Real-world optimization problems often involve complex objective functions with costly evaluations. While Bayesian optimization (BO) with Gaussian processes is effective for these challenges, it suffers in high-dimensional spaces due to performance degradation from limited function evaluations. To overcome this, simplification techniques like dimensionality reduction have been employed, yet they often rely on assumptions about the problem characteristics, potentially underperforming when these assumptions do not hold. Trust-region-based methods, which avoid such assumptions, focus on local search but risk stagnation in local optima. In this study, we propose a novel acquisition function, regional expected improvement (REI), designed to enhance trust-region-based BO in medium to high-dimensional settings. REI identifies regions likely to contain the global optimum, improving performance without relying on specific problem characteristics. We provide a theoretical proof that REI effectively identifies optimal trust regions and empirically demonstrate that incorporating REI into trust-region-based BO outperforms conventional BO and other high-dimensional BO methods in medium to high-dimensional real-world problems.

We propose a surrogate-assisted reference vector adaptation (SRVA) method to solve expensive multi- and many-objective optimization problems with various Pareto front shapes. SRVA is coupled with a multi-objective Bayesian optimization (MBO) algorithm using reference vectors for scalarization of objective functions. The Kriging surrogate models for MBO is used to estimate the Pareto front shape and generate adaptive reference vectors uniformly distributed on the estimated Pareto front. We combine SRVA with expected improvement of penalty-based boundary intersection as an infill criterion for MBO. The proposed algorithm is compared with two other MBO algorithms by applying them to benchmark problems with various Pareto front shapes. Experimental results show that the proposed algorithm outperforms the other two in the problems whose objective functions are reasonably approximated by the Kriging models. SRVA improves diversity of non-dominated solutions for these problems with continuous, discontinuous, and degenerated Pareto fronts. Besides, the proposed algorithm obtains much better solutions from early stages of optimization especially in many-objective problems.

Computationally expensive multiobjective optimization problems are difficult to solve using solely evolutionary algorithms (EAs) and require surrogate models, such as the Kriging model. To solve such problems efficiently, we propose infill criteria for appropriately selecting multiple additional sample points for updating the Kriging model. These criteria correspond to the expected improvement of the penalty-based boundary intersection (PBI) and the inverted PBI. These PBI-based measures are increasingly applied to EAs due to their ability to explore better nondominated solutions than those that are obtained by the Tchebycheff function. In order to add sample points uniformly in the multiobjective space, we assign territories and niche counts to uniformly distributed weight vectors for evaluating the proposed criteria. We investigate these criteria in various test problems and compare them with established infill criteria for multiobjective surrogate-based optimization. Both proposed criteria yield better diversity and convergence than those obtained with other criteria for most of the test problems.

Multi-objective optimization and data mining of vortex generators (VGs) on a transonic infinite-wing was performed using computational fluid dynamics (CFD), surrogate models, and a multi-objective genetic algorithm (MOGA). VGs arrangements were defined by five design variables: height, length, incidence angle, spacing, and chord location. The objective functions which should be maximized were three: lift-drag ratio at low angle of attack, lift coefficient at high angle of attack, and chordwise separation location at high angle of attack. In order to evaluate these objective functions of each individual in MOGA, the response surface methodology with Kriging model and the modified version of it was employed because CFD analysis of the wing with VG requires a large computational time. Two types of data mining method: analysis of variance (ANOVA) and self-organizing map (SOM), were applied to the result of the optimization. It was revealed by ANOVA that the ratio of spacing to height and the incidence angle had significant influences to maximizing each objective function. By using SOM, VG designs were split into four types which have different aerodynamic characteristics respectively. The appropriate values of parameters were identified by SOM.

In order to construct a response surface of an unknown function robustly, a hybrid method between the Kriging model and the radial basis function (RBF) networks is proposed in this paper. In the hybrid method, RBF approximates the macro trend of the function and the Kriging model estimates the micro trend. Then, hybrid methods using two types of model selection criteria (MSC): leave-one-out cross-validation and generalized cross-validation for RBF and the ordinary Kriging (OK) model for comparison are applied to three types of one dimensional test problems, in which the accuracy of each response surface is compared by shapes and root mean square errors. As a result, the hybrid models are more accurate than the OK model for highly nonlinear functions because the hybrid models can capture the macro trend of the function properly by RBF, but the OK model cannot. However, because the accuracy of the hybrid method turns down significantly when RBF causes overfitting, stable MSC is required. In addition, the hybrid models can find out the global optimum with a few sample points by using the Kriging model's approximation errors effectively.