  We demonstrate that a recently introduced heuristic optimization algorithm
[Phys. Rev. E 83, 046709 (2011)] that combines a local search with triadic
crossover genetic updates is capable of sampling nearly uniformly among
ground-state configurations in spin-glass-like Hamiltonians with p-spin
interactions in d space dimensions that have highly degenerate ground states.
Using this algorithm we probe the zero-temperature ferromagnet to spin-glass
transition point q_c of two example models, the disordered version of the
two-dimensional three-spin Baxter-Wu model [q_c = 0.1072(1)] and the
three-dimensional Edwards-Anderson model [q_c = 0.2253(7)], by computing the
Binder ratio of the ground-state magnetization.
