[FEATURE] Add ZCAT1-ZCAT20 many-objective benchmark problems

[NicolasRodriguezUribe]

Problem

Add ZCAT1-ZCAT20 many-objective benchmark problems

Proposed Solution

#769

Alternatives

No response

Additional Context

No response

[blankjul]

Thanks for the feature request — the ZCAT problems were merged in PR #769.

One open question before we close this issue: what is the source of the Pareto front reference files stored in pymoo-data?

The current implementation in _calc_pareto_front loads .pf files from the pymoo/pf/ZCAT/ folder in pymoo-data (e.g. ZCAT1.pf, ZCAT1.2D.pf, etc.). These are used for benchmarking and indicator computation, so correctness matters.

Two possibilities:

1. The files were generated by running the ZCAT code itself — which only validates self-consistency, not correctness against the true Pareto front.
2. The files come from the original ZCAT authors or a trusted reference implementation.

Could @NicolasRodriguezUribe (or anyone familiar with the implementation) clarify the origin of those .pf files? Ideally we'd want a PR to pymoo-data with reference fronts derived from the analytical definition or the original authors' code.

[NicolasRodriguezUribe]

Hi again.

If I remember correctly, I extracted them from jMetal.

In addition, as far as I know, the authors of ZCAT included a generator for Pareto-optimal solutions. The problem is that the generator does not guarantee that the points generated will be uniformly distributed. Over 100,000 solutions were generated, added to an unbounded file, and the most diverse ones were selected. And the files are the results.

I hope I've been of some help