An Algorithm for the Maximum Likelihood Problem on Evolutionary Trees

We investigate the problem of reconstructing evolutionary trees with maximum likelihood (MLET). In the MLET problem, a set of genetic sequences is given and a feasible solution is sought, consisting of an evolutionary tree (where general nodes correspond to sequences and input sequences occur as leaves) along with assignments for the interior nodes. Due to the difficulty of solving the MLET directly, we consider two restricted versions of the problem: the ancestral maximum likelihood (AML) and the maximum parsimony (MP) problems. If we let d_e denote the number of different characters occurring in two nodes linked by edge e, then the objective function of the AML problem is min ∑_{eσ E(T)} H(d_e/k), where H is the entropy function and k is the length of each sequence. In the MP we consider the objective function min σ_{e∊ E(T)} d_e/k. Both the AML and the MP are NP-hard. We propose a new approach for computing solutions for these problems, based on genetic algorithms.