Noisy Univariate Marginal Distribution Algorithm and its mathematical model

In the present article, a new algorithm called Noisy Univariate Marginal Distribution Algorithm (NUMDA) is proposed as an improvement of UMDA. The main idea is to introduce stochastic item into the probabilistic model of the selected solutions. Numerical experiments show that NUMDA has a better performance on some problems than UMDA. In addition, the updating progress of this new algorithm can be described by a set of stochastic differential equations (SDEs) approximately. The strategy of constructing a potential function has been applied to study the new evolutionary algorithm theoretically. And some interesting results can be drawn from this novel methodology.