Increasing the density of available pareto optimal solutions

The set of available multi-objective optimization algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult - mainly due to the computational cost - to use a population large enough to ensure the likelihood of obtaining a solution close to the DMs preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimization algorithm. This method, which we refer to as Pareto estimation, is tested against a set of 2 and 3-objective test problems and a 3-objective portfolio optimization problem to illustrate its’ utility for a real-world problem

Integrated system to perform surrogate based aerodynamic optimisation for high-lift airfoil

This work deals with the aerodynamics optimisation of a generic two-dimensional three element high-lift configuration. Although the high-lift system is applied only during take-off and landing in the low speed phase of the flight the cost efficiency of the airplane is strongly influenced by it [1]. The ultimate goal of an aircraft high lift system design team is to define the simplest configuration which, for prescribed constraints, will meet the take-off, climb, and landing requirements usually expressed in terms of maximum L/D and/or maximum CL. The ability of the calculation method to accurately predict changes in objective function value when gaps, overlaps and element deflections are varied is therefore critical. Despite advances in computer capacity, the enormous computational cost of running complex engineering simulations makes it impractical to rely exclusively on simulation for the purpose of design optimisation. To cut down the cost, surrogate models, also known as metamodels, are constructed from and then used in place of the actual simulation models. This work outlines the development of integrated systems to perform aerodynamics multi-objective optimisation for a three-element airfoil test case in high lift configuration, making use of surrogate models available in MACROS Generic Tools, which has been integrated in our design tool. Different metamodeling techniques have been compared based on multiple performance criteria. With MACROS is possible performing either optimisation of the model built with predefined training sample (GSO) or Iterative Surrogate-Based Optimization (SBO). In this first case the model is build independent from the optimisation and then use it as a black box in the optimisation process. In the second case is needed to provide the possibility to call CFD code from the optimisation process, and there is no need to build any model, it is being built internally during the optimisation process. Both approaches have been applied. A detailed analysis of the integrated design system, the methods as well as th

MULTI-DIMENSIONAL SURROGATE BASED AFT FORM OPTIMIZATION OF SHIPS USING HIGH FIDELITY SOLVERS

Surrogate (metamodel) based optimization has numerous potential applications in the field of naval architecture. It is aimed here to establish a methodology for the aft form optimization for minimum viscous resistance, thus the present study is focused on the aft form where the viscous effects become dominant. It is necessary to solve this problem within acceptable time span from practical naval architectural point of view which requires metamodeling techniques currently under investigation. Accordingly, the present paper investigates the metamodeling ability of the Kriging interpolation and attempts to explore its capabilities and limitations in the aft form optimization from viscous resistance point of view. As metamodeling techniques become more widely used, their constraints are more apparent. Especially in highly nonlinear design spaces, the effect of dimensionality should be taken into consideration. Taking all those factors into account, the present paper is to examine the capabilities of Kriging and to establish the learning performance in terms of RMS error, correlation coefficient and required number of training points according to selected optimization algorithm for multidimensional ship design problem. The results show that, at least 5% reduction in viscous pressure drag can be attained by the present optimization methodology