For our application, we have several two-dimensional visualizations that we need to explain. The first is the two-dimensional plot of the function optimization, be it maximized or minimized. This visualization is shown as follows. Remember, for this we are using Microsoft Chart control, which is available from: https://www.microsoft.com/en-us/download/details.aspx?id=14422:

For each particle that we are plotting (up to a maximum of 10), we will have a different marker style. A marker is the diamonds, circles, x's, and so on that you see plotted in the preceding diagram. We will also rotate colors based upon each particle being a different color. If you are not viewing this book in color, you hopefully will have shades of grey.

The lines you are seeing in the preceding diagram (or, to be more technically accurate, the splines you are seeing above them) are the plots of each particle in the swarm. The global optimum value (gbest) is the black diamond in the middle of the plot area. As you can see, we always remain within the bounds of our hyperparameters.