From 902f892c287b2836a071525e56eb98325c301a9f Mon Sep 17 00:00:00 2001 From: bamboo1997 Date: Wed, 21 Aug 2024 15:22:05 +0900 Subject: [PATCH 1/3] Add implementation of the Nelder-Mead method. --- package/samplers/nelder_mead/LICENSE | 22 ++ package/samplers/nelder_mead/README.md | 87 ++++++ package/samplers/nelder_mead/__init__.py | 4 + package/samplers/nelder_mead/example.py | 55 ++++ .../nelder_mead/generate_initial_simplex.py | 104 +++++++ package/samplers/nelder_mead/images/nm.png | Bin 0 -> 333237 bytes package/samplers/nelder_mead/nelder_mead.py | 293 ++++++++++++++++++ package/samplers/nelder_mead/requirements.txt | 1 + 8 files changed, 566 insertions(+) create mode 100644 package/samplers/nelder_mead/LICENSE create mode 100644 package/samplers/nelder_mead/README.md create mode 100644 package/samplers/nelder_mead/__init__.py create mode 100644 package/samplers/nelder_mead/example.py create mode 100644 package/samplers/nelder_mead/generate_initial_simplex.py create mode 100644 package/samplers/nelder_mead/images/nm.png create mode 100644 package/samplers/nelder_mead/nelder_mead.py create mode 100644 package/samplers/nelder_mead/requirements.txt diff --git a/package/samplers/nelder_mead/LICENSE b/package/samplers/nelder_mead/LICENSE new file mode 100644 index 00000000..b8efa3cd --- /dev/null +++ b/package/samplers/nelder_mead/LICENSE @@ -0,0 +1,22 @@ + +MIT License + +Copyright (c) 2024 Shintaro Takenaga + +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. diff --git a/package/samplers/nelder_mead/README.md b/package/samplers/nelder_mead/README.md new file mode 100644 index 00000000..36bec090 --- /dev/null +++ b/package/samplers/nelder_mead/README.md @@ -0,0 +1,87 @@ +--- +author: Shintaro Takenaga +title: NelderMead Sampler +description: Local search heuristic using a simplex method with effective initialization. +tags: [sampler, heuristic, local search, Nelder-Mead] +optuna_versions: [3.6.1] +license: MIT License +--- + +## Abstract + +This Nelder-Mead method implemenation employs the effective initialization method proposed by Takenaga et al., 2023. + +![The search view](images/nm.png) + +## Class or Function Names + +- NelderMeadSampler + +## Installation + +```bash +pip install -r https://raw.githubusercontent.com/optuna/optunahub-registry/main/package/samplers/nelder_mead/requirements.txt +``` + +## Example + +```python +from __future__ import annotations + +import optuna +from optuna.distributions import BaseDistribution +from optuna.distributions import FloatDistribution +import optuna.study.study +import optunahub + + +def objective(x: float, y: float) -> float: + return x**2 + y**2 + + +def optuna_objective(trial: optuna.trial.Trial) -> float: + x = trial.suggest_float("x", -5, 5) + y = trial.suggest_float("y", -5, 5) + return objective(x, y) + + +if __name__ == "__main__": + # You can specify the search space before optimization. + # This allows the sampler to generate the initial simplex based on the specified search space at the first trial. + search_space: dict[str, BaseDistribution] = { + "x": FloatDistribution(-5, 5), + "y": FloatDistribution(-5, 5), + } + module = optunahub.load_module( + package="samplers/nelder_mead", + ) + + # study.optimize can be used with an Optuna-style objective function. + sampler = module.NelderMeadSampler(search_space, seed=123) + study = optuna.create_study(sampler=sampler) + study.optimize(optuna_objective, n_trials=100) + print(study.best_params, study.best_value) +``` + +## Others + +### Reference + +Takenaga, Shintaro, Yoshihiko Ozaki, and Masaki Onishi. "Practical initialization of the Nelder–Mead method for computationally expensive optimization problems." Optimization Letters 17.2 (2023): 283-297. + +See the [paper](https://doi.org/10.1007/s11590-022-01953-y) for more details. + +### BibTeX + +```bibtex +@article{takenaga2023practical, + title={Practical initialization of the Nelder--Mead method for computationally expensive optimization problems}, + author={Takenaga, Shintaro and Ozaki, Yoshihiko and Onishi, Masaki}, + journal={Optimization Letters}, + volume={17}, + number={2}, + pages={283--297}, + year={2023}, + publisher={Springer} +} +``` diff --git a/package/samplers/nelder_mead/__init__.py b/package/samplers/nelder_mead/__init__.py new file mode 100644 index 00000000..3878f3b1 --- /dev/null +++ b/package/samplers/nelder_mead/__init__.py @@ -0,0 +1,4 @@ +from .nelder_mead import NelderMeadSampler + + +__all__ = ["NelderMeadSampler"] diff --git a/package/samplers/nelder_mead/example.py b/package/samplers/nelder_mead/example.py new file mode 100644 index 00000000..0fbf9658 --- /dev/null +++ b/package/samplers/nelder_mead/example.py @@ -0,0 +1,55 @@ +from __future__ import annotations + +import optuna +from optuna.distributions import BaseDistribution +from optuna.distributions import FloatDistribution +import optuna.study.study +import optunahub + + +def objective(x: float, y: float) -> float: + return x**2 + y**2 + + +def optuna_objective(trial: optuna.trial.Trial) -> float: + x = trial.suggest_float("x", -5, 5) + y = trial.suggest_float("y", -5, 5) + return objective(x, y) + + +if __name__ == "__main__": + # You can specify the search space before optimization. + # This allows the sampler to generate the initial simplex based on the specified search space at the first trial. + search_space: dict[str, BaseDistribution] = { + "x": FloatDistribution(-5, 5), + "y": FloatDistribution(-5, 5), + } + module = optunahub.load_module( + package="samplers/nelder_mead", + ) + + sampler = module.NelderMeadSampler(search_space, seed=123) + study = optuna.create_study(sampler=sampler) + # Ask-and-Tell style optimizaiton. + for i in range(100): + trial = study.ask(search_space) + value = objective(**trial.params) + study.tell(trial, value) + print( + f"Trial {trial.number} finished with values: {value} and parameters: {trial.params}. " + f"Best it trial {study.best_trial.number} with value: {study.best_value}" + ) + print(study.best_params, study.best_value) + + # study.optimize can be used with an Optuna-style objective function. + sampler = module.NelderMeadSampler(search_space, seed=123) + study = optuna.create_study(sampler=sampler) + study.optimize(optuna_objective, n_trials=100) + print(study.best_params, study.best_value) + + # Without the search_space argument, the search space is estimated during the first trial. + # In this case, independent_sampler (default: RandomSampler) will be used instead of the Nelder-Mead algorithm for the first trial. + sampler = module.NelderMeadSampler(seed=123) + study = optuna.create_study(sampler=sampler) + study.optimize(optuna_objective, n_trials=100) + print(study.best_params, study.best_value) diff --git a/package/samplers/nelder_mead/generate_initial_simplex.py b/package/samplers/nelder_mead/generate_initial_simplex.py new file mode 100644 index 00000000..1114e3d9 --- /dev/null +++ b/package/samplers/nelder_mead/generate_initial_simplex.py @@ -0,0 +1,104 @@ +# This code is taken from aiaccel (https://github.com/aistairc/aiaccel) distributed under the MIT license. +# +# MIT License +# +# Copyright (c) 2022 National Institute of Advanced Industrial Science and Technology (AIST), Japan, All rights reserved. +# +# 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. + +import numpy as np + + +def generate_initial_simplex( + dim: int, + edge: float = 0.5, + centroid: float = 0.5, + rng: np.random.RandomState | None = None, +) -> np.ndarray: + """ + Generate an initial simplex with a regular shape. + """ + + assert 0.0 <= centroid <= 1.0, "The centroid must be exists in the unit hypercube. " + + assert ( + 0.0 < edge <= max(centroid, 1 - centroid) + ), f"Maximum edge length is {max(centroid, 1 - centroid)}" + + # Our implementation normalizes the search space to unit hypercube [0, 1]^n. + bdrys = np.array([[0, 1] for _ in range(dim)]) + + # Generate regular simplex. + initial_simplex = np.zeros((dim + 1, dim)) + b = 0.0 + for i in range(dim): + c = np.sqrt(1 - b) + initial_simplex[i][i] = c + r = ((-1 / dim) - b) / c + for j in range(i + 1, dim + 1): + initial_simplex[j][i] = r + b = b + r**2 + + # Rotate the generated initial simplex. + if rng is not None: + V = rng.random((dim, dim)) + else: + V = np.random.random((dim, dim)) + + for i in range(dim): + for j in range(0, i): + V[i] = V[i] - np.dot(V[i], V[j]) * V[j] + V[i] = V[i] / (np.sum(V[i] ** 2) ** 0.5) + for i in range(dim + 1): + initial_simplex[i] = np.dot(initial_simplex[i], V) + + # Scale up or down and move the generated initial simplex. + for i in range(dim + 1): + initial_simplex[i] = edge * initial_simplex[i] + Matrix_centroid = initial_simplex.mean(axis=0) + initial_simplex = initial_simplex + (centroid - Matrix_centroid) + + # Check the condition of the generated initial simplex. + if check_initial_simplex(initial_simplex, bdrys): + generate_initial_simplex(dim, edge, centroid) + y = np.array(initial_simplex) + + return y + + +def check_initial_simplex(initial_simplex: np.ndarray, bdrys: np.ndarray) -> bool: + """ + Check whether there is at least one vertex of the generated simplex in the search space. + """ + dim = len(initial_simplex) - 1 + if dim + 1 > sum([out_of_boundary(vertex, bdrys) for vertex in initial_simplex]): + return False + return True + + +def out_of_boundary(y: np.ndarray, bdrys: np.ndarray) -> bool: + """ + Check whether the input vertex is in the search space. + """ + for yi, b in zip(y, bdrys): + if float(b[0]) <= float(yi) <= float(b[1]): + pass + else: + return True + return False diff --git a/package/samplers/nelder_mead/images/nm.png 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z(Vq>4L39*2HLNTzw&gnngT1s5n*Ula&iY|sb;V#K4uG&VsSn|XNQ0*uZxkM@CLefs zu%)fd;X=nrxpQ4zU0^LpfN*b9RLlgED$i>yPrp&%oEtqkLhx2*29ra~ii-w2m-TFctU?wow)klSL!43-_u4`y&#woQq1TV98y#mxt z#nSW}hsDorqobpw6`kb~3t1Ba5j<5(U6imTUMhI$`}h8aU#Nt2j;lXPIaNe>`h)Fp|m 1`. + + 2. If it is run "define-by-run" (no search space defined), the first trial is ignored because this trial is not involved in the Nelder-Mead algorithm. + + 3. When a sampled solution is out of search space, our implementation employs the extreme barrier method, which is the box constraint handling method. + This method provides a large constraint value (= "inf", representing infeasible) as the objective function value. + + Args: + search_space: + A dictionary of :class:`~optuna.distributions.BaseDistribution` that defines the search space. + If this argument is :obj:`None`, the search space is estimated during the first trial. + In this case, ``independent_sampler`` is used instead of the Nelder-Mead algorithm during the first trial. + + centroid: + A centroid of the initial simplex. + + edge: + A distance from the centroid of the initial simplex to each vertex. + + seed: + A seed number. + + """ + + def __init__( + self, + search_space: dict[str, optuna.distributions.BaseDistribution] | None = None, + centroid: float = 0.5, + edge: float = 0.5, + seed: int | None = None, + ) -> None: + super().__init__(search_space) + + assert 0.0 <= centroid <= 1.0, "The centroid must be exists in the unit hypercube. " + + assert ( + 0.0 < edge <= max(centroid, 1 - centroid) + ), f"Maximum edge length is {max(centroid, 1 - centroid)}" + + if search_space is None: + self._NM_state = "estimate_search_space" + self._ignore_trial_number = 1 + else: + self._NM_state = "generate_initial_simplex" + self._ignore_trial_number = 0 + + self._edge = edge + self._centroid = centroid + self._seed = seed + self._rng = np.random.RandomState(self._seed) + + self._coef = {"r": 1.0, "ic": -0.5, "oc": 0.5, "e": 2.0, "s": 0.5} + self._f: list[float] = [] + self._shrink_num = 0 + + self._independent_sampler = optuna.samplers.RandomSampler(seed=self._seed) + + def order_by(self) -> None: + """ + Sorting the vertices of the simplex based on their objective function values. + Computing the centroid excluding the best vertex. + """ + order = np.argsort(self._f) + self._y: np.ndarray = self._y[order] + self._f = np.asarray(self._f)[order].tolist() + self._yc = self._y[:-1].mean(axis=0) + + def out_of_boundary(self, y: np.ndarray) -> bool: + """ + Check whether the input vertex is in the search space. + """ + for yi, b in zip(y, self._bdrys): + if float(b[0]) <= float(yi) <= float(b[1]): + pass + else: + return True + return False + + def suggest_eval_param( + self, + search_space: dict[str, optuna.distributions.BaseDistribution], + eval_solution: np.ndarray, + ) -> tuple[dict, bool, np.ndarray]: + params = {} + for i, (name, distribution) in enumerate(search_space.items()): + if isinstance(distribution, optuna.distributions.FloatDistribution): + params[name] = float( + distribution.low + eval_solution[i] * (distribution.high - distribution.low) + ) + elif isinstance(distribution, optuna.distributions.IntDistribution): + params[name] = int( + distribution.low + eval_solution[i] * (distribution.high - distribution.low) + ) + else: + raise NotImplementedError + + if self.out_of_boundary(eval_solution): + out_of_boundary = True + else: + out_of_boundary = False + + return params, out_of_boundary, eval_solution + + def search( + self, + trial: optuna.trial.FrozenTrial, + search_space: dict[str, optuna.distributions.BaseDistribution], + study: optuna.study.Study, + f_val: float | None = None, + ) -> tuple[dict, bool]: + # Initialization + if self._NM_state == "Initialization": + if trial.number > self._ignore_trial_number: + self._f.append(study.trials_dataframe()["value"].values[-2]) + + if f_val == float("inf"): + self._f.append(float("inf")) + + if len(self._y) != len(self._f): + params, out_of_boundary, normalized_param = self.suggest_eval_param( + search_space, self._y[len(self._f)] + ) + else: + self._NM_state = "Reflection_org" + # Reflection, Expansion, Outside contraction, Inside Contraction, Shrinkage. + else: + if f_val is None: + objective_value = study.trials_dataframe()["value"].values[-2] + else: + objective_value = f_val + + if self._NM_state == "Reflection": + self._fr = objective_value + if self._f[0] <= self._fr < self._f[-2]: + self._y[-1] = self._yr + self._f[-1] = self._fr + self._NM_state = "Reflection_org" + elif self._fr < self._f[0]: + self._NM_state = "Expansion" + elif self._f[-2] <= self._fr < self._f[-1]: + self._NM_state = "Outside_constraction" + elif self._f[-1] <= self._fr: + self._NM_state = "Inside_constraction" + + elif self._NM_state == "Expansion": + self._fe = objective_value + if self._fe < self._fr: + self._y[-1] = self._ye + self._f[-1] = self._fe + else: + self._y[-1] = self._yr + self._f[-1] = self._fr + self._NM_state = "Reflection_org" + + elif self._NM_state == "Outside_constraction": + self._foc = objective_value + if self._foc <= self._fr: + self._y[-1] = self._yoc + self._f[-1] = self._foc + self._NM_state = "Reflection_org" + else: + self._NM_state = "Shrinkage" + + elif self._NM_state == "Inside_constraction": + self._fic = objective_value + if self._fic < self._f[-1]: + self._y[-1] = self._yic + self._f[-1] = self._fic + self._NM_state = "Reflection_org" + else: + self._NM_state = "Shrinkage" + + elif self._NM_state == "Shrinkage": + self._fs = objective_value + self._y[self._shrink_num + 1] = self._ys + self._f[self._shrink_num + 1] = self._fs + self._shrink_num += 1 + if self._shrink_num == self._dim: + self._NM_state = "Reflection_org" + self._shrink_num = 0 + + if self._NM_state == "Reflection_org": + self.order_by() + self._yr: np.ndarray = self._yc + self._coef["r"] * (self._yc - self._y[-1]) + params, out_of_boundary, normalized_param = self.suggest_eval_param( + search_space, self._yr + ) + self._NM_state = "Reflection" + + elif self._NM_state == "Expansion": + self._ye: np.ndarray = self._yc + self._coef["e"] * (self._yc - self._y[-1]) + params, out_of_boundary, normalized_param = self.suggest_eval_param( + search_space, self._ye + ) + + elif self._NM_state == "Outside_constraction": + self._yoc: np.ndarray = self._yc + self._coef["oc"] * (self._yc - self._y[-1]) + params, out_of_boundary, normalized_param = self.suggest_eval_param( + search_space, self._yoc + ) + + elif self._NM_state == "Inside_constraction": + self._yic: np.ndarray = self._yc + self._coef["ic"] * (self._yc - self._y[-1]) + params, out_of_boundary, normalized_param = self.suggest_eval_param( + search_space, self._yic + ) + + elif self._NM_state == "Shrinkage": + self._ys: np.ndarray = self._y[0] + self._coef["s"] * ( + self._y[self._shrink_num + 1] - self._y[0] + ) + params, out_of_boundary, normalized_param = self.suggest_eval_param( + search_space, self._ys + ) + + self._current_y = self._y.copy() + if self._NM_state != "Initialization": + if self._NM_state == "Shrinkage": + self._current_y[self._shrink_num + 1] = normalized_param + else: + self._current_y[-1] = normalized_param + + return params, out_of_boundary + + def sample_relative( + self, + study: optuna.study.Study, + trial: optuna.trial.FrozenTrial, + search_space: dict[str, optuna.distributions.BaseDistribution], + ) -> dict[str, Any]: + self._raise_error_if_multi_objective(study) + + if search_space == {}: + self._NM_state = "generate_initial_simplex" + return {} + + if self._NM_state == "generate_initial_simplex": + self._dim = len(search_space) + + # Our implementation normalizes the search space to unit hypercube [0, 1]^n. + self._bdrys = np.array([[0, 1] for _ in range(self._dim)]) + self._y = generate_initial_simplex( + dim=self._dim, edge=self._edge, centroid=self._edge, rng=self._rng + ) + self._NM_state = "Initialization" + + params, out_of_boundary = self.search(trial, search_space, study) + + if out_of_boundary: + while True: + params, out_of_boundary = self.search( + trial, search_space, study, f_val=float("inf") + ) + if not out_of_boundary: + break + trial.set_user_attr("simplex", self._current_y) + + return params + + def sample_independent( + self, + study: optuna.study.Study, + trial: optuna.trial.FrozenTrial, + param_name: str, + param_distribution: optuna.distributions.BaseDistribution, + ) -> Any: + return self._independent_sampler.sample_independent( + study, trial, param_name, param_distribution + ) + + def reseed_rng(self) -> None: + self._independent_sampler.reseed_rng() diff --git a/package/samplers/nelder_mead/requirements.txt b/package/samplers/nelder_mead/requirements.txt new file mode 100644 index 00000000..1411a4a0 --- /dev/null +++ b/package/samplers/nelder_mead/requirements.txt @@ -0,0 +1 @@ +pandas \ No newline at end of file From b748b75f9c92df75d1f2a30eeca08564c8975803 Mon Sep 17 00:00:00 2001 From: bamboo1997 Date: Wed, 21 Aug 2024 15:30:12 +0900 Subject: [PATCH 2/3] fix Nelder-Mead method. --- package/samplers/nelder_mead/nelder_mead.py | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/package/samplers/nelder_mead/nelder_mead.py b/package/samplers/nelder_mead/nelder_mead.py index de2d44f4..5b39d1e5 100644 --- a/package/samplers/nelder_mead/nelder_mead.py +++ b/package/samplers/nelder_mead/nelder_mead.py @@ -2,12 +2,13 @@ from typing import Any -from generate_initial_simplex import generate_initial_simplex import 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