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Application of topological derivative to accelerate genetic algorithm in shape optimization of coupled models

In the paper we consider a new method based on the genetic algorithm for finding the location and size of small holes in the domain, in which the coupled linear and nonlinear boundary value problems are defined. The linear and nonlinear components are connected by the transmission conditions on the interface boundary. The expansion with respect to small parameter of the shape functional for nonlinear component and the expansion of Steklov-Poincaré operator for linear component are derived in order to determine the form of topological derivative for shape functional defined for coupled model. Then the topological derivative is employed for evaluation of the probability density applied to generation of location of holes by the genetic algorithm.