Use model building on discretization algorithms for discrete EDAs To work on real-valued problems

Discretization algorithms have been combined with discrete estimation of distribution algorithms (EDAs) to work on real-valued problems. Existing discretization algorithms, such as the fixed-height histogram (FHH) and the split-on-demand (SoD), utilize merely densities of selected chromosomes to build next-generation population, and therefore have limited exploration. This paper adds the concept of model building to FHH and SoD to solve these problems. The model utilizes a variety of information from selected chromosomes to improve the abilities of FHH and SoD to identify promising regions for future exploration. Specifically, a model of expected values of selected chromosomes is combined with FHH and SoD to form expected-value FHH and expected-value SoD. The expected-value-discretization algorithms outperform their original versions on an exploration test function as well as the 25 benchmark functions used in the SoD paper. This paper also introduces a model of differential-expected-value of selected chromosomes. The differential-expected-value FHH and differential-expected-value SoD outperform their expected-value versions when tested on the exploration test function and the 25 benchmark functions.