Parameter-Less Hierarchical BOA

The parameter-less hierarchical Bayesian optimization algorithm (hBOA) enables the use of hBOA without the need for tuning parameters for solving each problem instance. There are three crucial parameters in hBOA: (1) the selection pressure, (2) the window size for restricted tournaments, and (3) the population size. Although both the selection pressure and the window size influence hBOA performance, performance should remain low-order polynomial with standard choices of these two parameters. However, there is no standard population size that would work for all problems of interest and the population size must thus be eliminated in a different way. To eliminate the population size, the parameter-less hBOA adopts the population-sizing technique of the parameter-less genetic algorithm. Based on the existing theory, the parameter-less hBOA should be able to solve nearly decomposable and hierarchical problems in quadratic or subquadratic number of function evaluations without the need for setting any parameters whatsoever. A number of experiments are presented to verify scalability of the parameter-less hBOA.