|
Response surface technology in details
In IOSO Technology algorithms each iteration
consists of two steps:
- constructing response surface approximations for objective function
and constraints;
- optimizing the response surface approximations.
When moving from one iteration to the next we use special moving strategy
that adapts algorithm parameters and structure for the particular optimization
problem.
Several highly efficient algorithms are used to construct the response
surface approximations:
Adaptive algorithms of regression analysis
Adaptive algorithms of regression analysis are based on modified least
squares method. These algorithms adaptively define basis functions, parameters,
and structure of such a regression function that provides the best approximation
properties while requiring minimal number of points in the experiment
plan. Such algorithms are successfully used in optimization problems of
small and moderate dimensionality.
Some examples of adaptive algorithms application:
| Original function |
Responce surface approximation |
 |
 |
 |
 |
Evolutionary self-organizing algorithms
The unique properties of the evolutionary self-organizing algorithms
allow constructing response surface approximations with high predictive
capabilities for the objective functions dependent on the large number
of design variables (hundreds). Such function can potentially have very
complex topology. However, the number of points required to construct
such approximations using evolutionary self-organizing algorithms is minimal
(30-40).
The evolutionary self-organizing algorithms are based on the modified
version of the Method of Accounting for the Groups of Arguments.
Approximation process scheme.
Such algorithms employ the evolutionary procedure of constructing approximation
function in the form of multilevel graph, solving structure-parametric
approximation problem in the process.
Example of the response surface structure.
Neural network algorithms
The distinct feature of the developed neural network algorithms for constructing
the responses surface approximations is that such methods allow approximating
the functions of complex topology (with multiple optima, non-differentiable,
etc.). In addition the resulting approximations exhibit good extrapolation
properties. Applying these algorithms for multidisciplinary,
parallel, multilevel
optimization strategies, and for robust design optimization
results in considerable (up tot two orders of magnitude) computational
savings, particularly for complex practical problems.
IOSO Technology uses two types of neural network algorithms to construct
response surface approximations: MultiLayer Perceptron nets (MLP) and
Radial Basis Function nets (RBF).
Some application examples:
The test functions
The neural networks results
Back...
|
