In our work we studied the problem of generating r-regular families of permutations. At the beginning we described those families and their relations with different fields in mathematics. Then we showed connection to tripartite graphs and their triangulation. After that we introduced different approaches for generating those families. Since this problem is NP-complete, we used backtracking with different optimizations. Then we designed a system for generating and analyzing of r-regular families. Because the amount of the data and the high time complexity of the algorithm we decided to use concurrency to boost the speed of computations. We implemented parallel processing by using GPU. We also prepared tools for the data analysis. Those tools are completely implemented in python, therefore anyone can use them without the need to have GPU. In the end, we analyzed generated data and stated theorems about impossibility of generating r-regular families just by combining 1-regular families. Keywords: r-regularity, Latin square, concurrency, backtracking, permutations