N.Kroll (DLR) (20.4.)
Need and use of multiobjective optimization in large scale engineering applications
Aerospace industry is increasingly relying on advanced numerical flow simulation tools in the early aircraft design phase. Today s flow solvers based on the solution of the compressible Euler and Navier-Stokes equations are able to predict aerodynamic behaviour of aircraft components under different flow conditions quite well. Due to the high computational expense required for flow simulations around realistic 3D configurations, in industry computational fluid dynamics tools are rather used for analysis and assessment of given geometries than for shape design and optimization. However, within the next few years numerical shape optimization will play a strategic role for future aircraft design. It offers the possibility of designing or improving aircraft components with respect to a pre-specified figure of merit subject to geometrical and physical constraints. Very often the design problems lead to multipoint and multi-objective optimizations. In order to address these large scale optimization problems efficient and robust optimization strategies are required. In terms of multi-criteria optimization the relative importance of the various objectives are often not known until the best solution candidates are determined and the tradeoffs between the objectives are fully understood. The concept of Pareto optimality can be used to characterize the objectives. The goal of the numerical optimization is then to provide a set of Pareto optimal solutions (Pareto front) that represent a trade-off of information amongst the objectives.
This lecture gives an overview of the requirements, status and needs of
single-objective and multi-objective optimization problems in detailed
aerospace design. At the end some promising techniques to calculate
Pareto optimal points are discussed.
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A.Griewank (HU) (27.4.)
Mathematical Characterization of the Pareto Front (and why simple scalarization is not good enough)
T.Steihaug (Uni Bergen & HU) (4.5.17.00 Uhr )
A review of the normal-boundary intersection (NBI) method
In two groundbreaking papers Indraneel Das and John. E. Dennis (SIAM J.
Optimization Vol. 8(1998) 631-657 and Structural Optimization 14(1997)63-69
presented the normal- boundary intersection method for multiobjective
optimization. Today, these two papers have close to 100 citations in the
Science Citation Index. and the NBI method has in few years become de facto
standard for multi objective optimization. In this talk we will review the
(close to) trivial observation that lead to the method and discuss some of
its strengths and weaknesses seen from a computational view. We will discuss
the need for better warm starts in the optimization routines and we review
some of the more recent improvements in terms of scaling and introducing a
filter.
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N.Gauger (HU) (11.5. / 18.5. )
Efficient Optimization of Aerodynamic Coefficients I/II
There are many ingredients required to establish an efficient and
flexible numerical optimization capability. These include suitable
techniques for geometry parametrization, meshing and mesh movement
methods, efficient and accurate flow solvers as well as a flexible
tool-set containing both deterministic and stochastic based optimizers.
Over the last years, numerical shape optimization is one of the major
issues of the Institute of Aerodynamics and Flow Technology at DLR. One
key activity is the derivation and implementation of a continuous
adjoint approach for the DLR flow simulation software MEGAFLOW based on
the solution of the Euler and Navier-Stokes equations. Its potential for
efficient aerodynamic shape design in compressible flow will be
demonstrated.
The two lectures will contain the following three sections: First, the
adjoint method will be explained by means of simple linear equations.
Second, as an exercise the continuous adjoint equations will be derived
for the convection-diffusion equations. Third, the continuous adjoint
Euler equations will be derived and their applications will be presented
for 2D airfoil designs, wing-body optimizations as well as wing designs
in MDO context.
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D.Bestle (TU Cottbus) (25.5.)
Some applications of multicriteria strategies in mechanical engineering
Some applications of multicriteria strategies in mechanical engineering
Multi-criterion optimization has the potential to improve technical
design processes remarkably.
In contrast to scalar optimization it
reflects the typical design situation of multiple contradicting
objectives which cannot be fulfilled by a unique solution but leaves
space for multiple, non-comparable optimal compromises. It thus keeps
the design engineer as part of the decision process but cuts down the
costs of time-consuming parameter studies by avoiding non-optimal
designs.
Typical fields of application are finding better solutions in
case of problems with existing machines, identification of passive and
active systems or system components, and virtual prototyping.
The
lecture shows successful applications to a platform insulation problem
involving modeling, identification and optimization of air springs, and
compressor design of aircraft engines. Especially in the latter case,
success of optimization depends on adequate parameterization and problem
formulation. Due to non-robust analysis algorithms Genetic Algorithms
seem to have some advantages over deterministic gradient-based
optimization algorithms which however offer better results for the
Pareto boundary.
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N.Gauger (HU) (8.6.)
One Shot Approaches in Aerodynamic Shape Optimization
A.Griewank (HU) (15.6.)
The Pareto front as range boundary and its generic singularities
J.Guddat (HU) (29.6.)
Calculation of a feasible point of a non-convex set with application in multiobjective optimization
The calculation of a feasible point of non-convex set M described by non- linear equations and inequalities with an arbitrarily chosen starting point is an open problem until now.
We propose an algorithm (CAFENOCS) using pathfollowing methods and jumps in the set of non-degenerate critical points that are not stationary. We assume that the considered embeddings are Jongen-Jonker-Twilt regular.
There are a lot of interesting applications. We restrict ourself in
this lecture to the applications in multiobjective optimization.
Computational results are presented.
P.Mbunga (HU) (6.7.)
Vector optimization problems and parameteric optimization
N.Gauger (HU) (13.7.)
Roundout