Abstract
We describe the application of two global optimization methods, namely of genetic and random search type algorithms in shape optimization. When the so-called fictitious domain approaches are used for the numerical realization of state problems, the resulting minimized function is non-differentiable and stair-wise, in general. Such complicated behaviour excludes the use of classical local methods. Specific modifications of the above-mentioned global methods for our class of problems are described. Numerical results of several model examples computed by different variants of genetic and random search type algorithms are discussed.
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Haslinger, J., Jedelský, D., Kozubek, T. et al. Genetic and Random Search Methods in Optimal Shape Design Problems. Journal of Global Optimization 16, 109–131 (2000). https://doi.org/10.1023/A:1008380715489
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DOI: https://doi.org/10.1023/A:1008380715489