MapReduce algorithm inspired by the map and reduces functions commonly used in functional programming. The use of this model is more beneficial when optimization of the distributed mappers in the MapReduce framework comes into the account. In standard mappers, each mapper operates independently and has no collaborative function or content relationship with other mappers. We propose a new technique to improve performance of the inter-processing tasks in MapReduce functions. In the proposed method, the mappers are connected and collaborated through a shared coordinator with a distributed metadata store called DMDS. In this new structure, a parallel and co-evolutionary genetic algorithm has been used to optimize and match the matrix processes simultaneously. The proposed method uses a genetic algorithm with a parallel and evolutionary executive structure in the mapping process of the mappers program to allocate resources, transfer and store data. The co-evolutionary MapReduce mappers can simplify and optimize relational data processing in the large clusters. MapReduce using a co-evolutionary mapper, provide successful convergence and better performance. Our experimental evaluation shows that collaborative techniques improves performance especially in the big size computations, and dramatically improves processing time across the MapReduce process. Even though the execution time in MapReduce varies with data volume, in the proposed method the overhead processing in low volume data is considerable where in high volume data shows more competitive advantage. In fact, with increasing the data volume, advantage of the proposed method becomes more considerable.