Data Grid technology is developed to share data across many sites in different geographical locations primarily to improve data access and transfer performance. When different sites hold a copy of the files, there are significant benefits realized when selecting the best set of sites that cooperate to speed up the file transfer process. In this paper, we describe a new optimization technique used to optimize two things when a new transfer replica file is requested. First it is minimizing total file transferring time by applying a Pincer-Search algorithm of Data mining approach to discover associated distributed replicas sites to share the transferring file process. Second, it is minimizing the cost (price) of requested file(s) by using Hungarian algorithm.