  We study the critical behavior of the q-state Potts model with random
ferromagnetic couplings. Working with the cluster representation the partition
sum of the model in the large-q limit is dominated by a single graph, the
fractal properties of which are related to the critical singularities of the
random Potts model. The optimization problem of finding the dominant graph, is
studied on the square lattice by simulated annealing and by a combinatorial
algorithm. Critical exponents of the magnetization and the correlation length
are estimated and conformal predictions are compared with numerical results.
