Efficient computing budget allocation for finding simplest good designs

In many applications some designs are easier to implement, require less training data and shorter training time, and consume less storage than others. Such designs are called simple designs and are usually preferred over complex ones when they all have good performance. Despite the abundant existing studies on how to find good designs in simulation-based optimization, there exist few studies on finding simplest good designs. This article considers this important problem and the following contributions are made to the subject. First, lower bounds are provided for the probabilities of correctly selecting the m simplest designs with top performance and selecting the best m such simplest good designs, respectively. Second, two efficient computing budget allocation methods are developed to find m simplest good designs and to find the best m such designs, respectively, and their asymptotic optimalities have been shown. Third, the performance of the two methods is compared with equal allocations over six academic examples and a smoke detection problem in a wireless sensor network.