Semiparametric Estimation of Distribution Algorithms for Continuous Optimization
Vicente P. Soloviev, Concha Bielza, Pedro Larrañaga · IEEE Transactions on Evolutionary Computation · 2023
Traditional estimation of distribution algorithms (EDAs) often use Gaussian densities to optimize continuous functions, such as the estimation of Gaussian network algorithms (EGNAs) which use Gaussian Bayesian networks (GBNs). However, this assumes a parametric density function, and, in GBNs, linear dependencies between variables. Furthermore, the EGNA baseline learns a GBN at each iteration based on the best individuals in the last iteration, which may lead to local optimum convergence or large variance between solutions across multiple independent runs of the algorithm. In this work we propose a semiparametric EDA in which the restriction of assuming Gaussianity in the variables is relaxed using semiparametric Bayesian networks, in which nodes estimated by kernels coexist with nodes that assume Gaussianity, and the algorithm itself is able to determine where to use each type of node. Additionally, our approach takes into account information from several past iterations to learn the semiparametric Bayesian network from which the new solutions are sampled in each iteration. The empirical results show that semiparametric EDAs are a useful tool for continuous scenarios compared to different kinds of EDAs and other optimization techniques in continuous environments.