Kriging as a surrogate fitness landscape in evolutionary optimization

Abstract

The problem of finding optimal values in complex parameter optimization problems has often been solved with success by evolutionary algorithms (EAs). In many cases, these algorithms are employed as black-box methods over imprecisely known domains. Such problems arise frequently in engineering design. The principal barrier to the general use of EAs for those problems is the huge number of function evaluations that is often required. This makes EAs an impractical approach when the function evaluation depends on numerically heavy design analysis tools, for example, finite elements methods. This paper presents the use of kriging interpolation as a function approximation method for the construction of an internal model of the fitness landscape. This model is intended to guide the search process with a reduced number of fitness function evaluations.

A study on metamodeling techniques, ensembles, and multi-surrogates in evolutionary computation

“…To alleviate this problem, in EA it has been a standard practice for computationally cheap approximation or surrogate models to be used in lieu of exact model, hence the term Surrogate-Assisted Evolutionary Algorithm (SAEA). Among these techniques, Polynomial Regression (PR, also known as response surface method), Artificial Neural Network (ANN), Radial Basis Function (RBF), and Gaussian Process (GP) (also referred to as Kriging or Design and Analysis of Computer Experiments (DACE) models) are the most prominent and commonly used [6] [7]. In [6], Ratle proposed a strategy for integrating GA with Kriging metamodel and uses a heuristic convergence criterion to decide when the model should be updated.…”

“…Among these techniques, Polynomial Regression (PR, also known as response surface method), Artificial Neural Network (ANN), Radial Basis Function (RBF), and Gaussian Process (GP) (also referred to as Kriging or Design and Analysis of Computer Experiments (DACE) models) are the most prominent and commonly used [6] [7]. In [6], Ratle proposed a strategy for integrating GA with Kriging metamodel and uses a heuristic convergence criterion to decide when the model should be updated. The work was extended by El-Beltagy et al [8] who considered the issue of balancing the concerns of optimization with those of Design of Experiments (DOE).…”

Enhanced Hybrid Cat Swarm Optimization Based on Fitness Approximation Method for Efficient Motion Estimation

“…Recently, several fitness estimators have been reported in the literature [37][38][39] in which the number of function evaluations is considerably reduced to hundreds, dozens or even less. However, most of these methods produce complex algorithms whose performance is conditioned to the quality of the training phase and the learning algorithm in the construction of the approximation model.…”

On the efficiency of worst improvement for climbing NK-landscapes

“…Originally, a fitness landscape is a genotype-phenotype mapping [11] which emphasizes the effect of mutations (genotype modifications) on fitness (lifetime reproductive success). Nowadays, this concept is frequently used to characterize combinatorial optimization problems within an evolutionary computation context [7,6,9].…”