Meta-modeling and Optimization for Varying Dimensional Search Space

Abstract

High-fidelity computer simulations are used widely in several scientific and engineering domains to study, analyze and optimize process responses and reduce the time, cost and risk associated with conducting a physical experiment. However, many such simulations are computationally expensive and impractical for optimization. Meta-models have been successfully used to give quick approximation of the process responses in simulations and facilitate the analysis and optimization of designs.

Despite the abundance of literature in meta-modeling for continuous variables, there have been very few studies in the domain where the design spaces are discrete or mixed or with dependencies between discrete and real variables. These problems are widespread in engineering, science, economics and several other fields. Through this work, we wish to address the lack of a technique to handle such problems from front to end i.e. selecting design samples, meta-modeling and subsequent optimization.

This paper presents novel methods for choosing design samples, meta-modeling of design spaces having binary and real variables using padding in Kriging technique and single-objective constrained optimization of the meta-model using a new genetic algorithm VDGA. These scalable generic methodologies have the potential for solving optimization problems that are very expensive or impractical due to the extremely high computational cost and time associated with the simulations. We also present the results of these techniques on several test problems.