Roulette-wheel selection via stochastic acceptance

Roulette-wheel selection is a frequently used method in genetic and evolutionary algorithms or in modeling of complex networks. Existing routines select one of N individuals using search algorithms of O(N) or O(logN) complexity. We present a simple roulette-wheel selection algorithm, which typically has O(1) complexity and is based on stochastic acceptance instead of searching. We also discuss a hybrid version, which might be suitable for highly heterogeneous weight distributions, found, for example, in some models of complex networks. With minor modifications, the algorithm might also be used for sampling with fitness cut-off at a certain value or for sampling without replacement.