Roulette-wheel selection via stochastic acceptance

TL;DR

This paper introduces a simple, efficient roulette-wheel selection algorithm with typically constant time complexity, suitable for genetic algorithms and complex network modeling, especially with heterogeneous weights.

Contribution

The authors propose a stochastic acceptance-based roulette-wheel selection algorithm that reduces complexity from linear or logarithmic to typically constant time, with a hybrid version for diverse weight distributions.

Findings

Typically O(1) selection time complexity

Effective for highly heterogeneous weight distributions

Adaptable for sampling with fitness cut-off or without replacement

Abstract

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(log(N)) 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.