Optimization

Optimization is a numerical technique for finding the minimum (or maximum) of a specific function given a number of variables, and perhaps some constraints on their values. Zebulon has an optimization module which can handle a wide variety of functions, including a overall measure of error between a large set of file-file comparisions. Many FEA optimization codes are meant as design tools, altering geometry or what ever to maximize the efficiancy of design. Although this capability exists in Zebulon also, the use of optimization with FEA has a much broader range of application.

One of the greatest problems when doing FEA is finding the appropriate set of boundary conditions to apply. One component in the solution of this problem is a FEA code must be able to apply a very diverse range of boundary conditions -- something Zebulon is particularly good at. But even still, the values of these BCs may simply be unknown... this is an optimization probem. Another issue is the characterization of material coefficients for complex models.

Here is an example function with many local minima. Most optimization methods will come to rest in one of the local minima which is not the global minimum. Unfortunately for us, functions with many local minima are extremely common in the real world.

Here is an optimization history for the above function using Zebulons optimizer with the genetic algorithm chosen. This algorithm was able to find the global minimum by using a randomness in genetic evolution of a "population" of trial points.

Up: Z-mat Software
Back: ZebFront
Next: Simulation