Basic usage
===========

PolyNondom expects either a feasible domain and corresponding
objectives or pre-computed points in objective space.

Usage with a feasible domain and objectives
++++++++++++++++++++++++++++++++++

Let's assume we want to compute and visualise the non-dominated points
of an assignment problem (with 4 agents and 4 jobs). Furthermore, let
*/tmp/objs.txt* be the file with the objective functions having the
following content:

| [3, 6, 4, 5, 2, 3, 5, 4, 3, 5, 4, 2, 4, 5, 3, 6]
| [2, 3, 5, 4, 5, 3, 4, 3, 5, 2, 6, 4, 4, 5, 2, 5]
| [4, 2, 4, 2, 4, 2, 4, 6, 4, 2, 6, 3, 2, 4, 5, 3]
|
   
Using the python shell we could do the following:

``import polynondom as pnd``

``objs = pnd.Objectives.read("/tmp/objs.txt", delimiter=',')``  # create *Objectives* instance

``ad = pnd.AssignmentDomain(4)`` # create *AssignmentDomain* instance

``poly = pnd.PolyNondom.compute_points(ad, objs)`` # create *PolyNondom* instance

``print("computed", poly)``  # print points sets to shell

``poly.visualise('n', my_color="blue")``  # visualise non-dominated points

``poly.save_figure("/tmp/my_figure.png", dpi=150, azimuth=96, elevation=21)`` # save visualisation to file

The result is:

.. image:: nondom_points.png

Usage with pre-computed points
++++++++++++++++++++++++++++++
   
Let's assume we have pre-computed (feasible) points of a bi-criteria
knapsack problem and want to visualise the points. Let
*/tmp/points.txt* be the file with the pre-computed points having the
following content:

| [ 13 4 ] 
| [ 15 6 ] 
| [ 7 10 ] 
| [ 3 19 ]
| [ 6 10 ]
| [ 12 12 ]
| 

Using the python shell we could do the following:

``import polynondom as pnd``

``poly = pns.PolyNondom.read_points("/tmp/points.txt", delimiter=' ')`` # read points from file

``poly.visualise('nd')`` # visualise non-dominated points (in red) and dominated points (in black)

``poly.save_figure('/tmp/points.png', azimuth=-89, elevation=88, dpi=150)`` # save visualisation to file

The result is:

.. image:: points.png