Quality Analysis of Discretization Methods for Estimation of Distribution Algorithms

Abstract

Estimation of distribution algorithms (EDAs). since they were introduced, have been successfully used to solve discrete optimization problems and hence proven to be an effective methodology for discrete optimization. To enhance the applicability of EDAs, researchers started to integrate EDAs with discretization methods such that the EDAs designed for discrete variables can be made capable of solving continuous optimization problems. In order to further our understandings of the collaboration between EDAs and discretization methods, in this paper, we propose a quality measure of discretization methods for EDAs. We then utilize the proposed quality measure to analyze three discretization methods: fixed-width histogram (FWH). fixed-height histogram (FHH), and greedy random split (GRS). Analytical measurements are obtained for FHH and FWH, and sampling measurements are conducted for FHH. FWH, and GRS. Furthermore, we integrate Bayesian optimization algorithm (BOA), a representative EDA, with the three discretization methods to conduct experiments and to observe the performance difference. A good agreement is reached between the discretization quality measurements and the numerical optimization results. The empirical results show that the proposed quality measure can be considered as an indicator of the suitability for a discretization method to work with EDAs.