Abstract. A major task in evolutionary biology is to determine the ancestral relationships among the known species, a process generally referred as phylogenetic reconstruction. In the past decade, a new type of data based on genome rearrangements has attracted increasing attention from both biologists and computer scientists. Methods for reconstructing phylogeny based on genome rearrangement data include distance-based methods, direct optimization methods (GRAPPA and MGR), and Markov Chain Monte Carlo (MCMC) methods (Badger). Extensive testing on simulated and biological datasets showed that the latter three methods are currently the best methods for genome rearrangement phylogeny. However, all these tools are dealing with extremely large searching spaces; the total number of possible trees grows exponentially when the number of genomes increases and makes it computationally very expensive. Various heuristics are used to explore the tree space but with no guarantee of optimum being fou...