I propose new combined randomized methods for global optimization problems. These methods are based on the Nested Partitions(NP) method, a useful method for simulation optimization which guarantees global optimal solution but has several shortcomings. To overcome these shortcomings I hired various statistical selection methods and combined with NP method. I first explain the NP method and statistical selection method. And after that I present a detail description of proposed new combined methods and show the results of an application. As well as, I show how these combined methods can be considered in case of computing budget limit problem.