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
qc of two example models, the disordered version of the two-dimensional three-spin Baxter-Wu model [
qc=0.1072(1)] and the three-dimensional Edwards-Anderson model [
qc=0.2253(7)], by computing the Binder ratio of the ground-state magnetization.