I experimented with the packing of triangles using previous model and Matlab’s fmincon() optimizer. For each setting 100 runs were performed with the following initial conditions. Triangles have the same initial positions in the initial unit cell with random rotations. The algorithm used was interior point with supplied objective gradient.
3 triangle setting
Out of 100 runs 45 resulted in feasible solutions. 40 with exitflag== -2, 0 with exitflag== -1, 21 with exitflag== 0., 0 with exitflag== 1, 39 with exitflag== 2. Mean density in the feasible solution cases was 0.5827 and variance 0.0197. The best case had density 0.8118.
Left is the initial setup and right is the best found solution.
4 triangle setting
Out of 100 runs 20 resulted in feasible solutions. 66 with exitflag== -2, 0 with exitflag== -1, 14 with exitflag== 0., 0 with exitflag== 1, 20 with exitflag== 2. Mean density in the feasible solution cases was 0.5850 and variance 0.0127. The best case had density 0.7959.
Left is the initial setup and right is the best found solution.
5 triangle setting
Out of 100 runs 9 resulted in feasible solutions. 71 with exitflag== -2, 0 with exitflag== -1, 20 with exitflag== 0., 0 with exitflag== 1, 9 with exitflag== 2. Mean density in the feasible solution cases was 0.5637 and variance 0.0111. The best case had density 0.7246.
Left is the initial setup and right is the best found solution.
4 triangle setting and GA
I did similiar thing with the GA algorithm. Out of 49 runs 19 resulted in feasible solutions. Mean density in the feasible solution cases was 0.7667 and variance 0.0115. The best case had density 0.9230.
