A consideration on robust design optimization problem through formulation of multiobjective optimization
The robust design optimization (RDO) problem is generally formulated as a weighted sum of the nominal objective function and the robust term. In the RDO problem, a deterministic optimum design is regarded as one of the local optima. However, this property is not well understood. Even though robust o...
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| Format: | Article |
| Language: | English |
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The Japan Society of Mechanical Engineers
2018-06-01
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| Series: | Journal of Advanced Mechanical Design, Systems, and Manufacturing |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/jamdsm/12/2/12_2018jamdsm0058/_pdf/-char/en |
| _version_ | 1828782179558096896 |
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| author | Makoto ITO Nozomu KOGISO Taku HASEGAWA |
| author_facet | Makoto ITO Nozomu KOGISO Taku HASEGAWA |
| author_sort | Makoto ITO |
| collection | DOAJ |
| description | The robust design optimization (RDO) problem is generally formulated as a weighted sum of the nominal objective function and the robust term. In the RDO problem, a deterministic optimum design is regarded as one of the local optima. However, this property is not well understood. Even though robust optimum designs are known to be significantly different from deterministic designs in certain cases, they are nearly identical in other cases, for reasons that are not intuitively understandable. This is due to the fact that the trade-off relationship between deterministic and robust optimum designs and the effects of uncertainty on the latter are not evaluated by the weighted sum approach. In this study, the properties of robust optimum designs are investigated by formulating the RDO problem as a multiobjective optimization problem, where the nominal value of the performance function and the worst value in the uncertainty region are adopted as the objective functions. The problem considered in this study is limited in that for simplicity, only the design variable is assumed to have uncertainty. That is, the mean value of the random variable is regarded as the design variable. The Pareto solutions are obtained by an evolutionary algorithm whereby the worst design in each individual during the evolutionary process is selected by a sampling method so that the approximation error may be avoided. Through simple numerical examples under several distribution types for random variables, the trade-off relationship between deterministic and robust optimum designs and the effects of uncertainty on the latter are investigated. |
| first_indexed | 2024-12-11T17:45:36Z |
| format | Article |
| id | doaj.art-6dbe29264f1c4586b9c60b3c431cacb6 |
| institution | Directory Open Access Journal |
| issn | 1881-3054 |
| language | English |
| last_indexed | 2024-12-11T17:45:36Z |
| publishDate | 2018-06-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Journal of Advanced Mechanical Design, Systems, and Manufacturing |
| spelling | doaj.art-6dbe29264f1c4586b9c60b3c431cacb62022-12-22T00:56:24ZengThe Japan Society of Mechanical EngineersJournal of Advanced Mechanical Design, Systems, and Manufacturing1881-30542018-06-01122JAMDSM0058JAMDSM005810.1299/jamdsm.2018jamdsm0058jamdsmA consideration on robust design optimization problem through formulation of multiobjective optimizationMakoto ITO0Nozomu KOGISO1Taku HASEGAWA2Department of Aerospace Engineering, Osaka Prefecture UniversityDepartment of Aerospace Engineering, Osaka Prefecture UniversityDepartment of Computer Science and Intelligent System, Osaka Prefecture UniversityThe robust design optimization (RDO) problem is generally formulated as a weighted sum of the nominal objective function and the robust term. In the RDO problem, a deterministic optimum design is regarded as one of the local optima. However, this property is not well understood. Even though robust optimum designs are known to be significantly different from deterministic designs in certain cases, they are nearly identical in other cases, for reasons that are not intuitively understandable. This is due to the fact that the trade-off relationship between deterministic and robust optimum designs and the effects of uncertainty on the latter are not evaluated by the weighted sum approach. In this study, the properties of robust optimum designs are investigated by formulating the RDO problem as a multiobjective optimization problem, where the nominal value of the performance function and the worst value in the uncertainty region are adopted as the objective functions. The problem considered in this study is limited in that for simplicity, only the design variable is assumed to have uncertainty. That is, the mean value of the random variable is regarded as the design variable. The Pareto solutions are obtained by an evolutionary algorithm whereby the worst design in each individual during the evolutionary process is selected by a sampling method so that the approximation error may be avoided. Through simple numerical examples under several distribution types for random variables, the trade-off relationship between deterministic and robust optimum designs and the effects of uncertainty on the latter are investigated.https://www.jstage.jst.go.jp/article/jamdsm/12/2/12_2018jamdsm0058/_pdf/-char/enrobust designmultiobjective optimizationuncertaintypareto settrade-off |
| spellingShingle | Makoto ITO Nozomu KOGISO Taku HASEGAWA A consideration on robust design optimization problem through formulation of multiobjective optimization Journal of Advanced Mechanical Design, Systems, and Manufacturing robust design multiobjective optimization uncertainty pareto set trade-off |
| title | A consideration on robust design optimization problem through formulation of multiobjective optimization |
| title_full | A consideration on robust design optimization problem through formulation of multiobjective optimization |
| title_fullStr | A consideration on robust design optimization problem through formulation of multiobjective optimization |
| title_full_unstemmed | A consideration on robust design optimization problem through formulation of multiobjective optimization |
| title_short | A consideration on robust design optimization problem through formulation of multiobjective optimization |
| title_sort | consideration on robust design optimization problem through formulation of multiobjective optimization |
| topic | robust design multiobjective optimization uncertainty pareto set trade-off |
| url | https://www.jstage.jst.go.jp/article/jamdsm/12/2/12_2018jamdsm0058/_pdf/-char/en |
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