Despite the advances in genotyping technologies which have led to large reduction in genotyping cost, the Tag SNP Selection problem remains an important problem for computational biologists and geneticists. Selecting the smallest subset of tag SNPs that can predict the other SNPs would considerably minimize the complexity of genome-wide or block-based SNP-disease association studies. These studies would lead to better diagnosis and treatment of diseases. In this work, we propose three variations of a genetic algorithm based on two-marker linkage disequilibrium, multi-marker linkage disequilibrium, and a third measure that we denote by prediction power. The performance of the three algorithms are compared with those of a recognized tag SNP selection algorithm using three different real data sets from the HapMap project. The results indicate that the multi-marker linkage disequilibrium based genetic algorithm yields better prediction accuracy.