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Starting with the protein-coding mitochondrial DNA sequences of 20 different species, we reconstruct the primate evolutionary tree using maximum likelihood fitness functions based on a general Markov model of evolution. There is evidence that first and second codon sites in this DNA evolve under different conditions. Thus, we used a combination of a genetic algorithm (GA) and both single and multi-objective optimisation (MOO) to search tree-space for optimal solutions. Various genetic operators were used to search the combinatorial space of evolutionary trees, and a Pareto set was obtained. The implications of the common evolutionary subtrees to all trees found on the Pareto set are that the first codon sites play a far more important role in determining the optimal tree for these data. In the present case, the evolutionary relationship among the simian and other primates considered here remains in question.