Abstract
We propose a new topological shape optimization scheme based on the artificial bee colony algorithm (ABCA). Since the level set method (LSM) and phase field method (PFM) in topological shape optimization have been developed, one of any algorithms in this field has not yet been proposed. To perform the topological shape optimization based on the ABCA, a variable called the “Boundary Element Indicator (BEI),” is introduced, which serves to define the boundary elements whenever a temporary candidate solution is found in the employed and onlooker bee phases. Numerical examples are provided to verify the performance of the suggested ABCA compared with the discrete LSM and the ABCA for topology optimization. The numerical examples showed that holes in the structure are naturally created in the ABCA for topological shape optimization. Moreover, the objective function of the suggested ABCA is lower than that of the ABCA for topology optimization, and is similar to that of the discrete LSM. The convergence rate of the suggested ABCA is the fastest among the comparison methods. Therefore, it can be verified that the suggested topological shape optimization scheme, based on the ABCA, is the most effective among the comparison methods.
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Sethian, J. A. and Wiegmann, A., “Structural Boundary Design via Level Set and Immersed Interface Methods,” Journal of Computational Physics, Vol. 163, No. 2, pp. 489–528, 2000.
Challis, V. J., “A Discrete Level-set Topology Optimization Code Written in Matlab,” Structural and Multidisciplinary Optimization, Vol. 41, No. 3, pp. 453–464, 2010.
Xia, Q. and Wang, M. Y., “Topology Optimization of Thermoelastic Structures Using Level Set Method,” Computational Mechanics, Vol. 42, No. 6, pp. 837–857, 2008.
Allaire, G. and Jouve, F., “Minimum Stress Optimal Design with the Level Set Method,” Engineering Analysis with Boundary Elements, Vol. 32, No. 11, pp. 909–918, 2008.
Allaire, G., Jouve, F., and Toader, A.-M., “Structural Optimization Using Sensitivity Analysis and a Level-Set Method,” Journal of Computational Physics, Vol. 194, No. 1, pp. 363–393, 2004.
Bourdin, B. and Chambolle, A., “Design-Dependent Loads in Topology Optimization,” ESAIM: Control, Optimisation and Calculus of Variations, Vol. 9, pp. 19–48, 2003.
Burger, M. and Stainko, R., “Phase-Field Relaxation of Topology Optimization with Local Stress Constraints,” SIAM Journal on Control and Optimization, Vol. 45, No. 4, pp. 1447–1466, 2006.
Zhou, S. and Wang, M. Y., “Multimaterial Structural Topology Optimization with a Generalized Cahn-Hilliard Model of Multiphase Transition,” Structural and Multidisciplinary Optimization, Vol. 33, No. 2, pp. 89–111, 2007.
Takezawa, A., Nishiwaki, S., and Kitamura, M., “Shape and Topology Optimization Based on the Phase Field Method and Sensitivity Analysis,” Journal of Computational Physics, Vol. 229, No. 7, pp. 2697–2718, 2010.
Allen, S. M. and Cahn, J. W., “A Microscopic Theory for Antiphase Boundary Motion and Its Application to Antiphase Domain Coarsening,” Acta Metallurgica, Vol. 27, No. 6, pp. 1085–1095, 1979.
Cahn, J. W. and Hilliard, J. E., “Free Energy of a Nonuniform System. I. Interfacial Free Energy,” The Journal of Chemical Physics, Vol. 28, No. 2, pp. 258–267, 1958.
Osher, S. and Sethian, J. A., “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” Journal of Computational Physics, Vol. 79, No. 1, pp. 12–49, 1988.
Dunning, P. D. and Kim, H. A., “A New Hole Insertion Method for Level Set Based Structural Topology Optimization,” International Journal for Numerical Methods in Engineering, Vol. 93, No. 1, pp. 118–134, 2013.
Sigmund, O. and Maute, K., “Topology Optimization Approaches,” Structural and Multidisciplinary Optimization, Vol. 48, No. 6, pp. 1031–1055, 2013.
Colorni, A., Dorigo, M., and Maniezzo, V., “Distributed Optimization by Ant Colonies,” Proc. of the 1st European Conference on Artificial Life, pp. 134–142, 1991.
Karaboga, D., “An Idea Based on Honey Bee Swarm for Numerical Optimization,” Erciyes University, Technical Report-TR06, 2005.
Karaboga, D. and Basturk, B., “A Powerful and Efficient Algorithm for Numerical Function Optimization: Artifical Bee Colony (ABC) Algorithm,” Journal of Global Optimization, Vol. 39, No. 3, pp. 459–471, 2007.
Karaboga, D. and Basturk, B., “On the Performance of Artificial Bee Colony (ABC) Algorithm,” Applied Soft Computing, Vol. 8, No. 1, pp. 687–697, 2008.
Mirjalili, S., Mirjalili, S. M., and Lewis, A., “Grey Wolf Optimizer,” Advances in Engineering Software, Vol. 69, pp. 46–61, 2014.
Yang, X.-S., “A New Metaheuristic Bat-inspired Algorithm,” in: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), González J. R., Pelta D. A., Cruz C., Terrazas G., Krasnogor N., (Eds.), Springer, Vol. 284, pp. 65–74, 2010.
Holland, J. H., “Adaptation in Natural and Artificial Systems,” University of Michigan Press, 1975.
Storn, R. and Price, K., “Differential Evolution–A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces,” Journal of Global Optimization, Vol. 11, No. 4, pp. 341–359, 1997.
Kennedy, J., “Particle Swarm Optimization,” in: Encyclopedia of Machine Learning, Sammut, C., Webb, G. I., (Eds.), Springer, pp. 760–766, 2010.
Bäck, T., “Evolutionary Algorithms in Theory and Practice,” Oxford University Press, 1996.
Sonmez, M., “Artificial Bee Colony Algorithm for Optimization of Truss Structures,” Applied Soft Computing, Vol. 11, No. 2, pp. 2406–2418, 2011.
Park, J.-Y. and Han, S.-Y., “Swarm Intelligence Topology Optimization Based on Artificial Bee Colony Algorithm,” Int. J. Precis. Eng. Manuf., Vol. 14, No. 1, pp. 115–121, 2013.
Park, J.-Y. and Han, S.-Y., “Application of Artificial Bee Colony Algorithm to Topology Optimization for Dynamic Stiffness Problems,” Computers and Mathematics with Applications, Vol. 66, No. 10, pp. 1879–1891, 2013.
Kaveh, A., Hassani, B., Shojaee, S. and Tavakkoli, S. M., “Structural Topology Optimization Using Ant Colony Methodology,” Engineering Structures, Vol. 30, No. 9, pp. 2559–2565, 2008.
Bendsøe, M. P. and Sigmund, O., “Topology Optimization: Theory, Methods and Applications,” Springer Science & Business Media, pp. 1–69, 2003.
Huang, X. and Xie, Y., “Convergent and Mesh-Independent Solutions for the Bi-Directional Evolutionary Structural Optimization Method,” Finite Elements in Analysis and Design, Vol. 43, No. 14, pp. 1039–1049, 2007.
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Kim, YH., Han, SY. Topological shape optimization scheme based on the artificial bee colony algorithm. Int. J. Precis. Eng. Manuf. 18, 1393–1401 (2017). https://doi.org/10.1007/s12541-017-0166-5
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DOI: https://doi.org/10.1007/s12541-017-0166-5