Computational phylogenetics, phylogeny inference, or phylogenetic inference focuses on computational and optimization algorithms, heuristics, and approaches involved in phylogenetic analyses. The goal is to find a phylogenetic tree representing optimal evolutionary ancestry between a set of genes, species, or taxa. Maximum likelihood, parsimony, Bayesian, and minimum evolution are typical optimality criteria used to assess how well a phylogenetic tree topology describes the sequence data. Nearest Neighbour Interchange (NNI), Subtree Prune and Regraft (SPR), and Tree Bisection and Reconnection (TBR), known as tree rearrangements, are deterministic algorithms to search for optimal or the best phylogenetic tree. The space and the landscape of searching for the optimal phylogenetic tree is known as phylogeny search space.
Maximum Likelihood (also likelihood) optimality criterion is the process of finding the tree topology along with its branch lengths that provides the highest probability observing the sequence data, while parsimony optimality criterion is the fewest number of state-evolutionary changes required for a phylogenetic tree to explain the sequence data.