A brief overview of the concept of objective functions and decision or design variables.
This video is part of an introductory optimization series.
TRANSCRIPT:
Hello, and welcome to Introduction To Optimization. This video covers some basic optimization vocabulary.
Like any technical field, optimization has its own set of words that may be unfamiliar to anyone just starting out. To make complicate things further, different sub-fields within optimization use different words to describe the same ideas. In the next few videos, we’ll go through some of the basic ideas in optimization, the words used to describe them, and some alternative words you might hear. This video will cover objective functions and design variables.
Objective Function/CVs
The objective function is the value that you are trying to optimize. For example, if you were trying to make a square as big as possible, the area would be the objective function. One of the main goals of optimization is to try to improve the objective value, whether that means minimizing it, maximizing it, or trying to bring it to a certain value. Looking at the objective function value is one of the most common ways to tell how well an optimization has worked. In the case where there are multiple objectives, they are usually summed, multiplied, or otherwise combined to form a single value. In dynamic optimization, control variables also form part of the objective function.
Optimization problems are commonly written in the form minimize f(x). Here, f is the objective function. Other examples of objective functions might be to minimize cost, maximize speed, minimize weight, maximize profit, or minimize waste. The specific objective function chosen depends on the problem to be solved, and your goals in solving it.
Decision/design/manipulated variables
Decision variables are the inputs to your problem that your optimizer is allowed to change to try to improve the objective function value. In our square example from before, the decision variables would be the lengths of the two sides. These variables are also called design variables, or manipulated variables. As was stated before, optimization problems are commonly written in the form minimize f(x). Here, x represents one or more decision variables. In general, the more decision variables there are, the more difficult an optimization problem becomes to solve.
In Summary
The objective function is the value that you, and hopefully your optimization program are trying to optimize. The objective function is either minimized or maximized
Decision variables are the values that the optimization algorithm is allowed to choose or change. They are also known as design variables or manipulated variables.