Otimização de estruturas com gradação funcional utilizando algoritmos heurísticos e modelos substitutos

Abstract

The design of material structures with functional gradation has received a lot of attention from the academic community, since they present excellent performance in the most diverse applications, added to the ease of control that the designer has in the smooth and continuous gradation of this material. In order to enhance its performance in relation to a particular characteristic of interest, several optimization techniques have been used. The heuristic algorithms stand out in this application, especially the Particle Swarm Optimization (PSO). Although in many applications Differential Evolution (DE) outperforms PSO in terms of precision and efficiency, they have not yet been compared in the case of structures with functional gradation. Another important topic in these algorithms is the treatment of design restrictions that can be carried out from different methodologies that will be studied in the present work. However, the high computational cost of structural analysis can present itself as a limitation for this optimization strategy, since heuristic algorithms perform a large number of evaluations of the analysis model. In this context, the surrogate models will be used as an alternative to help reduce the computational cost and allow the optimization of complex structures. In this work, the surrogate model that will be studied is the Radial Basis Functions (RBF). An extremely important aspect in the construction of these models is the number of points that will be adopted in the Experiments Project, which is one of the study parameters of this work. The surrogate models will be incorporated into an optimization methodology known as Sequential Approximate Optimization (SAO), where the approximate response surface is continually updated and improved by the insertion of new points. The new points will be chosen in order to maximize the expected improvement. For this, PSO and DE will be used and evaluated. A comparison between the different methodologies will be carried out in terms of precision, efficiency and robustness. The results obtained were excellent, the efficiency of the Sequential Approximate Optimization was verified through numerical examples, being found very small differences in comparison with the conventional optimization at a much lower computational cost. The DE also showed excellent results and greater efficiency than PSO.