ABSTRACT
The main goal in structural Topology Optimization is to find an optimal distribution of material within a defined design domain, under specified boundary conditions. This task is frequently solved with gradient-based methods, but for some problems, e.g. in the domain of crash Topology Optimization, analytical sensitivity information is not available. The recent Evolutionary Level Set Method (EA-LSM) uses Evolutionary Strategies and a representation based on geometric Level Set Functions to solve such problems. However, computational costs associated with Evolutionary Algorithms are relatively high and grow significantly with rising dimensionality of the optimization problem. In this paper, we propose an improved version of EA-LSM, exploiting an adaptive representation, where the number of structural components increases during the optimization. We employ a learning-based approach, where a pre-trained neural network model predicts favorable topological changes, based on the structural state of the design. The proposed algorithm converges quickly at the beginning, determining good designs in low-dimensional search spaces, and the representation is gradually extended by increasing structural complexity. The approach is evaluated on a standard minimum compliance design problem and its superiority with respect to a random adaptive method is demonstrated.
- Nikola Aulig. 2017. Generic topology optimization based on local state features. Fortschritt-Berichte VDI. Reihe 20: Rechnerunterstützte Verfahren, Vol. 468. VDI Verlag, Düsseldorf.Google Scholar
- Thomas Bäck. 1996. Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford, UK. Google ScholarDigital Library
- Martin Philip Bendsee and Ole Sigmund. 2004. Topology Optimization. Springer Berlin Heidelberg, Germany.Google Scholar
- Mariusz Bujny, Nikola Aulig, Markus Olhofer, and Fabian Duddeck. 2016. Evolutionary Crashworthiness Topology Optimization of Thin-Walled Structures. ASMO UK, Munich, Germany.Google Scholar
- Mariusz Bujny, Nikola Aulig, Markus Olhofer, and Fabian Duddeck. 2016. Evolutionary Level Set Method for Crashworthiness Topology Optimization. ECCOMAS, Crete Island, Greece.Google Scholar
- Mariusz Bujny, Nikola Aulig, Markus Olhofer, and Fabian Duddeck. 2016. Hybrid Evolutionary Approach for Level Set Topology Optimization. IEEE, Vancouver, Canada.Google Scholar
- Mariusz Bujny, Nikola Aulig, Markus Olhofer, and Fabian Duddeck. 2017. Identification of optimal topologies for crashworthiness with the evolutionary level set method. International Journal of Crashworthiness (2017).Google Scholar
- Fabian Duddeck. 2008. Multidisciplinary optimization of car bodies. Structural and Multidisciplinary Optimization 35, 4 (2008), 375--389.Google ScholarCross Ref
- Alexander Forrester, Andras Sobester, and Andy Keane. 2008. Engineering Design via Surrogate Modelling: A Practical Guide (1 ed.). Wiley, Chichester, West Sussex, England; Hoboken, NJ.Google Scholar
- Xu Guo, Weisheng Zhang, and Wenliang Zhong. 2014. Doing topology optimization explicitly and geometrically: a new moving morphable components based framework. In Frontiers in Applied Mechanics. Imperial College Press, London, UK, 31--32.Google Scholar
- Takao Hagishita and Makoto Ohsaki. 2009. Topology optimization of trusses by growing ground structure method. Structural and Multidisciplinary Optimization 37, 4 (2009), 377--393.Google ScholarCross Ref
- Karim Hamza, Mohamed Aly, and Hesham Hegazi. 2013. A Kriging-Interpolated Level-Set Approach for Structural Topology Optimization. Journal of Mechanical Design 136, 1 (2013).Google ScholarCross Ref
- Nikolaus Hansen and Andreas Ostermeier. 2001. Completely Derandomized Self-Adaptation in Evolution Strategies. Evolutionary Computation 9, 2 (2001), 159--195. Google ScholarDigital Library
- Markus Olhofer, Yaochu Jin, and Bernhard Sendhoff. 2001. Adaptive encoding for aerodynamic shape optimization using evolution strategies. In Proceedings of the 2001 Congress on Evolutionary Computation, 2001, Vol. 1. 576--583 vol. 1.Google ScholarCross Ref
- Christopher Ortmann and Axel Schumacher. 2013. Graph and heuristic based topology optimization of crash loaded structures. Structural and Multidisciplinary Optimization 47, 6 (2013), 839--854. Google ScholarDigital Library
- Elena Raponi, Mariusz Bujny, Markus Olhofer, Nikola Aulig, Simonetta Boria, and Fabian Duddeck. 2017. Kriging-guided level set method for crash topology optimization. GACM, Stuttgart, Germany.Google Scholar
- Hans-Paul Schwefel. 1987. Collective phenomena in evolutionary systems. Universität Dortmund. Abteilung Informatik, Germany.Google Scholar
- Kenneth Owen Stanley and Risto Miikkulainen. 2002. Evolving Neural Networks Through Augmenting Topologies. Evolutionary Computation 10, 2 (2002), 99--127. Google ScholarDigital Library
- Duo Zeng and Fabian Duddeck. 2017. Improved hybrid cellular automata for crashworthiness optimization of thin-walled structures. Structural and Multidisciplinary Optimization 56, 1 (2017), 101--115. Google ScholarDigital Library
- Learning-based topology variation in evolutionary level set topology optimization
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