Setting Up an Optimization Analysis   

Cost Function

Optimetrics manipulates the model's design variable values to find the minimum location of the cost function; therefore, you should define the cost function so that a minimum location is also the optimum location. For example, if you vary a design to find the maximum transmission from Wave Port 1 to Wave Port 2 (S₂₁=>1), define the cost function to be -mag(S(WavePort2,WavePort1)).

When using the Quasi Newton optimizer, which is appropriate for designs that are not sensitive to noise, the best cost function is a smooth, second-order function that can be approximated well by quadratics in the vicinity of the minimum; the slope of the cost function should decrease as Optimetrics approaches the optimum value. The preferred cost function takes values between 0 and 1. In practice, most functions that are smooth around the minimum are acceptable as cost functions. Most importantly, the cost function should not have a sharp dip or pole at the minimum. A well designed cost function can significantly reduce the optimization process time.

The cost function is defined in the Setup Optimization dialog box when you set up an optimization analysis. If you know the exact syntax of the solution quantity on which you want to base the cost function, you can type it directly in the Calculation text box. You can also use Setup Calculations to add a solution quantity via the Add/Edit Calculation dialog box, or to create an output variable that represents the solution quantity in the Output Variables dialog box.

Related Topics

Adding a Cost Function

Acceptable Cost

Cost Function Noise

Linear Constraints

Goal Weight

Step Size

Explanation of L1, L1, Norm Costs in Optimization