Hierarchical Bayesian optimization algorithm: toward a new generation of evolutionary algorithms

Over the last few decades, genetic and evolutionary algorithms (GEAs) have been successfully applied to many problems of business, engineering, and science. This paper discusses probabilistic model-building genetic algorithms (PMBGAs), which are among the most important directions of current GEA research. PMBGAs replace traditional variation operators of GEAs by learning and sampling a probabilistic model of promising solutions. The paper describes two advanced PMBGAs: the Bayesian optimization algorithm (BOA), and the hierarchical BOA (hBOA). The paper argues that BOA and hBOA can solve an important class of nearly decomposable and hierarchical problems in a quadratic or subquadratic number of function evaluations with respect to the number of decision variables.