The Adaptive Response Surface Method (ARSM) is a single-objective optimization approach. Within this method the objective and constraint functions are approximated by polynomial regression using linear or quadratic order.
Based on an initial DOE scheme having a single start design as center point, the approach generates a new adapted design scheme in each iteration step. Based on the improvement of the objective function the new DOE scheme is obtained either by moving, shrinking or expanding the previous scheme. Convergence of the algorithm is achieved if the change of the position and the objective value of the best design is below the specified tolerances or if the DOE scheme reaches a minimal size. Dependent on the specified start range, the algorithm shows a local or more global behavior.
The ARSM approach is very robust against solver noise and few failed designs. It is very efficient for problems having up to 20 design variables and can handle discrete variables. Approximation of signals is not supported. The obtained value will be approximated then. Vectors and matrices will only be approximated for constant length.
Further information about methods of multidisciplinary optimization used in optiSLang can be found here.
Relevant Parameters
Only parameters with deterministic properties (Optimization or Opt.+Stoch.) are relevant for optimization.
Initialization Options
To access the options shown in the following table, double-click the ARSM system on the Scenery pane and switch to the ARSM tab.
| Option | Description |
|---|---|
| Approximation | |
| Order | Order of used polynomial regression models. |
| DOE method | Method used to create the underlying support points. |
| Start range | Percentage of the design space used for the first iteration. The boundaries are calculated in relation to the start point. |
| Computational aspects | |
| Minimum iterations | Number of iterations that are performed before the convergence criteria is tested. |
| Maximum iterations | Maximum number of iteration cycles for the algorithm. |
| Minimum range | Minimal percentage of the design space of each parameter. When a new subspace is created with zooming, it cannot be smaller than the given value. |
| Convergence test | |
| Objective | Compares the objective value of the actual optimum with the optimum of the previous iteration step. |
| Parameter | Compares the parameter values at the actual optimum with the values from the previous iteration step. The criteria must be fulfilled by all parameters independently. |
| Approx | Tests the approximated values. |
| Real space | Tests the values in real space. |
| Stop at first non violated | The algorithm stops as soon as a design in real space is found that fulfils all constraints. |
Additional Options
This algorithm allows Additional Options.