An optimization method for nacelle design

A multi-objective optimiZation method is demonstrated using an evolutionary genetic algorithm. The applicability of this method to preliminary nacelle design is demonstrated by coupling it with a response surface model of a wide range of nacelle designs. These designs were modelled using computational fluid dynamics and a Kriging interpolation was carried out on the results. The NSGA-II algorithm was tested and verified on established multi-dimensional problems. Optimisation on the nacelle model provided 3-dimensional Pareto surfaces of optimal designs at both cruise and off-design conditions. In setting up this methodology several adaptations to the basic NSGA-II algorithm were tested including constraint handling, weighted objective functions and initial sample size. The influence of these operators is demonstrated in terms of the hyper volume of the determined Pareto set

On the Construction of Pareto-Compliant Combined Indicators

The most relevant property that a quality indicator (QI) is expected to have is Pareto compliance, which means that every time an approximation set strictly dominates another in a Pareto sense, the indicator must reflect this. The hypervolume indicator and its variants are the only unary QIs known to be Pareto-compliant but there are many commonly used weakly Pareto-compliant indicators such as R2, IGD+,andɛ+. Currently, an open research area is related to finding new Pareto-compliant indicators whose preferences are different from those of the hypervolume indicator. In this article, we propose a theoretical basis to combine existing weakly Pareto-compliant indicators with at least one being Pareto-compliant, such that the resulting combined indicator is Pareto-compliant as well. Most importantly, we show that the combination of Paretocompliant QIs with weakly Pareto-compliant indicators leads to indicators that inherit properties of the weakly compliant indicators in terms of optimal point distributions. The consequences of these new combined indicators are threefold: (1) to increase the variety of available Pareto-compliant QIs by correcting weakly Pareto-compliant indicators, (2) to introduce a general framework for the combination of QIs, and (3) to generate new selection mechanisms for multiobjective evolutionary algorithms where it is possible to achieve/adjust desired distributions on the Pareto front