Sequential approximate optimization using kriging and radial basis functions

Abstract

Despite steady advance in computing power, the number of function evaluations in global optimization problems is often limited due to time-consuming analyses. In structural optimization problems, for instance, these analyses are typically carried out using the Finite Elements Method (FEM). This issue is especially critical when dealing with bio-inspired algorithms, where a high number of trial designs are usually required. Therefore, surrogate models are a valuable alternative to help reduce computational cost. With that in mind, present work proposes three Sequential Approximate Optimization (SAO) techniques. For that purpose, two surrogate models were chosen: the Radial Basis Functions (RBF) and Kriging. As for the infill criteria, three methodologies were investigated: the Expected Improvement, the Density Function and the addition of the global best. Two bio-inspired meta-heuristics were used in different stages of the optimization, namely Particle Swarm Optimization and Genetic Algorithm. To validate the proposed methodologies, a set of benchmarks functions were selected from the literature. Results showed a significant reduction in the number of high-fidelity evaluations. In terms of accuracy, efficiency, and robustness, Kriging excelled in most categories for all problems. Finally, these techniques were applied to the solution of a laminated composite plate, which demands a more complex analysis using FEM.