1 research outputs found
Monte Carlo Integration with adaptive variance selection for improved stochastic Efficient Global Optimization
In this paper, the minimization of computational cost on evaluating
multi-dimensional integrals is explored. More specifically, a method based on
an adaptive scheme for error variance selection in Monte Carlo integration
(MCI) is presented. It uses a stochastic Efficient Global Optimization (sEGO)
framework to guide the optimization search. The MCI is employed to approximate
the integrals, because it provides the variance of the error in the
integration. In the proposed approach, the variance of the integration error is
included into a Stochastic Kriging framework by setting a target variance in
the MCI. We show that the variance of the error of the MCI may be controlled by
the designer and that its value strongly influences the computational cost and
the exploration ability of the optimization process. Hence, we propose an
adaptive scheme for automatic selection of the target variance during the sEGO
search. The robustness and efficiency of the proposed adaptive approach were
evaluated on global optimization stochastic benchmark functions as well as on a
tuned mass damper design problem. The results showed that the proposed adaptive
approach consistently outperformed the constant approach and a multi-start
optimization method. Moreover, the use of MCI enabled the method application in
problems with high number of stochastic dimensions. On the other hand, the main
limitation of the method is inherited from sEGO coupled with the Kriging
metamodel: the efficiency of the approach is reduced when the number of design
variables increases.Comment: 24 page