Implement NSGA-III #4436

Alnusjaponica · 2023-02-17T08:47:51Z

Motivation

Implement NSGA-III algorithm, which is a modified version of NSGA-II for many-objective optimization problem. This algorithm is also desired at #4075.

Description of the changes

Implement NSGAIIISampler which realizes NSGA-III algorithm. The main change in the algorithms is the strategy used to determine who survives from the boundary front, where NSGA-II uses crowding distance while NSGA-III uses reference points.
The difference between NSGA-II and NSGA-III in implementation is the following two points:

NSGAIIISampler has attribute reference_points used in _select_elite_population()
_crowding_distance_sort() called from _select_elite_population() is replaced with new procedure proposed in NSGA-III algorithm.

Other part of nsgaiii.py is almost the same as nsgaii/_sampler.py.

As confirmed in the following benchmark results on test problems, NSGA-III is competitive enough compared to NSGA-II in terms of hyper volume metric.

In addition, the results of NSGA-III tends to be more diverse as observed in the following plots.

This is because the crowding distance is set to infinite when an individual has the largest or smallest value on any of the objective axes, and such individuals always survive. Therefore, the resulting points of NSGA-II tend to concentrate near the axes (i.e., take extreme values) in situations where the dimension is large and the first front often becomes the boundary rank front.

Alnusjaponica · 2023-02-24T04:20:57Z

The detailed descriptions of the experiment are as follows:

How hypervolume is improved as number of trials is increased
This experiment
- compares NSGA-II and NSGA-III with dividing parameter p=5,8
- runs 5000 trials 5 times for each setting
- uses WFG6 with objective dimension 3, 5, 8
- determines reference point for hypervolume as the nadir point of best_trials at each step (number of trials = 500,1000,...5000)
What the geometrical feature of the results is like
This experiment
- compares NSGA-II and NSGA-III with dividing parameter p=5
- run 3000 trials and extract best trials among all 6000 trials
- uses DTLZ1 with objective dimension 9
- plots the objective values by 3 dimension

codecov-commenter · 2023-03-02T14:48:16Z

Codecov Report

Merging #4436 (7cae1e3) into master (906f6a6) will increase coverage by 0.01%.
The diff coverage is 97.02%.

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@@            Coverage Diff             @@
##           master    #4436      +/-   ##
==========================================
+ Coverage   90.88%   90.90%   +0.01%     
==========================================
  Files         184      186       +2     
  Lines       13959    14269     +310     
==========================================
+ Hits        12687    12971     +284     
- Misses       1272     1298      +26

Impacted Files	Coverage Δ
optuna/samplers/_nsgaiii.py	`97.01% <97.01%> (ø)`
optuna/samplers/__init__.py	`100.00% <100.00%> (ø)`

... and 11 files with indirect coverage changes

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optuna/samplers/nsgaiii.py

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

HideakiImamura

Thanks for the PR. I have some early comments and questions. I will review the details of _normalize,_associate, and _niching in the next week.

optuna/samplers/nsgaiii.py

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

…optuna into implement-nsgaiii

HideakiImamura

Thanks for your long running. LGTM!

toshihikoyanase · 2023-05-08T03:05:28Z

I found that the module of optuna.samplers.nsgaii was public. I think users import NSGAIIISampler like from optuna.samplers import NSGAIIISampler like the other samplers, and optuna.samplers.nsgaii does not provide any public classes/functions excepting for NSGAIIISampler. So, I guess we can rename nsgaiii.py to _nsgaiii.py.

Alnusjaponica · 2023-05-08T13:52:48Z

Thanks for your comment. I renamed the module and changed the import paths.

toshihikoyanase

Thank you for your update. I found two functions which are not used in the test cases. Could you check them?

tests/samplers_tests/test_nsgaiii.py

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

toshihikoyanase

Thanks for your update. I have two minor comments.

optuna/samplers/_nsgaiii.py

toshihikoyanase

The change basically looks good to me. Let me add some minor comments.

optuna/samplers/_nsgaiii.py

toshihikoyanase · 2023-05-11T05:47:03Z

optuna/samplers/_nsgaiii.py

+    asf_value = np.max(
+        np.einsum("nm,dm->dnm", objective_matrix, weights),
+        axis=2,
+    )


I guess this corresponds to eq. 4 of https://www.egr.msu.edu/~kdeb/papers/k2012009.pdf. We might mention it in the code comment, but we can work on it in a follow-up PR.

toshihikoyanase · 2023-05-11T05:55:07Z

optuna/samplers/_nsgaiii.py

+    perpendicular_vectors_to_reference_lines = np.einsum(
+        "ni,pi,p,pm->npm",
+        objective_matrix,
+        reference_points,
+        1 / reference_point_norm_squared,
+        reference_points,
+    )
+    distance_from_reference_lines = np.linalg.norm(
+        objective_matrix[:, np.newaxis, :] - perpendicular_vectors_to_reference_lines,
+        axis=2,
+    )


ditto. This seems to correspond to L5 to 7 of Algorithm 3 in https://www.egr.msu.edu/~kdeb/papers/k2012009.pdf. We'd like to improve the readability in a follow-up PR.

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

toshihikoyanase

LGTM. Thank you for completing such a long-running PR!

We have possible follow-up tasks, but I don't think they are critical:

Implement NSGA-III

a7b139c

github-actions bot added the optuna.samplers Related to the `optuna.samplers` submodule. This is automatically labeled by github-actions. label Feb 17, 2023

Alnusjaponica marked this pull request as ready for review February 17, 2023 13:26

cross32768 requested review from toshihikoyanase and HideakiImamura February 20, 2023 03:29

toshihikoyanase added the feature Change that does not break compatibility, but affects the public interfaces. label Feb 20, 2023

cross32768 assigned toshihikoyanase and HideakiImamura Feb 20, 2023

cross32768 removed request for toshihikoyanase and HideakiImamura February 20, 2023 05:21

Alnusjaponica and others added 3 commits March 2, 2023 16:02

Merge branch 'optuna:master' into implement-nsgaiii

c6da216

Remove duplication

bc1a41a

Fix flake8 error

7dc2e64

Alnusjaponica added 2 commits March 3, 2023 13:45

Add test from test_nsgaii

dd68af5

Apply changes in nsgaii sampler

df06287

toshihikoyanase reviewed Mar 3, 2023

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Alnusjaponica and others added 6 commits March 3, 2023 15:55

Cleanup test_nsgaiii.py

217340b

Fix assert False

e73dc46

Correct indent in docstring

9253d5e

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Remove unnecessary blank

37a83cd

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Add NSGAIIISampler to the document

a89c3c6

Fix docstring

6ea5ba0

HideakiImamura reviewed Mar 3, 2023

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Alnusjaponica added 3 commits March 9, 2023 10:27

Fix rng

2ac8756

Revise variable name

86d6fc1

Correct rng usage

fe20e04

Alnusjaponica and others added 9 commits April 27, 2023 15:34

Fix typo in optuna/samplers/nsgaiii.py

9bfdd1e

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Fix argument notation in docstrings in optuna/samplers/nsgaiii.py

1611f13

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Fix docstrings in optuna/samplers/nsgaiii.py

2b376d3

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Sort argument of NSGAIIISampler

83203eb

Merge branch 'implement-nsgaiii' of https://github.com/Alnusjaponica/…

594ec25

…optuna into implement-nsgaiii

Add experimental_class decorator

721b5ee

Sort attribute initialization

c5831ba

Privatize reference_point

62708e2

Remove reference_points property test

9efa849

HideakiImamura approved these changes May 1, 2023

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Rename nsgaiii.py to _nsgaiii.py

11f35e5

toshihikoyanase reviewed May 9, 2023

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Alnusjaponica and others added 4 commits May 9, 2023 12:32

isort samplers/__init__.py

6d680e9

Remove _nan_equal()

dc0ca4e

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Remove unused _create_frozen_trial()

3042ca8

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Remove unused typing.Any

7eb4e31

toshihikoyanase reviewed May 11, 2023

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Alnusjaponica and others added 6 commits May 11, 2023 15:47

Fix exception type

efb3c4d

Fix typo in optuna/samplers/nsgaiii.py

6f88e89

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Make if condition clear in _preserve_niche_individuals()

3cee822

Co-authored-by: Toshihiko Yanase <toshihiko.yanase@gmail.com>

Add period to docstring

6207be1

Add comment for _multi_choose()

aadb3c4

Fix exception type

7cae1e3

toshihikoyanase approved these changes May 11, 2023

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toshihikoyanase merged commit 3d3aeec into optuna:master May 11, 2023

toshihikoyanase added this to the v3.2.0 milestone May 11, 2023

Alnusjaponica deleted the implement-nsgaiii branch May 11, 2023 09:34

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Implement NSGA-III #4436

Implement NSGA-III #4436

Alnusjaponica commented Feb 17, 2023 •

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Implement NSGA-III #4436

Implement NSGA-III #4436

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Alnusjaponica commented Feb 17, 2023 • edited Loading

Motivation

Description of the changes

Alnusjaponica commented Feb 24, 2023 • edited Loading

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Alnusjaponica commented Feb 17, 2023 •

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