An algorithm for gauge fixing to the Landau gauge in the fundamental modular region in lattice QCD is described. The method, a combination of an evolutionary algorithm with a steepest descent method, is able to solve the problem of the nonperturbative gauge fixing. The performance of the combined algorithm is investigated on 8, β = 5.7, and 16, β = 6.0, lattice SU(3) gauge configurations. Latti...