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

A test problem for visual investigation of high-dimensional multi-objective search

An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions

A multifidelity multiobjective optimization framework for high-lift airfoils

High-lift devices design is a challenging task as it involves highly complex flow features while being critical for the overall performance of the aircraft. When part of an optimization loop, the computational cost of the Computational Fluid Dynamics becomes increasingly problematic. Methods to reduce the optimization time has been of major interest over the last 50 years. This paper presents a multiobjective multifidelity optimization framework that takes advantage of two approximation levels of the flow equations: a rapid method that provides quick estimates but of relatively low accuracy and a reference method that provides accurate estimations at the cost of a longer run-time. The method uses a sub-optimization, under a trust-region scheme, performed on the low-fidelity model corrected by a surrogate model that is fed by the high-fidelity tool. The size of the trust region is changed according to the accuracy of the corrected model. The multiobjective optimizer is used to set the positions of the ap and slat of a two-dimensional geometry with lift and drag as objectives with an empirical-based method and a Reynolds Averaged Navier-Stokes equations solver. The multifidelity method shows potential for discovering the complete Pareto front, yet it remains less optimal than the Pareto front from the high-fidelity-only optimization

On the evolutionary optimisation of many conflicting objectives

This inquiry explores the effectiveness of a class of modern evolutionary algorithms, represented by Non-dominated Sorting Genetic Algorithm (NSGA) components, for solving optimisation tasks with many conflicting objectives. Optimiser behaviour is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal trade-off surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behaviour are offered via the concepts of dominance resistance and active diversity promotion