Fitnessproportionate

Fitnessproportionate, or fitness-proportionate selection, is a method in which an individual's chance of being chosen for reproduction is proportional to its fitness value. In natural populations, fitness reflects relative reproductive success; individuals with higher fitness contribute more offspring and thus shift allele frequencies across generations. In evolutionary computation and genetic algorithms, fitness-proportionate selection is a classic operator for selecting parent solutions according to their fitness scores.

If there are n individuals with fitness values f1 through fn, the probability of choosing individual i is p_i = f_i / sum_j f_j, provided all fitness values are nonnegative. When fitnesses are negative or allow zero, scaling or shifting is used to create nonnegative values before normalization. Common implementations include roulette wheel selection, where a roulette wheel is spun to pick a parent, and stochastic universal sampling, which reduces sampling bias. Variants may apply fitness scaling to maintain selective pressure and prevent premature convergence.

Advantages of fitness-proportionate selection include intuitive alignment with objective of optimization, and a straightforward implementation. Drawbacks include loss of diversity when a few individuals dominate; susceptibility to scaling effects; and sensitivity to noisy fitness evaluations. To mitigate these issues, practitioners use rank-based or tournament selection, fitness scaling, niching, or hybrid methods.

This concept is foundational in both biology and computational optimization, where it helps translate fitness into reproductive odds or selection probability, guiding the evolution of populations toward higher-performing solutions.