Definition

Roulette-wheel selection defines a cumulative relative fitness value, $\phi_{j}$, for each individual $j$ as $$\phi_{j}=\frac{\sum\limits_{i=1}^{j}F_{i}}{\sum\limits_{i=1}^{N}F_{i}}, \ j=1,\ldots,N$$where each $F_{i}$ is the fitness of individual $i$. Next a random number $r$ is drawn and the selected individual is the taken as the one with the smallest $j$ that satisfies $\phi_{j}>r$.