I have been running some ADMIXTURE experiments recently. This is with my world dataset and about 180,000 SNPs.
I ran ADMIXTURE at K=15 ancestral components with different random seeds. Let's take a look at the final log likelihood and cross-validation errors I got for 11 runs.
As you can see, as the log likelihood increases, the cross-validation error decreases, though there is a fair bit of variation there.
For different runs, I got fairly different ancestral components. Remember that the only difference between the different runs was the random seed used to initialize the algorithm. Some ancestral components stayed very similar across the runs but others appeared and disappeared or switched subtly between different populations in a broad region.
The cross-validation (CV) error is important in my opinion since it gives you an idea of which run has results that generalize better. Basically, it is calculated by removing a portion of the individuals in the dataset.
At K=15, the minimum CV error I got was 0.52200 and the median was 0.52206. The maximum CV error was 0.52241, which is pretty large for this data. Let's superimpose this maximum CV value on a graph showing how CV error varies for different values of K (number of ancestral components).
The set of runs in this graph (other than the red line for the maximum CV error at K=15) used the default random seed for ADMIXTURE.
What this shows is that running ADMIXTURE only once using the default random seed (or any other seed) is fraught with problems. A better approach is to run it multiple times with different seeds so you can be sure that you have arrived at a computationally optimum solution.