## NUMERICAL OPTIMIZATION ALGORITHM BASED ON GENETIC ALGORITHM FOR A DATA COMPLETION PROBLEM

## NUMERICAL OPTIMIZATION ALGORITHM BASED ON GENETIC ALGORITHM FOR A DATA COMPLETION PROBLEM

*B. Jouilik, J. Daoudi, C. Tajani, J. Abouchabaka*

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## Abstract

This work presents numerical optimization algorithm based on genetic algo- rithm 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 ac- cessible part. This problem is known to be severely ill-posed in Hadamard sense; then, regularization methods must be exploited. Metaheuristics are methods inspired by nat- ural phenomena and which have shown their e ectiveness in solving several optimization problems in di erent 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 e ciency of the proposed algo- rithm.

## Keywords

Inverse problem, cauchy problem, genetic algorithm, nite element method.