L.D. Chiwiacowsky, H.F. de Campos Velho, A.J. Preto, S. Stephany (2003): Identifying Initial Condition in Heat Conduction Transfer by a Genetic Algorithm: A Parallel Approach, XXIV Iberian Latin-american Congress on Computational Methods in Engineering (CILAMCE-2003), 29-31 October, Ouro Preto (MG), Brazil.

Abstract: A parallel implementation of a genetic algorithm is proposed to solve the one-dimensional inverse heat conduction problem of determining the initial temperature distribution from the transient temperature noisy profile at a given time, considering insulated boundary conditions. Genetic algorithms are efficient search methods based on natural and genetic selection of population being inherently parallel [1]. This ill-posed problem requires the use of a regularization technique [2]. The solution is given by the candidate function which minimizes the functional given by the square differences between the experimental and simulated temperatures at a given time, plus the regularization term weighted by a regularization parameter. Therefore, this inverse problem is formulated as an optimization problem, which is solved by a parallel implementation of a specifically developed genetic algorithm method. This proposed method is based on individuals with genotypes formed by a set of real numbers [3]. The parallel code was generated using calls to the message passing communication library MPI (Message Passing Interface) [4]. Usually, parallel genetic algorithms work with sub-populations (demes) which are placed on each processor and it was used the migration policy given by the island model [5], In such model, individuals are free to migrate to any other processor, subjected to specific rules. The inversions were accomplished for two different population sizes (336 and 1008), being the individuals equally distributed among the processors. Number of processors was 2 to 16, and processing times show efficiencies between 0.9 and 1.14 for the 1008 individuals and between 0.83 and 0.89 for 336 individuals.

References:

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[3] Z. Michalewicz (1996): "Genetic algorithms + data structures = evolution programs", Springer-Verlag, USA.

[4] P. Pacheco, W.C. Ming (1995): "Introduction to message passing programming - MPI user guides in FORTRAN and C", Department of Mathematics, University of San Francisco, USA.

[5] M. Nowostawski, R. Poli (1999): "Parallel genetic algorithm taxonomy", Proc. of 3rd Int. Conference on Knowledge-based Intelligent Information Engineering Systems (KES'99), Adelaide, Australia.