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In the paper we consider a new variant of the genetic algorithm for finding the location and size of small holes in the domain, in which the coupled linear and non-linear boundary value problems are defined. The linear and non-linear parts are connected by the transmission condition on 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 then used for computing the probability density applied later in generating location of holes by the genetic algorithm.
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Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.