Application of topological derivative to accelerate genetic algorithm in shape optimization for semilinear elliptic equation

A new variant of the genetic algorithm for finding the location and size of small holes in the domain described by the non-linear boundary value problem is considered. The expansion of the shape functional defined in non-linear domain is provided in order to determine the form of topological derivative. The value of topological derivative is used for computing the probability density applied later to generate location and size of holes by the genetic algorithm.