A Two-Level Genetic Algorithm for Large Optimization Problems

A Surrogate-Based Two-Level Genetic Algorithm Optimization Through Wavelet Transform

“…For comparison purposes, the number of generations in the DWTGA, for Hartmann 6 function, was the same used in [4]: ν 1 = 10, ν 2 = 10, and ν 3 = 5, at fine and coarse levels. The values of those parameters to Schwefel and Griewank functions were (50, 20, and 10), respectively.…”

“…The traditional GA and the two-level approach based on the principal components analysis GA (PCAGA) have been used for comparison. For the Hartmann 6 problem, the fine model used here is the same applied in [4].…”

“…To overcome this limitation, many two-level algorithms have been proposed for accelerating the optimization using a combination of fine and coarse models in the procedure [4]- [6]. In general, the coarse model is created as an approximation of the fine model in an appropriate subspace and it is often cheaper to evaluate.…”

“…The success of these approaches has motivated more studies to improve weaknesses. In [4], for example, the principal components subspace was used for mapping the problem subspace and creating a global coarse model. The coarse model should be built just once but requires the calculation of the covariance matrix of a set of design parameter values and its eigenvalues and eigenvectors.…”

“…The coarse model should be built just once but requires the calculation of the covariance matrix of a set of design parameter values and its eigenvalues and eigenvectors. This paper proposes the use of the wavelet transform to create the coarse model subspace in the two-level genetic algorithm (GA) presented in [4]. The wavelet transform enables the exploration of the approximation characteristics of Manuscript the several wavelet functions and it allows creating a coarse model subspace with a relative few float point operations.…”