Significance-based Estimation-of-Distribution Algorithms

TL;DR

This paper introduces a significance-based EDA that uses statistical significance to update models, achieving faster optimization on benchmark functions compared to existing EDAs and evolutionary algorithms.

Contribution

The paper proposes the sig-cGA, a new EDA that updates models based on statistical significance, and proves its efficiency on standard benchmark functions.

Findings

sig-cGA optimizes OneMax, LeadingOnes, and BinVal in quasilinear time

scGA and convex search algorithms do not achieve polynomial-time optimization of OneMax

The significance-based approach prevents erratic model updates in EDAs

Abstract

Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that create a probabilistic model of the solution space, which is updated iteratively, based on the quality of the solutions sampled according to the model. As previous works show, this iteration-based perspective can lead to erratic updates of the model, in particular, to bit-frequencies approaching a random boundary value. In order to overcome this problem, we propose a new EDA based on the classic compact genetic algorithm (cGA) 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 commonly regarded benchmark functions OneMax, LeadingOnes, and BinVal all in quasilinear 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 its hypothetical population size. Similarly, we show that the convex search algorithm cannot optimize OneMax in polynomial time.