Many automation or manufacturing systems are large, complex, and stochastic. Since closed-form analytical solutions generally do not exist for such systems, simulation is the only faithful way for performance evaluation. From the practical engineering perspective, the designs (or solution candidates) with low complexity (called simple designs) have many advantages compared with complex designs, such as requiring less computing and memory resources, and easier to interpret and to implement. Therefore, they are usually more desirable than complex designs in the real world if they have good enough performance. Recently, Jia (IEEE Trans. Autom. Sci. Eng., vol. 8, no. 4, pp. 720-732, Oct. 2010) discussed the importance of design simplicity and introduced an adaptive simulation-based sampling algorithm to sequentially screen the designs until one simplest good enough design is found. In this paper, we consider a more generalized problem and introduce two algorithms OCBA-mSG and OCBA-bSG to identify a subset of m simplest and good enough designs among a total of K (K >; m) designs. By controlling the simulation allocation intelligently, our approach intends to find those simplest good enough designs using a minimum simulation time. The numerical results show that both OCBA-mSG and OCBA-bSG outperform some other approaches on the test problems.