal of Mathematical Sciences and Modelling desirability functions matlab multi-response optimization |
| title | An Application of Infinite Programming on Desirability Functions |
| title_full | An Application of Infinite Programming on Desirability Functions |
| title_fullStr | An Application of Infinite Programming on Desirability Functions |
| title_full_unstemmed | An Application of Infinite Programming on Desirability Functions |
| title_short | An Application of Infinite Programming on Desirability Functions |
| title_sort | application of infinite programming on desirability functions |
| topic | desirability functions matlab multi-response optimization |
| url | https://dergipark.org.tr/tr/download/article-file/2730569 |
| work_keys_str_mv | AT basakozturk anapplicationofinfiniteprogrammingondesirabilityfunctions AT basakozturk applicationofinfiniteprogrammingondesirabilityfunctions |