Add NSGAIISampler with TPESampler warmup

package/samplers/nsgaii_with_tpe_warmup/LICENSE

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+MIT License
+
+Copyright (c) 2024 Shuhei Watanabe
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

package/samplers/nsgaii_with_tpe_warmup/README.md

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+---
+author: Shuhei Watanabe
+title: NSGAIISampler Using TPESampler for the Initialization
+description: This sampler uses TPESampler for the initialization to warm start.
+tags: [sampler, tpe, nsgaii, warmstart]
+optuna_versions: [4.1.0]
+license: MIT License
+---
+
+## Abstract
+
+This sampler uses `TPESampler` instead of `RandomSampler` for the initialization of `NSGAIISampler`.
+
+## APIs
+
+- NSGAIIWithTPEWarmupSampler
+
+This class takes the identical interface as the Optuna [`NSGAIISampler`](https://optuna.readthedocs.io/en/stable/reference/samplers/generated/optuna.samplers.NSGAIISampler.html).
+
+## Example
+
+```python
+from __future__ import annotations
+
+import optuna
+import optunahub
+
+
+def objective(trial: optuna.Trial) -> tuple[float, float]:
+    x = trial.suggest_float("x", -5, 5)
+    y = trial.suggest_float("y", -5, 5)
+    return x**2 + y**2, (x - 2) ** 2 + (y - 2) ** 2
+
+
+package_name = "samplers/nsgaii_with_tpe_warmup"
+sampler = optunahub.load_module(package=package_name).NSGAIIWithTPEWarmupSampler()
+study = optuna.create_study(sampler=sampler, directions=["minimize"]*2)
+study.optimize(objective, n_trials=60)
+
+```

package/samplers/nsgaii_with_tpe_warmup/__init__.py

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+from __future__ import annotations
+
+from typing import Any
+from typing import TYPE_CHECKING
+
+from optuna.samplers import NSGAIISampler
+from optuna.samplers import TPESampler
+from optuna.samplers.nsgaii._sampler import _GENERATION_KEY
+
+
+if TYPE_CHECKING:
+    from optuna import Study
+    from optuna.distributions import BaseDistribution
+    from optuna.trial import FrozenTrial
+
+
+MAX_INT32 = (1 << 31) - 1
+
+
+class NSGAIIWithTPEWarmupSampler(NSGAIISampler):
+    def sample_relative(
+        self,
+        study: Study,
+        trial: FrozenTrial,
+        search_space: dict[str, BaseDistribution],
+    ) -> dict[str, Any]:
+        if trial.number < self._population_size:
+            seed = self._rng.rng.randint(MAX_INT32)
+            sampler = TPESampler(
+                multivariate=True, constraints_func=self._constraints_func, seed=seed
+            )
+            study._storage.set_trial_system_attr(trial._trial_id, _GENERATION_KEY, 0)
+            return sampler.sample_relative(study, trial, search_space)
+
+        return super().sample_relative(study, trial, search_space)

package/samplers/nsgaii_with_tpe_warmup/example.py

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+from __future__ import annotations
+
+import optuna
+import optunahub
+
+
+def objective(trial: optuna.Trial) -> tuple[float, float]:
+    x = trial.suggest_float("x", -5, 5)
+    y = trial.suggest_float("y", -5, 5)
+    return x**2 + y**2, (x - 2) ** 2 + (y - 2) ** 2
+
+
+package_name = "samplers/nsgaii_with_tpe_warmup"
+sampler = optunahub.load_module(package=package_name).NSGAIIWithTPEWarmupSampler()
+study = optuna.create_study(sampler=sampler, directions=["minimize"] * 2)
+study.optimize(objective, n_trials=60)