nmoo.noises

 1"""
 2Noise wrappers.
 3* `nmoo.noises.gaussian.GaussianNoise`
 4* `nmoo.noises.uniform.UniformNoise`
 5
 6Warning:
 7
 8    In `pymoo`, constrained problems have a `G` component used to measure the
 9    validity of the inputs. Sometimes, that component depends on the actual
10    value of the problem (i.e. the `F` component). See for instance [the
11    implementation of
12    CTP1](https://github.com/anyoptimization/pymoo/blob/7b719c330ff22c10980a21a272b3a047419279c8/pymoo/problems/multi/ctp.py#L84).
13    Let $\\mathcal{P}$ be such a problem. Evaluating $\\mathcal{P}$ on an input
14    $x$ gives the following output:
15    $$
16        \\mathcal{P} (x) = \\begin{cases}
17            F = f (x)
18            \\\\\\
19            G = g (x, f (x))
20        \\end{cases}
21    $$
22    where $f$ and $g$ are the non-noisy objective and constraint function,
23    respectively. Now, let $\\mathcal{E}$ be a noise wrapper adding some random
24    noise $\\varepsilon$ on the `F` component of $\\mathcal{P}$. Then we have
25    $$
26        \\mathcal{E} (\\mathcal{P} (x)) = \\begin{cases}
27            F = f (x) + \\varepsilon
28            \\\\\\
29            G = g (x, f (x))
30        \\end{cases}
31    $$
32    which is **NOT** the same as
33    $$
34        \\begin{cases}
35            F = f (x) + \\varepsilon
36            \\\\\\
37            G = g (x, f (x) + \\varepsilon)
38        \\end{cases}
39    $$
40    The latter may seem more natural, but breaks the wrapper hierarchy, as
41    after getting the `F` value of $\\mathcal{P} (x)$, the noise layer
42    $\\mathcal{E}$ would have to query $\\mathcal{P}$ again to calculate `G`
43    while somehow substituting $f (x) + \\varepsilon$ for $f (x)$ in
44    calculations.
45
46"""
47__docformat__ = "google"
48
49from .gaussian import GaussianNoise
50from .uniform import UniformNoise