FFR120 Project ht08

The guess

Each individual guess is made by defining a set of parameters <math>\mu</math> and <math>\sigma</math> and then choosing a guess from the gaussian probability distribution defined by the parameters, where the distribution is defined as <math></math>

<math>\varphi_{\mu,\sigma^2}(x) = \frac{1}{\sigma\sqrt{2\pi}} \,e^{ -\frac{(x- \mu)^2}{2\sigma^2}} ,\quad x\in\mathbb{R},</math>

where <math>\sigma > 0</math> is the standard deviation, the real parameter <math>\mu</math> is the expected value.

GA - Landscape of self

The algorithm

This is a standard GA with chromosomes encoding the distribution parameters,<math>(\mu,\sigma)</math>.

Results

Fil:BinDistApprox large.png

Binomial PDF and normal approximation for n = 6 and p = 0.5.

• 1 is a good guess in most cases
• 1, or low number, generates determenistic chromosome
• high best uess generates non-determenistic chromosome
• Guess-distribution behaves as one or several, in themselves, stable distribution bells