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"""Ackley function, 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 Ackley(BaseExperiment): |
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"""Ackley class.""" |
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r"""Ackley function, common benchmark for optimization algorithms. |
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The Ackley function is a non-convex function used to test optimization algorithms. |
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It is defined as: |
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.. math:: |
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f(x) = -a \cdot \exp(-\frac{b}{\sqrt{d}\left\|x\right\|}) - \exp(\frac{1}{d} \sum_{i=1}^d\cos (c x_i) ) + a + \exp(1) |
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where :math:`a` (= `a`), :math:`b` (= `b`), and :math:`c` (= `c`) are constants, |
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:math:`d` (= `d`) is the number of dimensions of the real input vector :math:`x`, |
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and :math:`\left\|x\right\|` is the Euclidean norm of the vector :math:`x`. |
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The components of the function argument :math:`x` |
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are the input variables of the `score` method, |
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and are set as `x0`, `x1`, ..., `x[d]` respectively. |
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Parameters |
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---------- |
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a : float, optional, default=20 |
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Amplitude constant used in the calculation of the Ackley function. |
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b : float, optional, default=0.2 |
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Decay constant used in the calculation of the Ackley function. |
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c : float, optional, default=2*pi |
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Frequency constant used in the calculation of the Ackley function. |
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d : int, optional, default=2 |
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Number of dimensions for the Ackley function. The default is 2. |
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Example |
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------- |
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>>> from hyperactive.experiment.toy import Ackley |
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>>> ackley = Ackley(a=20) |
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>>> params = {"x0": 1, "x1": 2} |
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>>> score, add_info = ackley.score(params) |
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Quick call without metadata return or dictionary: |
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>>> score = ackley(x0=1, x1=2) |
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""" # noqa: E501 |
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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, a=20, b=0.2, c=2 * np.pi, d=2): |
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self.a = a |
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self.b = b |
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self.c = c |
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self.d = d |
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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.d)] |
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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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x_vec = np.array([params[f"x{i}"] for i in range(self.d)]) |
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loss1 = -self.a * np.exp(-self.b * np.sqrt(np.sum(x_vec**2) / self.d)) |
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loss2 = -np.exp(np.sum(np.cos(self.c * x_vec)) / self.d) |
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loss3 = np.exp(1) |
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loss4 = self.a |
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loss = loss1 + loss2 + loss3 + loss4 |
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return loss, {} |
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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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return [{"a": 0}, {"a": 20, "d": 42}, {"a": -42, "b": 0.5, "c": 1, "d": 10}] |
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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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params0 = {"x0": 0, "x1": 0} |
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params1 = {f"x{i}": i + 3 for i in range(42)} |
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params2 = {f"x{i}": i**2 for i in range(10)} |
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return [params0, params1, params2] |
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SimonBlanke /
Hyperactive
