Global Opti­miza­tion using Response Surfaces

For the opti­miza­tion of flow-exposed products, CAESES® offers a set of strate­gies that allows users to automate the intel­li­gent design creation process. Design vari­ables are linked to the variable geometry and get con­trolled by algo­rithms that are called design engines. Besides some standard engines for para­me­ter studies and opti­miza­tions, CAESES® offers an addi­tional method set of advanced strate­gies based on the opti­miza­tion package Dakota. In par­tic­u­lar, so-called Response Surface Methods (RSM) — i.e. approx­i­ma­tion models of an expen­sive high-fidelity model — are fully inte­grated and easy to apply in the design process. This short article shows you how to run such an RSM opti­miza­tion in CAESES®. 

Design Vari­ables and Objec­tive Functions

First of all, you have to create some design vari­ables in your CAD model or CFD setup. Objec­tive func­tions can be defined by using results from a CFD sim­u­la­tion. The software con­nec­tor in CAESES® connects any external tool includ­ing the result data for the def­i­n­i­tion of an objec­tive function.

Design Engine

All opti­miza­tion strate­gies in CAESES® are listed in the ​“opti­miza­tion” menu. Choose the Dakota engine at the bottom which creates a new design engine in the tree. 

Now you have to choose ​“Global Opti­miza­tion on Response Surface” as method. Similar to all other engines in CAESES®, you have to con­fig­ure your design variable ranges and you need to select one or several objec­tive func­tions as well as optional inequality/​equality con­straints. The fol­low­ing screen­shot shows such a setup: 

Opti­miza­tion on a Response Surface

In order to under­stand the strategy-specific settings, we briefly have to explain what the method actually does as soon as we start it: 

In the first phase, a set of random samples is gen­er­ated and used for creating the initial response surface. These samples can also be taken from previous runs or a sen­si­tiv­ity analysis and CAESES® offers a result pool func­tion­al­ity to recycle them. In most cases, these samples are design can­di­dates for which full CFD sim­u­la­tions are triggered. 

Now in the next phase, the internal opti­miza­tion is started: A genetic algo­rithm is run on the response surface, to find the global optimum on this initial sur­ro­gate model. Since there can be several optimum designs, the user controls how many of the best design can­di­dates should be picked from the Pareto Front (for multi-objec­tive tasks; oth­er­wise it is simply 1 solution). We labeled this input ​“Solu­tions Con­sid­ered” in the picture above. These best designs are eval­u­ated with CFD again in the next step, and the results are trans­ferred back as infor­ma­tion to the response surface. This approx­i­ma­tion model gets then regen­er­ated by using the new data base and hence steadily improves its quality during each iteration. 

Result Assess­ment

When running a design engine in CAESES®, a table shows up which gives you the current status includ­ing design variable values and objec­tive func­tions. The best design can­di­dates receive a ded­i­cated icon (colored blue with a star) for a quick visual iden­ti­fi­ca­tion in the tree and in the table. 

In the upper left of the table you can find a button for acti­vat­ing the 2D charts. This widget supports you in finding cor­re­la­tions and trends as well as detect­ing relevant design vari­ables in your engi­neer­ing problem. 

Finally, when con­sid­er­ing several com­pet­ing objec­tive func­tions, you can also visu­al­ize the Pareto Front. In the screen­shot below, the blue dots indicate the optimum design can­di­dates. The green ones are valid designs, and the red ones are designs that violate some of the constraints:

More Infor­ma­tion

The inter­face to Dakota as well as the 2D charts are part of the Advance­dOpt add-on of CAESES®. Let us know if you want to have more infor­ma­tion about it — don’t hesitate to drop us a line :-) Finally, check out a related blog post that shows how to create response surfaces in 4 easy steps without using design engines.