An efficient Kriging-based framework for computationally demanding constrained structural optimization problems

A literature survey reveals that many structural optimization problems involve constraint functions that demand high computational effort. Therefore, optimization algorithms which are able to solve these problems with just a few evaluations of such functions become necessary, in order to avoid prohibitive computational costs. In this context, surrogate models have been employed to replace constraint functions whenever possible, which are much faster to be evaluated than the original functions. In the present paper, a global optimization framework based on the Kriging surrogate model is proposed to deal with structural problems that have expensive constraints. The framework consists of building a single Kriging model for all the constraints and, in each iteration of the optimization process, the metamodel is improved only in the regions of the design space that are promising to contain the optimal design. In this way, many constraints evaluations in regions of the domain that are not important for the optimization problem are avoided. To determine these regions, three search strategies are proposed: a local search, a global search, and a refinement step. This optimization procedure is applied in benchmark problems and the results show that the approach can lead to results close to the best found in the literature, with far fewer constraints evaluations. In addition, when problems with more complex structural models are considered, the computational times required by the framework are significantly shorter than those required by other methods from the literature, including another Kriging-based adaptative method.