make more use of `moocore`

[MLopez-Ibanez]

Now that moocore is a dependency of pymoo (#667 ), you could make more use of it:

• Fast dominance filtering and Pareto ranking: https://multi-objective.github.io/moocore/python/reference/functions.dominance.html
• IGD+ computation: https://multi-objective.github.io/moocore/python/reference/functions.metrics.html
• Provide epsilon metric: https://multi-objective.github.io/moocore/python/reference/functions.metrics.html#epsilon-metric
• HV approximation: https://multi-objective.github.io/moocore/python/reference/generated/moocore.hv_approx.html
• HV contributions (HVC): https://multi-objective.github.io/moocore/python/reference/generated/moocore.hv_contributions.html

There are more things in moocore, like weighted hypervolume, empirical attainment function and Vorob'ev expectation and deviation, but those would require more work to make them available and useful to the users of pymoo.

[blankjul]

does moocore also have HVC? Approximate HV?

[MLopez-Ibanez]

https://multi-objective.github.io/moocore/python/reference/generated/moocore.hv_contributions.html (but the current implementation is only efficient for 2D and uses the naive algorithm for dimension > 2)

https://multi-objective.github.io/moocore/python/reference/generated/moocore.hv_approx.html (it is a Python implementation, so not as fast as it could be, but I will replace it with a much faster C implementation soon) It should be faster and more precise than anything you have in pymoo.

[blankjul]

can you check out my commit above?

with the test_hvc_monte_carlo test case I am getting some different results when comparing the approximate hvs.
i have commented out how I would use moocore for this.

[MLopez-Ibanez]

• Could you tell me which results are different from what is expected? Having a testcase that I could run of current pymoo vs moocore would help.
• In moocore, seed can be a numpy.random.Generator as the documentation says, so you don't need to pass an int if you already have Generator.
• In moocore v0.1.8 (not released yet), there are 2 methods for hv_approx(). The default is DZ2019-HW, which is deterministic, but you may wish to use DZ2019-MC, which is more similar to what you are currently using.
• I have not implemented an approximated HVC. There are several papers about how to do that, so it should be possible. In the meantime, I could simply copy what pymoo is doing. Is there any reference that explains the algorithm used by pymoo?
• What is n_exclusive?
• I don't understand how the test code works. Don't you need to call mc.calc() or mc.add() ?
  

  pymoo/tests/indicators/test_hv.py

  Lines 66 to 69 in 9b54237

  	exact = ExactHypervolume(ref_point).add(F)
  	mc = ApproximateHypervolume(ref_point, F=F, n_samples=20_000)
  	assert np.allclose(exact.hv, mc.hv, rtol=0, atol=1e-2)

[blankjul]

let me work on a clean PR. this one became a little messy.

I am currently working on using a RandomState to not change the global random seed while running algorithms. After that I will be coming back to HV.

Do you already know when the new version will be released?

[MLopez-Ibanez]

See https://multi-objective.github.io/moocore/python/whatsnew/index.html#version-0-1-8-15-07-2025

[MLopez-Ibanez]

I have added benchmarks of the approximation of the hypervolume: https://multi-objective.github.io/moocore/python/#approximation-of-the-hypervolume