This paper discusses and compares three different algorithms based on combinatorial optimization schemes for generating stochastic permeability fields. The algorithms are not restricted to generating Gaussian random fields and have the potential to accomplish geologic realism by combining data from many different sources. We have introduced a ''heat-bath'' algorithm for simulated annealing (SA) as an alternative to the commonly used ''Metropolis'' algorithm and a new stochastic modeling technique based on the ''genetic'' algorithm. We applied these algorithms to a set of outcrop and tracer flow data and examined the associated uncertainties in predictions. All three algorithms reproduce the major features of permeability distribution and fluid flow data. For relatively small problems, the Metropolis algorithm is the fastest. For larger problems, the heat-bath algorithm is at least as fast and often faster than the Metropolis algorithm, with significant potential for parallelization. The performance of the genetic algorithm is highly dependent on the choice of population size and probabilities of crossover, update, and mutation.