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# encoding=utf8 |
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# pylint: disable=anomalous-backslash-in-string |
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"""Implementation of Ackley function. |
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Date: 2018 |
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Author: Lucija Brezočnik |
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License: MIT |
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Function: Ackley function |
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Input domain: |
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The function can be defined on any input domain but it is usually |
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evaluated on the hypercube x_i ∈ [-32.768, 32.768], for all i = 1, 2,..., D. |
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Global minimum: |
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f(x*) = 0, at x* = (0,...,0) |
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LaTeX formats: |
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Inline: $f(x) = -a\;exp\left(-b \sqrt{\frac{1}{D} |
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\sum_{i=1}^D x_i^2}\right) - exp\left(\frac{1}{D} |
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\sum_{i=1}^D cos(c\;x_i)\right) + a + exp(1)$ |
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Equation: \begin{equation}f(x) = |
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-a\;exp\left(-b \sqrt{\frac{1}{D} \sum_{i=1}^D x_i^2}\right) - |
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exp\left(\frac{1}{D} \sum_{i=1}^D cos(c\;x_i)\right) + |
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a + exp(1) \end{equation} |
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Domain: $-32.768 \leq x_i \leq 32.768$ |
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Reference: https://www.sfu.ca/~ssurjano/ackley.html |
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""" |
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import math |
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__all__ = ['Ackley'] |
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class Ackley(object): |
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def __init__(self, Lower=-32.768, Upper=32.768): |
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self.Lower = Lower |
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self.Upper = Upper |
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@classmethod |
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def function(cls): |
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def evaluate(D, sol): |
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a = 20 # Recommended variable value |
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b = 0.2 # Recommended variable value |
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c = 2 * math.pi # Recommended variable value |
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val = 0.0 |
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val1 = 0.0 |
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val2 = 0.0 |
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for i in range(D): |
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val1 += math.pow(sol[i], 2) |
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val2 += math.cos(c * sol[i]) |
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temp1 = -b * math.sqrt(val1 / D) |
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temp2 = val2 / D |
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val = -a * math.exp(temp1) - math.exp(temp2) + a + math.exp(1) |
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return val |
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return evaluate |
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