Estimation of Distribution Algorithm Based on Sequential Importance Sampling Particle Filters and Cholesky Decomposition

Estimation of distribution algorithm is a new intelligent stochastic optimization algorithm. It is more effectively to solve the non-linear, variable coupling optimization problem. Estimation of distribution algorithm in continuous domains is generally based on the assumptions that variables subject to Gauss distribution and the probability model is single-peaked one, which is not capable of describing the solutions distribution effectively for complex optimization problems. Aiming to overcome such drawbacks, an estimation of distribution algorithm depending upon sequential importance sampling particle filters is presented. In this algorithm, the variables are not required to subject to Gauss distribution. Instead, the distribution of samples is represented by weighted particles through the particle filter iteration on selection set of population. The probability model of this algorithm is multi-peaked and the relations among each dimension are handled using the covariance matrix. In sampling, the covariance matrix is shrunken for each particle and the shrunken covariance matrix is decomposed using Cholesky decomposition, and a method of handling the situation that the covariance matrix is zero matrix is presented. The next generation of population is produced from the decomposition result. Finally, the experimental results of several benchmark functions for complex optimization problems indicate the validity of the algorithm.