A New Hybrid Differential Evolution with Gradient Search for Level Set Topology Optimization
Topology optimization is an effective structural optimization concept for optimal design of engineering structures. However, it has many difficulties due to high number of design variables and complex problems same as compliant mechanisms and crashworthiness. Conventional methods for topology optimization does not have enough adaptability with current computer aided design (CAD) softwares and they are not powerful in solving difficult optimization problems. Level set which is a novel boundary tracking method had been recently used to solve problems in conventional methods. This paper is dedicated to propose a new hybrid method based on differential evolution (DE) and globally convergent method of moving asymptotes (GCMMA) to use both gradient direction of GCMMA and excellent exploration of DE. The method has been validated in familiar benchmark problems in compliance minimization.
Bendsøe, M. P., & Sigmund, O. (1999). Material interpolation schemes in topology optimization. Archive of applied mechanics, 69(9-10), 635-654
Xie, Y. M., & Steven, G. P. (1993). A simple evolutionary procedure for structural optimization. Computers & structures, 49(5), 885-896.
Huang, X., & Xie, Y. M. (2007). Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elements in Analysis and Design, 43(14), 1039-1049.
Zuo, Z. H., & Xie, Y. M. (2015). A simple and compact Python code for complex 3D topology optimization. Advances in Engineering Software, 85, 1-11.
Ortmann, C., & Schumacher, A. (2013). Graph and heuristic based topology optimization of crash loaded structures. Structural and Multidisciplinary Optimization, 47(6), 839-854.
Tovar, A., Patel, N. M., Niebur, G. L., Sen, M., & Renaud, J. E. (2006). Topology optimization using a hybrid cellular automaton method with local control rules. Journal of Mechanical Design, 128(6), 1205-1216.
Osher, S., & Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of computational physics, 79(1), 12-49.
Allaire, G., Jouve, F., & Toader, A. M. (2004). Structural optimization using sensitivity analysis and a level-set method. Journal of computational physics, 194(1), 363-393.
Guo, X., Zhang, W., & Zhong, W. (2014). Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. Journal of Applied Mechanics, 81(8), 081009.
Bujny, M., Aulig, N., Olhofer, M., & Duddeck, F. (2016, July). Hybrid evolutionary approach for level set topology optimization. In Evolutionary Computation (CEC), 2016 IEEE Congress on (pp. 5092-5099). IEEE.
Bujny, M., Aulig, N., Olhofer, M., & Duddeck, F. (2018). Identification of optimal topologies for crashworthiness with the evolutionary level set method. International Journal of Crashworthiness, 23(4), 395-416.
Storn, R., & Price, K. (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization, 11(4), 341-359.
Svanberg, K. (1987). The method of moving asymptotes—a new method for structural optimization. International journal for numerical methods in engineering, 24(2), 359-373.
Tahk, M. J., Woo, H. W., & Park, M. S. (2007). A hybrid optimization method of evolutionary and gradient search. Engineering Optimization, 39(1), 87-104.
Woo, H. W., Kwon, H. H., & Tahk, M. J. (2004). A hybrid method of evolutionary algorithms and gradient search. In 2nd International Conference on Autonomous Robots and Agents.
Copyright (c) 2019 Javad Marzbanrad, Pooya Rostami Varnousfaderani
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