Plot the volume that is NOT dominated by the points.
Imagine we are minimizing all three objectives and we have a set with a single point (.5,.5.5) and the ranges go from 0 to 1. Then:
We can plot the cube with corners (.5,.5,.5) (1,1,1) and this corresponds to the volume dominated by the point.
We can plot the cubes with corners (0,0,0), (1,1,.5) and (0,0,0) (.5,1,1) and (0,0,0) (1,.5,1) and this corresponds to the volume NOT dominated by the point (the complement of option 1).
The situation is different if the objectives are maximised. Then plotting the cube (0,0,0) (.5,.5,.5) is correct for option 1 (dominated).
Thus, I think the plot should have 2 options: maximise with default value False and dominated with default value True (option 1, while dominated=False will plot option 2).
When plotting the 3D cube graph: https://auto-optimization.github.io/eafpy/examples/plot_datasets_examples.html#three-objective-cube-graph
There are two main options:
Imagine we are minimizing all three objectives and we have a set with a single point (.5,.5.5) and the ranges go from 0 to 1. Then:
Plotting the cube (0,0,0) (.5,.5,.5) is not correct as this is neither the complement nor the area dominated by the point. It seems the code in https://auto-optimization.github.io/eafpy/examples/plot_datasets_examples.html#three-objective-cube-graph is doing exactly that, thus it is not implementing option 1 nor 2.
The situation is different if the objectives are maximised. Then plotting the cube (0,0,0) (.5,.5,.5) is correct for option 1 (dominated).
Thus, I think the plot should have 2 options:
maximise
with default valueFalse
anddominated
with default valueTrue
(option 1, whiledominated=False
will plot option 2).