3.2 the Pareto Frontier

The general aim in single-objective optimization is to find one global optimum design. Instead in a multi-objective optimizazion problem - like the one examined in this tutorial - the aim is to find a set of non-dominated solutions, i.e. the designs that cannot be improved in one objective without deteriorating the values of the remaining objectives. This set is called the Pareto Frontier.

Now we introduce another kind of chart, the Scatter Chart : to access its icon, click on the little black triangle beside the History Chart icon, and then select the proper icon. It appears the Scatter Chart Creation dialog: select both the objectives Cost and D by clicking on them, while keeping the SHIFT or CTRL key pressed (see Fig. T3.2.1).

Fig. T3.2.1: the Scatter Chart Creation dialog.

Fig. T3.2.2: the Scatter Chart.

In the Scatter Chart window we have a graphic of the designs, where in absissa and in ordinate there are the items selected in the Scatter Chart Creation dialog.

You can interact with any chart in several ways, as seen in previous section. Now it can be useful to zoom the interesting part of the graphic: you can see the selection yellow rectangle in Fig. T3.2.2, and the result of the zooming action in Fig. T3.2.3 (SHIFT + drag to zoom).

Fig. T3.2.3: zoomed Scatter Chart.

Since the problem is to minimize the two objectives, the Pareto Frontier will be constituted by the designs located in the bottom-left border of the cluster formed by the set of all the points.
To mark the designs belonging to the Pareto Frontier, select Edit|Mark|Mark Pareto Designs|Only Real from the menu.
This set of designs represent the "solution" of our optimization problem.

Now, in order to visualize better the Pareto Frontier, we can do a useful exercise of table editing.
Return to the Design Table window by clicking on the proper bottom bar.
Select the unmarked designs from the menu with Edit|Select|Select Unmarked (see Fig. T3.2.4); then remove them selecting Edit|Cut or clicking on the corresponding icon . Now return to the Scatter Chart: the graphic should look like Fig. T3.2.5.

Fig. T3.2.4: Designs table: the unmarked designs are now selected.

Fig. T3.2.5: the Pareto Frontier.