A study on estimation of distribution algorithm based on a partial differential equation model

In this paper, we consider a mathematical basis of an estimation of distribution algorithm for continuous function optimization. We derived a function optimization procedure based on a partial differential equation in which an existence of a unique solution is analytically ensured and the solution converges to a stationary distribution and has same local optima as a given target function. By treating a target function as an objective function, we construct a bootstrap a procedure of particle sampling and giving a projection of a target distribution. Note that a point of this paper is not searching performance of the derived algorithm, rather the theoretical aspect is the main contribution because the proposed procedure is based on the mathematically proved convergence property. By numerical experiments, we show that our proposed algorithm has similar properties to a general evolutionary computation for function optimization.