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"""Sphere function, a common benchmark for optimization algorithms.""" |
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# copyright: hyperactive developers, MIT License (see LICENSE file) |
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import numpy as np |
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from hyperactive.base import BaseExperiment |
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class Sphere(BaseExperiment): |
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r"""Simple Sphere function, common benchmark for optimization algorithms. |
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Sphere function parameterized by the formula: |
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.. math:: |
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f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^n x_i^2 + c |
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where :math:`c` is a constant offset added to the sum of squares, |
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and :math:`n` is the number of dimensions. |
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Both :math:`c` (= `const`) and :math:`n` (= `n_dim`) can be set as parameters. |
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The function arguments :math:`x_1`, :math:`x_2`, ..., :math:`x_n` |
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are the input variables of the `score` method, |
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and are set as `x0`, `x1`, ..., `x[n]` respectively. |
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This function is a common test function for optimization algorithms. |
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Parameters |
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---------- |
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const : float, optional, default=0 |
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A constant offset added to the sum of squares. |
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n_dim : int, optional, default=2 |
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The number of dimensions for the Sphere function. The default is 2. |
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Example |
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------- |
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>>> from hyperactive.experiment.toy import Sphere |
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>>> sphere = Sphere(const=0, n_dim=3) |
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>>> params = {"x0": 1, "x1": 2, "x2": 3} |
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>>> score, add_info = sphere.score(params) |
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Quick call without metadata return or dictionary: |
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>>> score = sphere(x0=1, x1=2, x2=3) |
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Different number of dimensions changes the parameter names: |
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>>> sphere4D = Sphere(const=0, n_dim=4) |
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>>> score4D = sphere4D(x0=1, x1=2, x2=3, x3=4) |
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""" |
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_tags = { |
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"property:randomness": "deterministic", # random or deterministic |
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# if deterministic, two calls of score will result in the same value |
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# random = two calls may result in different values; same as "stochastic" |
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"property:higher_or_lower_is_better": "lower", |
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# values are "higher", "lower", "mixed" |
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# whether higher or lower scores are better |
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} |
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def __init__(self, const=0, n_dim=2): |
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self.const = const |
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self.n_dim = n_dim |
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super().__init__() |
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def _paramnames(self): |
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return [f"x{i}" for i in range(self.n_dim)] |
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def _evaluate(self, params): |
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"""Evaluate the parameters. |
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Parameters |
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---------- |
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params : dict with string keys |
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Parameters to evaluate. |
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Returns |
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------- |
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float |
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The value of the parameters as per evaluation. |
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dict |
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Additional metadata about the search. |
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""" |
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params_vec = np.array([params[f"x{i}"] for i in range(self.n_dim)]) |
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return np.sum(params_vec ** 2) + self.const, {} |
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@classmethod |
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def get_test_params(cls, parameter_set="default"): |
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"""Return testing parameter settings for the skbase object. |
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``get_test_params`` is a unified interface point to store |
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parameter settings for testing purposes. This function is also |
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used in ``create_test_instance`` and ``create_test_instances_and_names`` |
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to construct test instances. |
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``get_test_params`` should return a single ``dict``, or a ``list`` of ``dict``. |
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Each ``dict`` is a parameter configuration for testing, |
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and can be used to construct an "interesting" test instance. |
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A call to ``cls(**params)`` should |
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be valid for all dictionaries ``params`` in the return of ``get_test_params``. |
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The ``get_test_params`` need not return fixed lists of dictionaries, |
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it can also return dynamic or stochastic parameter settings. |
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Parameters |
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---------- |
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parameter_set : str, default="default" |
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Name of the set of test parameters to return, for use in tests. If no |
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special parameters are defined for a value, will return `"default"` set. |
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Returns |
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------- |
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params : dict or list of dict, default = {} |
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Parameters to create testing instances of the class |
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Each dict are parameters to construct an "interesting" test instance, i.e., |
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`MyClass(**params)` or `MyClass(**params[i])` creates a valid test instance. |
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`create_test_instance` uses the first (or only) dictionary in `params` |
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""" |
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params0 = {} |
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params1 = {"n_dim": 3, "const": 1.0} |
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return [params0, params1] |
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@classmethod |
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def _get_score_params(self): |
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"""Return settings for testing score/evaluate functions. Used in tests only. |
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Returns a list, the i-th element should be valid arguments for |
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self.evaluate and self.score, of an instance constructed with |
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self.get_test_params()[i]. |
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Returns |
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------- |
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list of dict |
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The parameters to be used for scoring. |
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""" |
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score_params0 = {"x0": 0, "x1": 0} |
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score_params1 = {"x0": 1, "x1": 2, "x2": 3} |
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return [score_params0, score_params1] |
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SimonBlanke /
Hyperactive
