Update Strength in EDAs and ACO: How to Avoid Genetic Drift

Abstract: We provide a rigorous runtime analysis concerning the update strength, a vital parameter in probabilistic model-building GAs such as the step size $1/K$ in the compact Genetic Algorithm (cGA) and the evaporation factor $\rho$ in ACO. While a large update strength is desirable for exploitation, there is a general trade-off: too strong updates can lead to genetic drift and poor performance. We demonstrate this trade-off for the cGA and a simple MMAS ACO algorithm on the OneMax function. More precisely, we obtain lower bounds on the expected runtime of $\Omega(K\sqrt{n} + n \log n)$ and $\Omega(\sqrt{n}/\rho + n \log n)$, respectively, showing that the update strength should be limited to $1/K, \rho = O(1/(\sqrt{n} \log n))$. In fact, choosing $1/K, \rho \sim 1/(\sqrt{n}\log n)$ both algorithms efficiently optimize OneMax in expected time $O(n \log n)$. Our analyses provide new insights into the stochastic behavior of probabilistic model-building GAs and propose new guidelines for setting the update strength in global optimization.