We present in this work a scalable distributed genetic algorithm of Data Ordering Problem with Inversion using the MapReduce paradigm. This specific topic is appealing for reduction of the power dissipation in VLSI and in bioinformatics. The capacitance and the switching activity influence the power consumption on the software level. The ordering of the data sequences is an unconditional consequence of switching activity. An optimization problem related to this topic is the ordering of sequences such that the total number of transitions will be minimized – Data Ordering Problem (DOP). Adding the bus-invert paradigm, some sequences can be complemented. The resulting problem is the DOP with Inversion (DOPI). These ordering problems are NP-hard. We establish a scalable distributed genetic approach - MapReduce Parallel Genetic Algorithm (MRPGA) for DOPI, MRPGA_DOPI and draw comparisons with greedy algorithms. The proposed methods are estimated and experiments show the efficiency of MRPGA_DOPI.