In this section, you are going to learn how to execute a series of simple optimizations. We’re going to work with the Paraboloid component that we defined in the basic tutorial. The equation in the Paraboloid component is a function of two input variables. Our goal is to find the minimum value of this equation over a particular range of interest. First, we will solve this problem with no constraints. Then we will add constraints and solve the problem again. Next we’ll take a look at how you can specify analytic derivatives for your components and what effect that has on the optimization. Lastly, We will run a Design of Experiments (DOE) on the problem and plot the results to visually identify the minimum.

If we express the problem as a block diagram, we can see how to set it up in OpenMDAO:

Diagram shows the Paraboloid component and optimizer with arrows going between them representing the variables and minimization objective.

A Simple Optimization Problem

The optimizer is the Driver. Its job is to manipulate the two design variables (x and y) to minimize the output of the paraboloid function (f). Both the driver and the component are contained in an Assembly, which maintains the connections between the driver and the component and knows how to run the whole analysis.

OpenMDAO Home

Previous topic

Simple Optimization

Next topic

Building a Model - Unconstrained Optimization

This Page