[QUESTIONS/FEATURE] pygmo.decompose_objectives

[Tomalwo]

Is your feature request related to a problem? Please describe.

I have three questions about pygmo.decompose_objectives.

1. Does this function assume that the objectives are normalized, i.e., all in the range [0,1]?

2. Should the ref_point be the "best" point or the "worst" point? I assume the best point, but in the example it looks like the worst point (assuming minimization).

3. The Tchebycheff decomposition is not "augmented", correct? (See pages 7 and 8 in this paper.)

Describe the solution you'd like

It would be helpful to update the documentation / example accordingly.

It would be helpful to implement the augmented Tchebycheff decomposition.

Describe alternatives you've considered

I have implemented the augmented Tchebycheff decomposition myself, but it would still be convenient if it were included in the library.

[bluescarni]

Gonna ping @darioizzo on this one.

[Tomalwo]

Thanks!

[darioizzo]

@Tomalwo

• The decompose does not normailize the objectives in [0,1] and will apply the formulas regardless on the units. For the Tchebyceff decomposition this may indeed an issue and the user needs to pass objectives that are scaled as for the formulas appied to be effective
• the ref_point is typically the best point as you mentioned. The code will work anyway and it is up to the user to provide a meaningful ref_point. What example are you referring to that is using the worst point?
• The implemented method is the one in https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4358754, not augmented.

PR are welcome if you feel you want to add your augmented method to the code base ... otherwise we may implement it when we revisit moea/D which is planned but not anytime soon.