Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape Optimization
Nowadays, product development times are constantly decreasing, while the requirements for the products themselves increased significantly in the last decade. Hence, manufacturers use Computer-Aided Design (CAD) and Finite-Element (FE) Methods to develop better products in shorter times. Shape optimi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/15/2/46 |
| _version_ | 1797483559895695360 |
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| author | Yannis Werner Tim van Hout Vijey Subramani Raja Gopalan Thomas Vietor |
| author_facet | Yannis Werner Tim van Hout Vijey Subramani Raja Gopalan Thomas Vietor |
| author_sort | Yannis Werner |
| collection | DOAJ |
| description | Nowadays, product development times are constantly decreasing, while the requirements for the products themselves increased significantly in the last decade. Hence, manufacturers use Computer-Aided Design (CAD) and Finite-Element (FE) Methods to develop better products in shorter times. Shape optimization offers great potential to improve many high-fidelity, numerical problems such as the crash performance of cars. Still, the proper selection of optimization algorithms provides a great potential to increase the speed of the optimization time. This article reviews the optimization performance of two different algorithms and frameworks for the structural behavior of a b-pillar. A b-pillar is the structural component between a car’s front and rear door, loaded under static and crash requirements. Furthermore, the validation of the algorithm includes a feasibility constraint. Recently, an optimization routine was implemented and validated for a Non-dominated Sorting Genetic Algorithm (NSGA-II) implementation. Different multi-objective optimization algorithms are reviewed and methodically ranked in a comparative study by given criteria. In this case, the Gap Optimized Multi-Objective Optimization using Response Surfaces (GOMORS) framework is chosen and implemented into the existing Institut für Konstruktionstechnik Optimizes Shapes (IKOS) framework. Specifically, the article compares the NSGA-II and GOMORS directly for a linear, non-linear, and feasibility optimization scenario. The results show that the GOMORS outperforms the NSGA-II vastly regarding the number of function calls and Pareto-efficient results without the feasibility constraint. The problem is reformulated to an unconstrained, three-objective optimization problem to analyze the influence of the constraint. The constrained and unconstrained approaches show equal performance for the given scenarios. Accordingly, the authors provide a clear recommendation towards the surrogate-based GOMORS for costly and multi-objective evaluations. Furthermore, the algorithm can handle the feasibility constraint properly when formulated as an objective function and as a constraint. |
| first_indexed | 2024-03-09T22:48:45Z |
| format | Article |
| id | doaj.art-c9a4dce8c4f742f486451af480a97a9b |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-09T22:48:45Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-c9a4dce8c4f742f486451af480a97a9b2023-11-23T18:24:09ZengMDPI AGAlgorithms1999-48932022-01-011524610.3390/a15020046Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape OptimizationYannis Werner0Tim van Hout1Vijey Subramani Raja Gopalan2Thomas Vietor3Institute for Engineering Design, Technische Universität Braunschweig, Hermann-Blenk-Str. 42, 38108 Brunswick, GermanyTechnische Universität Braunschweig, 38106 Brunswick, GermanyTechnische Universität Braunschweig, 38106 Brunswick, GermanyInstitute for Engineering Design, Technische Universität Braunschweig, Hermann-Blenk-Str. 42, 38108 Brunswick, GermanyNowadays, product development times are constantly decreasing, while the requirements for the products themselves increased significantly in the last decade. Hence, manufacturers use Computer-Aided Design (CAD) and Finite-Element (FE) Methods to develop better products in shorter times. Shape optimization offers great potential to improve many high-fidelity, numerical problems such as the crash performance of cars. Still, the proper selection of optimization algorithms provides a great potential to increase the speed of the optimization time. This article reviews the optimization performance of two different algorithms and frameworks for the structural behavior of a b-pillar. A b-pillar is the structural component between a car’s front and rear door, loaded under static and crash requirements. Furthermore, the validation of the algorithm includes a feasibility constraint. Recently, an optimization routine was implemented and validated for a Non-dominated Sorting Genetic Algorithm (NSGA-II) implementation. Different multi-objective optimization algorithms are reviewed and methodically ranked in a comparative study by given criteria. In this case, the Gap Optimized Multi-Objective Optimization using Response Surfaces (GOMORS) framework is chosen and implemented into the existing Institut für Konstruktionstechnik Optimizes Shapes (IKOS) framework. Specifically, the article compares the NSGA-II and GOMORS directly for a linear, non-linear, and feasibility optimization scenario. The results show that the GOMORS outperforms the NSGA-II vastly regarding the number of function calls and Pareto-efficient results without the feasibility constraint. The problem is reformulated to an unconstrained, three-objective optimization problem to analyze the influence of the constraint. The constrained and unconstrained approaches show equal performance for the given scenarios. Accordingly, the authors provide a clear recommendation towards the surrogate-based GOMORS for costly and multi-objective evaluations. Furthermore, the algorithm can handle the feasibility constraint properly when formulated as an objective function and as a constraint.https://www.mdpi.com/1999-4893/15/2/46multi-objective optimizationNSGA-IIGOMORScrash optimizationstructural optimizationshape optimization |
| spellingShingle | Yannis Werner Tim van Hout Vijey Subramani Raja Gopalan Thomas Vietor Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape Optimization Algorithms multi-objective optimization NSGA-II GOMORS crash optimization structural optimization shape optimization |
| title | Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape Optimization |
| title_full | Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape Optimization |
| title_fullStr | Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape Optimization |
| title_full_unstemmed | Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape Optimization |
| title_short | Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape Optimization |
| title_sort | test and validation of the surrogate based multi objective gomors algorithm against the nsga ii algorithm in structural shape optimization |
| topic | multi-objective optimization NSGA-II GOMORS crash optimization structural optimization shape optimization |
| url | https://www.mdpi.com/1999-4893/15/2/46 |
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