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

In the paper, a variant of the genetic algorithm for finding the location and size of small holes is considered. Both linear and non-linear elliptic boundary value problems are introduced in two domains with the conditions of transmission on the common boundary. The expansion of the shape functional for non-linear part and the expansion of Steklov-Poincare operator for linear part are provided in order to determine the form of topological derivative for the coupled model. The value of topological derivative is used for computing the probability density applied later in generating location of holes for genetic algorithm.