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In this paper, we investigate the use of multiple kernel functions for assisting single-objective Kriging-based efficient global optimization (EGO). The primary objective is to improve the robustness of EGO in terms of the choice of kernel function for solving a variety of black-box optimization problems in engineering design. Specifically, three widely used kernel functions are studied, that is, Gaussian, Matérn-3/2, and Matérn-5/2 function. We investigate both model selection and ensemble techniques based on Akaike information criterion (AIC) and cross-validation error on a set of synthetic (noiseless and noisy) and non-algebraic (aerodynamic and parameter tuning) optimization problems; in addition, the use of cross-validation-based local (i.e., pointwise) ensemble is also studied. Since all the constituent surrogate models in the ensemble scheme are Kriging models, it is possible to perform EGO since the Kriging uncertainty structure is still preserved. Through analyses of empirical experiments, it is revealed that the ensemble techniques improve the robustness and performance of EGO. It is also revealed that the use of Matérn-kernels yields better results than those of the Gaussian kernel when EGO with a single kernel is considered. Furthermore, we observe that model selection methods do not yield any substantial improvement over single kernel EGO. When averaged across all types of problem (i.e., noise level, dimensionality, and synthetic/non-algebraic), the local ensemble technique achieves the best performance. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and studied four variants of the UK methods, that is, a UK with a first-order polynomial, a UK with a second-order polynomial, a blind Kriging (BK) implementation from the ooDACE toolbox, and a polynomial-chaos Kriging (PCK) implementation. The UK-EGO framework with automatic trend function selection derived from the BK and PCK models works by building a UK surrogate model and then performing optimizations via expected improvement criteria on the Kriging model with the lowest leave-one-out cross-validation error. Next, we studied and compared the UK-EGO variants and standard EGO using five synthetic test functions and one aerodynamic problem. Our results show that the proper choice for the trend function through automatic feature selection can improve the optimization performance of UK-EGO relative to EGO. From our results, we found that PCK-EGO was the best variant, as it had more robust performance as compared to the rest of the UK-EGO schemes; however, total-order expansion should be used to generate the candidate trend function set for high-dimensional problems. Note that, for some test functions, the UK with predetermined polynomial trend functions performed better than that of BK and PCK, indicating that the use of automatic trend function selection does not always lead to the best quality solutions. We also found that although some variants of UK are not as globally accurate as the ordinary Kriging (OK), they can still identify better-optimized solutions due to the addition of the trend function, which helps the optimizer locate the global optimum. [ABSTRACT FROM AUTHOR]

We expose an efficient strategy to deal with shape optimization of dynamical systems exhibiting flutter-type instability induced by friction, such as the considered disc-pad system. The stability of such systems can be analyzed through complex eigenvalue analysis, through which we present a squeal noise criterion to be minimized as a computationally expensive black-box function. The computational domain is discretized through isogeometric formulation for its advantages in optimization and superior approximation properties which are well studied in structural dynamics. To be computationally efficient with the expensive black-box function, we defined the optimization based on efficient global optimization scheme in the context of multi-objective optimization, with the integration of Isogeometric design-through-analysis methodology. As gradient information is hard to access for such black-box functions, in addition to the presence of constraints, we relied on meta-heuristic approach as a more generic strategy for realizing optimization of such functions in multi-objective context. As one such scheme with its own advantages was observed to provide lack of resolution to define expected improvement (EI) with a single reference value, we propose a multi-reference acquisition strategy which can be defined through a fast and efficient algorithm with fewer adaptation to the existing scheme. Results show the efficiency of this approach for our applicative example, which can be extended to other such applications as well. [ABSTRACT FROM AUTHOR]