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1 Author s Accepted Manuscript Comments on Evolutionary and GPU computing for topology optimization of structures David Guirguis PII: DOI: Reference: S (16) SWEVO248 To appear in: Swarm and Evolutionary Computation Cite this article as: David Guirguis, Comments on Evolutionary and GPU computing for topology optimization of structures, Swarm and Evolutionary Computation, This is a PDF file of an unedited manuscript that has been accepted fo publication. As a service to our customers we are providing this early version o the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain

2 Comments on Evolutionary and GPU computing for topology optimization of structures David Guirguis Department of Mechanical & Industrial Engineering, University of Toronto, ON M5S 3G8, Canada. This short communication is a commentary on the recent published paper Evolutionary 1 and GPU computing for topology optimization of structures [1]. In this paper, the aim of the study is identified as addressing the limitations of generating infeasible structures and expensive computational cost. However, the old truss representation is used and then projected into a uniform distribution grid, ignoring the fact that this representation is only useful in case of truss-like structures. The variation in thickness of the structure s members is required to be presented. This issue is discussed comprehensively by Sigmund et al. in [2]. Additionally, the solved examples are simple, and the obtained results are sub-optimal solutions. In contrary, this limitation has already been addressed by Wang et al. [3] in 2006, proposing connectivity handling approaches to be used in continuum domain formulation. Furthermore, more advanced methods in the literature, were ignored by the referred paper. For instance, De Ruiter and Van Keulen [4] proposed a topology description function approach as an attempt to reduce the number of decision variables in the 0-1 representation. Toward the same aim, Bureerat and Limtragool [5] developed an approximate density distribution approach. Guest et al. [6] proposed an implicit formulation using a Heaviside projection method. Hamza et al. [7] proposed a kriginginterpolated level-set method; Guirguis et al. [8] demonstrated its further capability to capture complex topologies. Following this work, a small number of applications appeared, e.g., composite molding processes [9], fluid problems [10], and welded structures [11]. Very recently, a derivative-free level-set method [12] has been developed and demonstrated by a variety of numerical experiments how such a method can avoid the main limitations of the nongradient methods [13] (i.e., methods that depend solely on the objective value; no gradients or sensitivities are required). Moreover, the boundaries of the structure can be smooth and not directly dependent on the decision variables as illustrated in Fig. 1 [12]. Some topologies that are obtained by the Guirguis level-set method [12], in comparison with the inferior solutions of the two simple examples that are solved in the referred article [1], are shown in Fig. 2. Regarding the issue of computational cost, the usage of the graphical processing units to accelerate the computation is well known, and previously applied to topology optimization, e.g., [14 17]. From the perspective of 1 Evolutionary refers to the optimization methods that are inspired by the biological evolution theory. This word may confuse some readers, as the sensitivity-based topology optimization approaches are known as Evolutionary Structural Optimization (ESO) [19,20].

3 soft computing, developing implicit continuum domain formulations that are adequate for continuum structures, in addition to efficient optimization techniques are needed to reduce the complexity of the optimization problem. In conclusion, an adequate literature survey is mandatory to avoid constructing misleading knowledge gaps, confusion in the literature and wasting research efforts. Proposed approaches should be validated with exhaustive numerical experiments and the advantages of usage should be demonstrated. Finally, it worth noting that, this short communication is not the first critique of published papers on this research topic. Two forum articles, that were published by the ISSMO (International Society of Structural and Multidisciplinary Optimization), can be found in [13,18]. However, an attention in the community of the soft computation is needed as the most relevant community that could advance the research on the non-gradient topology optimization. a b Level-set function Smooth intersecting curves Fig. 1 A complex obtained topology by the Guirguis level-set method [12]: (a) the level-set function and the intersecting curves that could represent the smooth boundaries of the structure; (b) the obtained topology represented by the 2

4 a b Fig. 2 (a) Some of the obtained quasi-optimal topologies by the Guirguis level-set method [12], in comparison with (b) the sub-optimal solutions by the proposed approach in the referred article [1]. Note: the drawings are not up to scale. 3

5 References [1] L. Ram, D. Sharma, Evolutionary and GPU computing for topology optimization of structures, Swarm and Evolutionary Computation. (2016). doi: /j.swevo [2] O. Sigmund, N. Aage, E. Andreassen, On the (non-)optimality of Michell structures, Struct Multidiscip O. 54 (2016) doi: /s [3] S.Y. Wang, K. Tai, M.Y. Wang, An enhanced genetic algorithm for structural topology optimization, Int J Numer Methods Eng. 65 (2006) doi: /nme [4] M.J. de Ruiter, F. van Keulen, Topology optimization using a topology description function, Struct Multidiscip O. 26 (2004) doi: /s [5] S. Bureerat, J. Limtragool, Performance enhancement of evolutionary search for structural topology optimisation, Finite Elem Anal Des. 42 (2006) doi: /j.finel [6] J.K. Guest, L.C. Smith Genut, Reducing dimensionality in topology optimization using adaptive design variable fields, Int J Numer Methods Eng. (2009) n/a n/a. doi: /nme [7] K. Hamza, M. Aly, H. Hegazi, An Explicit Level-Set Approach for Structural Topology Optimization, in: Volume 3A: 39th Design Automation Conference, ASME, 2013: p. V03AT03A001. doi: /detc [8] D. Guirguis, M. Aly, K. Hamza, H. Hegazi, Image Matching Assessment of Attainable Topology via Kriging- Interpolated Level-Sets, in: Volume 2A: 40th Design Automation Conference, ASME, 2014: p. V02AT03A002. doi: /detc [9] Y. Zhou, K. Saitou, Data-Driven Predictive Model of Resin Filling Time of Composite Molding Process, in: Volume 4: 20th Design for Manufacturing and the Life Cycle Conference; 9th International Conference on Micro- and Nanosystems, ASME, 2015: p. V004T05A014. doi: /detc [10] M. Yoshimura, K. Shimoyama, T. Misaka, S. Obayashi, Topology optimization of fluid problems using genetic algorithm assisted by the Kriging model, Int J Numer Methods Eng. (2016). doi: /nme [11] D. Guirguis, K. Hamza, M. Aly, H. Hegazi, K. Saitou, Multi-objective topology optimization of multi-component continuum structures via a Kriging-interpolated level set approach, Struct Multidiscip O. 51 (2015) doi: /s [12] D. Guirguis, M.F. Aly, A derivative-free level-set method for topology optimization, Finite Elem Anal Des. 120 (2016) doi: /j.finel [13] O. Sigmund, On the usefulness of non-gradient approaches in topology optimization, Struct Multidiscip O. 43 (2011) doi: /s [14] T. Zegard, G.H. Paulino, Toward GPU accelerated topology optimization on unstructured meshes, Struct Multidiscip O. 48 (2013) doi: /s y. [15] V.J. Challis, A.P. Roberts, J.F. Grotowski, High resolution topology optimization using graphics processing units (GPUs), Struct Multidiscip O. 49 (2014) doi: /s z. [16] E. Wadbro, M. Berggren, Megapixel Topology Optimization on a Graphics Processing Unit, SIAM Rev. 51 (2009) doi: / [17] J. Wu, C. Dick, R. Westermann, A System for High-Resolution Topology Optimization., IEEE Trans Vis Comput Graph. 22 (2016) doi: /tvcg [18] R. Le Riche, R.T. Haftka, On global optimization articles in SMO, Struct Multidiscip O. 46 (2012) doi: /s [19] Y.M. Xie, G.P. Steven, Evolutionary Structural Optimization, Springer London, London, doi: / [20] Y.M. Xie, G.P. Steven, A simple evolutionary procedure for structural optimization, Comput Struct. 49 (1993) doi: / (93)90035-c. 4