NUMERICAL OPTIMIZATION ALGORITHM BASED ON GENETIC ALGORITHM FOR A DATA COMPLETION PROBLEM - Jouilik, B; Daoudi, J; Tajani, C; Abouchabaka, J (TWMS journal of applied and engineering mathematics, 2023)
This work presents numerical optimization algorithm based on genetic algorithm to solve the data completion problem for Laplace's equation. It consists of covering the missing data on the inaccessible part of the boundary from measurements on the accessible part. This problem is known to be severely ill-posed in Hadamard sense; then, regularization methods must be exploited. Metaheuristics are methods inspired by natural phenomena and which have shown their effectiveness in solving several optimization problems in different domains. Thus, adapted genetic operators for real coded genetic algorithm is proposed by formulating the problem into an optimization one. Numerical results with irregular domain are presented showing the efficiency of the proposed algorithm. Keywords: Inverse problem, cauchy problem, genetic algorithm, finite element method. AMS Subject Classification: 65N30, 31A25, 65C35.