Comparison of parallel infill sampling criteria based on Kriging surrogate model

One of the key issues that affect the optimization effect of the efficient global optimization (EGO) algorithm is to determine the infill sampling criterion. Therefore, this paper compares the common efficient parallel infill sampling criterion. In addition, the pseudo-expected improvement (EI) criterion is introduced to minimizing the predicted (MP) criterion and the probability of improvement (PI) criterion, which helps to improve the problem of MP criterion that is easy to fall into local optimum. An adaptive distance function is proposed, which is used to avoid the concentration problem of update points and also improves the global search ability of the infill sampling criterion. Seven test problems were used to evaluate these criteria to verify the effectiveness of these methods. The results show that the pseudo method is also applicable to PI and MP criteria. The DMP and PEI criteria are the most efficient and robust. The actual engineering optimization problems can more directly show the effects of these methods. So these criteria are applied to the inverse design of RAE2822 airfoil. The results show the criterion including the MP has higher optimization efficiency.

An exploitation-enhanced multi-objective efficient global optimization algorithm for expensive aerodynamic shape optimizations

The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic

Branch and Bound (B&B) algorithms in Global Optimization are used to perform an exhaustive search over the feasible area. One choice is to use simplicial partition sets. Obtaining sharp and cheap bounds of the objective function over a simplex is very important in the construction of efficient Global Optimization B&B algorithms. Although enclosing a simplex in a box implies an overestimation, boxes are more natural when dealing with individual coordinate bounds, and bounding ranges with Interval Arithmetic (IA) is computationally cheap. This paper introduces several linear relaxations using gradient information and Affine Arithmetic and experimentally studies their efficiency compared to traditional lower bounds obtained by natural and centered IA forms and their adaption to simplices. A Global Optimization B&B algorithm with monotonicity test over a simplex is used to compare their efficiency over a set of low dimensional test problems with instances that either have a box constrained search region or where the feasible set is a simplex. Numerical results show that it is possible to obtain tight lower bounds over simplicial subsets.

An efficient method for calculating system non-probabilistic reliability index

Collecting enough samples is difficult in real applications. Several interval-based non-probabilistic reliability methods have been reported. The key of these methods is to estimate system non-probabilistic reliability index. In this paper, a new method is proposed to calculate system non-probabilistic reliability index. Kriging model is used to replace time-consuming simulations, and the efficient global optimization is used to determine the new training samples. A refinement learning function is proposed to determine the best component (or performance function) during the iterative process. The proposed refinement learning function has considered two important factors: (1) the contributions of components to system nonprobabilistic reliability index, and (2) the accuracy of the Kriging model at current iteration. Two stopping criteria are given to terminate the algorithm. The system non-probabilistic index is finally calculated based on the Kriging model and Monte Carlo simulation. Two numerical examples are given to show the applicability of the proposed method.