  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)
%, mutation in genetic algorithm (GA) terminology, 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 $\beta$s, 2.0, 1.75 and 1.5, and report improvements in hit rate and/or
in time consumption, compared to other methods.
