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

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 sev...

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Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics Vol. 13; no. 1; p. 86
Main Authors: Jouilik, B, Daoudi, J, Tajani, C, Abouchabaka, J
Format: Journal Article
Language:English
Published: Istanbul Turkic World Mathematical Society 01.01.2023
Elman Hasanoglu
Subjects:
Algorithms
Boundary conditions
Cauchy problems
Chromosomes
Finite element analysis
Genetic algorithms
Heuristic methods
Inverse problems
Laplace equation
Mathematical optimization
Mathematics
Missing data
Mutation
Optimization
Optimization algorithms
Regularization
Regularization methods
Morocco
ISSN:2146-1147, 2146-1147
Online Access:Get full text
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Summary: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.
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ISSN:2146-1147
2146-1147