In this paper, we develop a new optimization framework that consists of the extended compact genetic algorithm (ECGA) and split-on-demand (SoD), an adaptive discretization technique, to tackle the characteristic determination problem for solid state devices. As most decision variables of characteristic determination problems are real numbers due to the modeling of physical phenomena, and ECGA is designed for handling discrete-type problems, a specific mechanism to transform the variable types of the two ends is in order. In the proposed framework, ECGA is used as a back-end optimization engine, and SoD is adopted as the interface between the engine and the problem. Moreover, instead of one mathematical model with various parameters, characteristic determination is in fact a set of problems of which the mathematical formulations may be very different. Therefore, in this study, we employ the proposed framework on three study cases to demonstrate that the technique proposed in the domain of evolutionary computation can provide not only the high quality optimization results but also the flexibility to handle problems of different formulations.