Significance-Based Estimation-of-Distribution Algorithms

Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that maintain a stochastic model of the solution space. This model is updated from iteration to iteration based on the quality of the solutions sampled according to the model. As previous works show, this short-term perspective can lead to erratic updates of the model, in particular, to bit-frequencies approaching a random boundary value. This can lead to significant performance losses. In order to overcome this problem, we propose a new EDA that takes into account a longer history of samples and updates its model only with respect to information which it classifies as statistically significant. We prove that this significance-based compact genetic algorithm (sig-cGA) optimizes the common benchmark functions OneMax and LeadingOnes both in O(n log n) time, a result shown for no other EDA or evolutionary algorithm so far. For the recently proposed scGA - an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model - we prove that it optimizes OneMax only in a time exponential in the hypothetical population size 1/ρ.