Classification in NIMBUS¶

The solution process with NIMBUS is iterative. Since there is usually not only one absolutely right solution, you are asked to ‘guide the solver to a desired direction’. The classification is a process in which the desires of the user are expressed. You can choose which of the function values should be decreased from the current level and which of the functions are less important (i.e. their values can be increased).

Classification background¶

In NIMBUS, preferences are expressed by choosing a class for each of the objective functions.

When considering minimization, the class alternatives are:

<

The value should be minimized.

<=

The value should be minimized until the specified limit is reached.

=

The current value is OK.

>=

Value can be increased. Value should be kept below the specified upper bound.

<>

Value can change freely.

For maximization, directional signs are inverted:

>

The value should be maximized.

>=

The value should be maximized until the specified limit is reached.

=

The current value is OK.

<=

Value can be decreased. Value should be kept above the specified lower bound.

<>

Value can change freely.

If the second or the fourth alternative is selected, you are asked to specify the limits: an aspiration level or an upper/lower bound respectively for the function values;.

Aspiration level defines a desired value for the objective function.
Upper/lower bound defines the limit value that the function should not exceed, if possible.

Since we are dealing with Pareto optimal solutions (compromises) we must be willing to give up something in order to improve some other objective. That is why the classification is feasible only if at least one objective function is in the first two classes and at least one objective function is in the last two classes.

In other words, you must determine at least one function whose value should be made better. However that can not be done if there are no functions whose value can be worsened.

Classification using the widget¶

You may find it useful to follow along with the cylinder notebook while reading this section.

The current solution is shown graphically as a parallel coordinate plot. The classification can be made by either clicking points on the axes, or by manually adjusting the classification selection boxes and limit fields.

By default, maximization and minimization are displayed in their original units. You may wish to reformulate the problem so everything is minimized. This means all maximized functions are negated. To enable this, click settings and then check Reformulate maximization as minimization. To change the default, add the following to the beginning of your notebooks:

from desdeo_vis.conf import conf
conf(max_as_min=True)

Let us assume that the function under classification should be minimized. When you click on the corresponding axis, the system considers the axis value at the point you clicked on as a new limit value and inserts the numerical data into the limit field automatically. Selecting the point below the current solution means that function should be minimized (<=) until that limit is reached. If the point is selected above the current solution, we allow the function value to increase (>=) to that limit. Clicking a point below the whole bar means that the function should be minimized as much as possible (<). Correspondingly, if the value is selected above the whole bar, the function value can change freely (<>). If the current value of some function is satisfactory (=), you can express it by clicking the numeric value beside the bar.

In the case of maximization, the logic above is reversed. For example, if you click a point above the current solution, it indicates that the function should be maximized as much as possible. The desired extreme point of each function is indicated by a small black triangle inside the top or the bottom of each bar.

You can refine the graphical classification by changing the class of each objective function using the selection box or adjusting the value in its limit field.

Classifying the cylinder problem¶

This section walks you through creating a classification with the widget for the cylinder notebook.

The first solution we get from NIMBUS is reasonable. However, we may decide at this point that we want to increase the cylinder’s volume as much as possible, while still keeping the surface area and height difference low.

To do this, we select ( <> ) from the volume dropdown, because we allow (for now) the volume to be varied freely. The next column describes the solution for the surface area function. We want to know how much the volume will be when the surface area is 1900, so we select ( >= ) from the dropdown and enter 1900 into the box. For height difference we select ( <= ).

Classification without the widget¶

It is also possible to make a classification without the widget. Possibly reasons you might do this are because you are constructing an artificial decision maker, you are making your own preference selection widget, or because you are unable to use Jupyter notebook. In this case, maximizations are always reformulated as minimizations.

The preference information is specified using a Python object called desdeo.preference.NIMBUSClassification. If we wanted to make the same classification as above, it can be done like so:

 classification = NIMBUSClassification(method, [
('>=', 1205.843),
('<=', 378.2263),
('=', 0.0)]
 )

Specifying subproblems¶

We can specify the maximum number of new solutions generated by the classification given. It’s also possible to specify particular scalarization functions. See desdeo.method.NIMBUS.next_iteration() for more information.