Recent advances of technology have made it easy to obtain and compare whole genomes. Rearrangements of genomes through operations such as reversals and transpositions are rare events that enable researchers to reconstruct deep evolutionary history among species. Some of the popular methods need to search a large tree space for the best scored tree, thus it is desirable to have a fast and accurate method that can score a given tree efficiently. During the tree scoring procedure, the genomic structures of internal tree nodes are also provided, which provide important information for inferring ancestral genomes and for modeling the evolutionary processes. However, computing tree scores and ancestral genomes are very difficult and a lot of researchers have to rely on heuristic methods which have various disadvantages. In this paper, we describe the first genetic algorithm for tree scoring and ancestor inference, which uses a fitness function considering co-evolution, adopts different initial seeding methods to initialize the first population pool, and utilizes a sorting-based approach to realize evolution. Our extensive experiments show that compared with other existing algorithms, this new method is more accurate and can infer ancestral genomes that are much closer to the true ancestors.