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In this study, we focus on a specific class of bilateral free boundaries problems. We approach this problem by formulating it as a shape optimization problem using a defined cost functional. The existence of an optimal solution for the optimization problem is proved. To tackle this problem, we propose an iterative approach that combines the particle swarm optimization and fuzzy logic methods. Additionally, we employ the finite element method as a discretization technique for the state equation. To validate our approaches, we investigate various types of domains. Furthermore, we compare the performance of these approaches in two scenarios: one with exact measurements used for identification and another with noisy measurements. [ABSTRACT FROM AUTHOR]

This contribution deals with a free boundary identification problem using the genetic algorithm combined with the finite element method. the inverse problem consists to determine the configuration of the unknown boundary, by introducing a cost functional J we formulate the free boundary problem to a shape optimization problem, and to minimize the involved cost functional we use a genetic algorithm with a finite element solver for the state problem. Initially, the population of boundaries is generated randomly and each subsequent iteration three stochastic processes are applied. The first, "reproduction", imposes a survival of fittest criterion to select a new population of boundaries; the second, "crossover", produces an efficient exchange of information between the surviving boundaries; the third, "mutation", introduces a purely random element that maintains diversity in the population. Finally we establish some numerical tests to improve the validity of the algorithm. [ABSTRACT FROM AUTHOR]