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Basic initialisation (i0)

Population size vs Dimension

Draw at random $N$ agents (positions) in the search space, according to an uniform distribution.


where $D$ is the dimension of the search space. Note that $N$ needs to be at least equal to $D+1$.

We will need the volume $V(0)$ of the previous simplex. As no one has been defined yet, we simply set it to 0:

Population cost

Evaluate the $N$ individuals, thanks to the function $f$ we are studying. Save the best one as $Best$.

The sum of all values (they are all supposed to be positive, which is always possible), is the initial population cost $C$. We are trying here to minimise it.