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The Kriging surrogate model is less frequently employed in high-dimensional expensive problems than is the radial basis function (RBF) model. This discrepancy is attributed to the challenge of hyperparameter tuning within the Kriging covariance function, which leads to relatively worse predictive performance. However, the Kriging model still plays a crucial role in providing the predicted uncertainty for new point infill that cannot be replaced by the RBF model. To leverage the advantages of both models, a surrogate information transfer and fusion algorithm is presented. Surrogate information transfer introduces global sensitivity information from the constructed RBF model to the hyperparameter optimization of the Kriging model, reducing the dimensions of hyperparameter tuning and improving its approximation performance. Surrogate information fusion combines the RBF and Kriging models, with the RBF model providing more accurate predictions of unknown points for exploitation, while the Kriging model provides predicted uncertainty for swarm updating and new point infilling to ensure exploration of the solution space. Compared with several state-of-the-art algorithms, the proposed algorithm is evaluated on eight benchmark problems and a in real-world optimization case. The experimental results demonstrate the effectiveness of the surrogate information transfer and fusion methods and the significant superiority of the proposed algorithm over the compared algorithms. [ABSTRACT FROM AUTHOR]

Expensive multiobjective optimization problem has been thoroughly studied in the past few years. However, one type of problem is often overlooked. Still, it is common in practice, whose partial target functions (objectives and constraints) are expensive that require approximations by surrogate models, while others have explicit formulas that can calculate immediately. To address this problem, a general representation is first defined as a highly heterogeneous optimization problem (HHOP) in this work. In terms of bi-objective constrained HHOP, an algorithm is proposed based on the Kriging surrogate model with a new exact 2-D expected hypervolume improvement (EHVI) calculation method and a new constraint handling approach considering both the expensive and inexpensive target functions. In EHVI calculation, the integral is only performed in the expensive objective dimension due to the deterministic of the inexpensive objective, resulting in the reduction of the time complexity and increase of the accuracy. Combining a multiobjective and a dominance-based constraint handling approaches, a new constraint handling strategy is proposed to deal with the constrained HHOP specifically. The effectiveness of the proposed EHVI calculation method and constraint handling strategy is verified by the benchmark comparison problems. whose results also indicate the superiority of the proposed algorithm compared with the other state-of-art algorithms. Furthermore, the proposed algorithm is implemented for a head sheave optimization problem to demonstrate its practicability in real-world problems. [ABSTRACT FROM AUTHOR]

Leave-one-out cross-validation (LOOCV) is a widely used technique in model estimation and selection of the Kriging surrogate model for engineering problems, such as structural optimization and reliability analysis. However, the traditional LOOCV method has some disadvantages in terms of accuracy and efficiency. This paper proposes an enhanced-LOOCV method that incorporates hyperparameters from the Kriging model based on the complete training dataset (i.e., the complete Kriging model) into the LOOCV error calculation. By keeping the model hyperparameters in LOOCV consistent with the complete Kriging model, it reduces the number of hyperparameter optimizations and significantly increases the accuracy and efficiency of the LOOCV process. Additionally, a decremental calculation is proposed to reduce the computational costs of the correlation matrix inversion without sacrificing accuracy, resulting in an improved time complexity of the traditional LOOCV from O (n 4) to O (n 3). Experimental results with thirty test functions verify that the enhanced-LOOCV has better estimation performance than the Kriging model with significantly higher efficiency compared to the traditional LOOCV. Numerical experiments and an engineering case in optimization demonstrate that the enhanced-LOOCV can reduce the number of samples needed for infilling in the Kriging model, and it is more suitable for expensive optimizations in engineering. [ABSTRACT FROM AUTHOR]

• A Kriging-assisted global reliability-based design optimization (KG-RBDO) algorithm is proposed. • KG-RBDO consists of a global optimization module and a local optimization module. • A new infill criterion considering both the optimality and the reliability requirement of the solutions is proposed. • KG-RBDO is more approximate to the global reliability-based design optimization problems. Surrogate models have been extensively used in reliability-based design optimization (RBDO); however, few studies have focused on the global optimality of RBDO. This paper proposes a global RBDO framework that employs Kriging surrogate models to approximate both the objective function and performance functions. The proposed algorithm comprises two major modules: the global optimization module and the local optimization module. The former module aims to identify the interested region containing potential optima, while the latter module refines the local optima. To address the time-consuming acquisition of samples, two different infill strategies are implemented in these two modules. Furthermore, in addition to evaluating the optimal solution in the local optimization module for infill, a reliability-constrained expected improvement infill criterion is developed for the global optimization module. This criterion inherits the property of the expected improvement from the Kriging model, which balances the exploration and the exploitation of the objective space, while taking reliability into account by introducing the shifting vector into the calculation of the probability of feasibility. Numerical experiments indicate that the performance of the proposed infill criterion is significantly superior to others in searching for optima. Several examples verify the global optimization capability of the proposed algorithm and illustrate that it is more suitable for RBDO problems with multiple local optima. [ABSTRACT FROM AUTHOR]