Sequential approximate optimization using kriging and radial basis functions - Maia, Marina Alves (2019)
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.