[en] A class of algorithms for the Landau gauge fixing is proposed, which makes the steepest ascent (SA) method be more efficient by concepts of genetic algorithm. Main concern is how to incorporate random gauge transformation (RGT) to gain higher achievement of the minimal Landau gauge fixing, and to keep lower time consumption. One of these algorithms uses the block RGT, and another uses RGT controlled by local fitness density, and the last uses RGT determined by Ising Monte Carlo process. We tested these algorithms on SU(2) lattice gauge theory in 4 dimension with small βs, 2.0,1.75 and 1.5, and report improvements in hit rate and/or in time consumption, compared to other methods