Our results show that using 2D crossover operators results in better performance than 1D crossover. We expect 2D crossover operators to do better since they tend to be less disruptive on two dimensional chromosomes. Features (schemas) that are close together in two dimensions (phenotype) may be far apart in one dimension (genotype). Thus schemas close together in 2D space may be more easily disrupted in one dimension by 1D crossover because their defining length is long in 1D space. Whether we use real crossover or simple real crossover makes little difference - block regions strongly affect fitness and velocity at a single cell is not very important. GAs with 2D crossover better recover the shape of the basin (for both BASIN and BBOX models) than 1D crossover in general, because 2D crossover better preserves model structure.
The results generated from genetic algorithms depend strongly on the fitness function. Many velocity models can have the same errors. The only criteria GAs know about is the size of calculated error value. We have to make the assumption that a velocity model with low error value is always a good model. This may not always be the case since the search space contains multiple optima some of which may not be geologically plausible.