Hexagon/triangle packing using improved least flexibility first principle algorithm

In the past, the known least flexibility first (LFF) principle algorithm has achieved outstanding results in rectangular packing problems. In this paper we will adapt and improve the original LFF algorithm to fit for the hexagon and triangle packing (HTP) problems. We will compare our packing densities and time complexity with the results produced by conventional simulated annealing (SA) based algorithms. Using our algorithms we can cut the run time from 166 minutes (by SA) to 18/5 seconds (by LFF/LFFT) on one test data set and from 310 minutes to 106/14 seconds on some other test set