Updating kriging surrogate models based on the hypervolume indicator in multi-objective optimization

This paper presents a comparison of the criteria for updating the Kriging surrogate models in multi-objective optimization: expected improvement (EI), expected hypervolume improvement (EHVI), estimation (EST), and those in combination (EHVI þ EST). EI has been conventionally used as the criterion considering the stochastic improvement of each objective function value individually, while EHVI has recently been proposed as the criterion considering the stochastic improvement of the front of nondominated solutions in multi-objective optimization. EST is the value of each objective function estimated nonstochastically by the Kriging model without considering its uncertainties. Numerical experiments were implemented in the welded beam design problem, and empirically showed that, in an unconstrained case, EHVI maintains a balance between accuracy, spread, and uniformity in nondominated solutions for Krigingmodel-based multiobjective optimization. In addition, the present experiments suggested future investigation into techniques for handling constraints with uncertainties to enhance the capability of EHVI in constrained cases

Data mining based multipoint design of next generation transonic wing with small sweep back

Multi-point aerodynamic optimization of a transonic wing using data mining is discussed. Design problem has two objectives which are minimization of drag coefficient at Mach number 0.6 and 0.8 respectively. Here, Mach number 0.6 is considered as a subsonic condition, and Mach number 0.8 is considered as a transonic condition with the local shock. To reduce the local shock that causes wave drag, the sweep back angle is required in transonic condition. On the other hand, the sweep back angle reduces lift to drag ratio in subsonic condition. Thus, a complex high lift device like a flap is required. Moreover, the torsion at wing root becomes stronger with high sweep back angle. As a result, the wing structure weight becomes heavy. To design high efficient new generation civil aircraft, the design knowledge which implements a subsonic and a transonic aerodynamic performance simultaneously with few structure penalty is expected. In this study, tapered wing geometry is defined with two cross sections. 31 sample designs are calculated by the unstructured Euler solver and Kriging surrogate models for the resulting drag coefficient of subsonic and transonic condition are constructed. Using these models, non-dominated solutions are obtained by genetic algorithm (GA). Analysis of variance (ANOVA) and Self-organized map (SOM), which are data mining techniques, are also applied to obtain the relationship between design space and solution space. According to this result, there is trade-off between two objective functions and compromised design can be considered. According to data mining result, there is possible to find the design which achieve low drag with low sweep back angle and contrived cross sections

Development of an Efficient Hull Form Design Exploration Framework

A high-efficiency design exploration framework for hull form has been developed. The framework consists of multiobjective shape optimization and design knowledge extraction. In multiobjective shape optimization, a multiobjective genetic algorithm (MOGA) using the response surface methodology is introduced to achieve efficient design space exploration. As a response surface methodology, the Kriging model, which was developed in the field of spatial statistics and geostatistics, is applied. A new surface modification method using shifting method and radial basis function interpolation is also adopted here to represent various hull forms. This method enables both global and local modifications of hull form with fewer design variables. In design knowledge extraction, two data mining techniques—functional analysis of variance (ANOVA) and self-organizing map (SOM)—are applied to acquire useful design knowledge about a hull form. The present framework has been applied to hull form optimization exploring the minimum wave drag configuration under a wide range of speeds. The results show that the present method markedly reduced the design period. From the results of data mining, it is possible to identify the design variables controlling wave drag performances at different speed regions and their corresponding geometric features

Knowledge discovery for multi-disciplinary design of silent super sonic transport based on efficient global optimization

A multi objective design exploration for a wing of a supersonic transport (SST) was carried out using efficient global optimization (EGO). The objective functions considered here are to maximize the lm to drag ratio at a supersonic cruise and minimize the sonic boom intensity, simultaneously. Kriging surrogate model which was constructed based on several sample designs is introduced. The solution space was explored based on the maximization of Expected Improvement (EI) value corresponding to objective functions on the Kriging models. The improvement of the model and the exploration of the optimum can be advanced at the same time by maximizing EI value. In this study, a total of 90 sample points are evaluated using the compressive potential solver with panel method for the construction of the Kriging model. In order to obtain the information of the design space, two data mining techniques are applied to design result. One is functional analysis of variance (ANOVA) which can show quantitative information and the other is self-organizing map (SOM) which can show qualitative information. The design process provides the useful information for the design of the SST design problem