TA Algorithm to find a lean design Runs n=36, Factors s=13. Initial Design: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 2 2 2 2 3 3 3 3 1 2 2 2 2 3 3 3 3 1 1 1 1 1 3 3 3 3 1 1 1 1 2 2 2 2 1 1 1 2 3 1 2 3 3 1 2 2 3 1 2 2 3 1 2 3 1 1 2 3 3 1 1 3 3 1 2 3 1 2 2 3 1 1 2 1 1 1 3 2 1 3 2 3 2 1 3 2 1 2 2 1 3 2 1 3 1 3 2 1 3 1 3 3 2 1 3 2 1 2 1 3 2 1 1 1 2 3 1 3 2 1 3 3 2 1 2 2 2 3 1 2 1 3 2 1 1 3 2 3 2 3 1 2 3 2 1 3 2 2 1 3 1 2 1 2 3 2 1 1 3 2 3 3 2 1 2 2 3 1 3 2 2 1 3 1 1 3 2 2 3 1 2 1 3 3 2 1 2 2 1 3 2 1 2 1 3 3 3 1 2 2 1 2 3 2 2 3 2 1 1 1 2 3 3 2 3 1 2 3 1 3 2 2 2 3 1 1 3 1 2 2 1 2 2 3 3 1 2 1 1 3 3 2 2 2 3 3 1 1 2 3 2 2 1 1 3 2 3 1 1 2 2 3 1 3 3 2 2 1 2 1 3 2 1 2 3 3 1 3 1 2 2 3 2 1 3 2 3 1 1 2 1 2 3 3 3 3 2 1 3 1 2 2 3 2 3 1 1 3 1 3 2 2 2 1 1 3 2 3 1 3 3 2 1 3 3 3 2 2 1 3 1 2 1 3 3 2 1 1 1 3 3 2 1 2 3 2 3 1 3 3 3 2 3 2 2 1 2 1 1 3 2 1 1 1 3 1 3 3 2 3 2 2 3 3 2 2 2 1 2 1 1 3 1 3 3 3 1 3 1 2 3 2 3 1 2 2 3 1 3 2 1 2 3 1 3 1 2 3 3 1 2 3 3 2 3 1 2 1 2 3 1 1 2 3 3 Criterion: maximize Det(X(5)'X(5))*...*Det(X(36)'X(36)) Search Type:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 1 2 3 3 3 1 1 2 2 2 1 3 2 2 3 3 1 2 3 1 1 2 3 1 2 3 1 3 2 3 2 1 2 3 3 1 1 2 2 3 1 3 2 1 2 1 3 3 2 1 2 1 2 1 1 3 2 3 3 2 3 2 1 1 2 3 2 1 1 2 2 3 3 2 1 1 3 3 2 2 2 2 1 1 3 1 3 3 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 2 3 2 3 2 1 3 1 2 1 3 1 2 3 3 2 2 1 2 3 1 1 3 3 3 1 3 1 1 3 1 2 2 2 2 1 1 2 3 1 1 3 3 2 3 1 2 2 3 3 1 2 2 2 3 3 1 1 1 3 2 2 3 2 1 2 1 3 1 2 2 3 3 1 2 3 1 1 2 3 1 2 2 3 1 2 3 3 2 3 2 1 3 1 3 2 2 1 3 1 1 1 1 1 1 3 3 2 3 2 2 3 2 3 2 1 3 3 1 1 2 2 1 3 3 2 3 3 2 2 1 3 1 1 3 1 3 2 2 2 2 2 3 2 3 3 2 3 1 1 1 1 1 3 3 2 1 1 3 2 2 1 2 1 3 2 2 2 1 3 3 2 1 1 3 1 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 3 1 3 1 3 2 1 2 3 1 1 1 2 1 2 2 1 2 3 3 3 3 1 2 3 1 2 2 1 1 3 1 2 3 3 3 1 3 3 2 1 2 2 1 2 1 3 3 2 3 3 3 3 2 2 1 2 1 1 2 1 3 3 2 3 1 2 1 2 1 3 2 3 1 1 2 1 3 1 3 2 3 1 1 2 2 3 2 1 1 3 2 2 1 3 3 2 3 2 1 2 1 2 1 3 2 3 2 1 1 3 2 3 1 1 3 2 2 3 3 1 1 3 2 2 1 3 1 2 2 3 1 2 3 3 1 2 3 1 3 2 3 1 1 1 2 2 3 3 3 2 1 2 3 3 3 3 3 3 3 3 3 3 3 3 1 Runs Permutation: 19 25 17 10 15 36 33 1 9 29 6 30 21 16 26 12 32 35 13 5 23 22 2 7 4 28 14 31 8 18 24 11 34 27 20 3 Factors Permutation: 3 2 6 4 5 7 1 8 11 9 10 12 13 Max Product Det: 5.8228e-013 ============================================ Expanded Matrix: 1 -1 -1 0 2 1 -1 1 -1 1 -1 -1 -1 -1 -1 0 2 0 2 0 2 -1 -1 1 -1 0 2 1 0 2 1 -1 1 -1 -1 -1 0 2 1 -1 -1 -1 -1 -1 0 2 1 -1 -1 -1 0 2 1 -1 1 -1 -1 1 -1 0 2 1 -1 0 2 -1 -1 0 2 1 -1 1 -1 -1 -1 -1 -1 0 2 0 2 1 1 -1 -1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 1 0 2 -1 -1 -1 -1 1 -1 0 2 1 -1 1 -1 0 2 1 -1 0 2 -1 -1 -1 -1 0 2 1 1 -1 0 2 -1 -1 -1 -1 0 2 0 2 1 -1 1 -1 0 2 -1 -1 -1 -1 1 -1 1 -1 1 0 2 0 2 0 2 0 2 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 0 2 1 -1 0 2 1 -1 0 2 -1 -1 1 -1 -1 -1 0 2 -1 -1 1 1 -1 -1 -1 0 2 1 -1 1 -1 0 2 0 2 -1 -1 0 2 1 -1 -1 -1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 0 2 0 2 0 2 0 2 -1 -1 1 -1 -1 0 2 1 -1 -1 -1 -1 -1 1 -1 1 -1 0 2 1 -1 -1 -1 0 2 0 2 1 -1 1 1 -1 -1 -1 0 2 0 2 0 2 1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 0 2 0 2 1 1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 -1 -1 0 2 0 2 1 -1 1 -1 -1 -1 0 2 1 1 -1 -1 -1 -1 -1 0 2 1 -1 -1 -1 0 2 0 2 1 -1 -1 -1 0 2 1 -1 1 -1 1 0 2 1 -1 0 2 -1 -1 1 -1 -1 -1 1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 1 -1 0 2 1 -1 0 2 0 2 1 -1 0 2 1 -1 1 0 2 -1 -1 1 -1 1 -1 -1 -1 -1 -1 0 2 0 2 -1 -1 1 -1 1 -1 0 2 1 -1 1 1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 0 2 0 2 0 2 1 0 2 0 2 1 -1 0 2 1 -1 1 -1 0 2 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 0 2 -1 -1 -1 -1 1 -1 0 2 0 2 -1 -1 0 2 -1 -1 1 -1 0 2 1 0 2 0 2 -1 -1 1 -1 1 -1 0 2 -1 -1 -1 -1 1 -1 -1 -1 1 -1 0 2 0 2 1 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 -1 -1 1 0 2 -1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 1 -1 0 2 -1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 -1 0 2 -1 -1 0 2 0 2 -1 -1 0 2 1 -1 1 -1 1 -1 1 -1 -1 -1 1 0 2 1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 1 -1 -1 -1 0 2 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 0 2 -1 -1 0 2 0 2 -1 -1 0 2 -1 -1 1 -1 1 -1 0 2 1 1 -1 1 -1 1 -1 1 -1 0 2 0 2 -1 -1 0 2 -1 -1 -1 -1 0 2 -1 -1 1 -1 1 1 -1 0 2 1 -1 -1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 0 2 1 -1 -1 -1 -1 -1 1 0 2 -1 -1 1 -1 -1 -1 1 -1 0 2 1 -1 -1 -1 -1 -1 0 2 0 2 1 -1 0 2 1 -1 -1 -1 -1 1 -1 0 2 0 2 -1 -1 1 -1 1 -1 0 2 1 -1 0 2 -1 -1 0 2 1 -1 -1 0 2 -1 -1 1 -1 0 2 1 -1 0 2 -1 -1 -1 -1 1 -1 0 2 1 -1 -1 -1 1 -1 -1 1 -1 0 2 0 2 1 -1 1 -1 -1 -1 -1 -1 1 -1 0 2 0 2 -1 -1 1 -1 1 -1 -1 0 2 0 2 1 -1 -1 -1 0 2 1 -1 1 -1 -1 -1 0 2 1 -1 -1 -1 1 -1 1 0 2 1 -1 -1 -1 -1 -1 -1 -1 0 2 0 2 1 -1 1 -1 1 -1 0 2 -1 -1 0 2 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 -1 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.103811 0.755082 4.192963 Top 6 Left 6 Corner: 0.152460 0.881367 5.646216 Top 7 Left 7 Corner: 0.169495 0.877479 6.902460 Top 8 Left 8 Corner: 0.194537 0.865168 7.415586 Top 9 Left 9 Corner: 0.219388 0.880303 8.975189 Top 10 Left 10 Corner: 0.226081 0.823336 8.768655 Top 11 Left 11 Corner: 0.264676 0.868992 10.859419 Top 12 Left 12 Corner: 0.269558 0.811864 10.576406 Top 13 Left 13 Corner: 0.278133 0.772339 11.434544 Top 14 Left 14 Corner: 0.303553 0.769226 12.008909 Top 15 Left 15 Corner: 0.316150 0.764435 13.016669 Top 16 Left 16 Corner: 0.338738 0.774514 13.484072 Top 17 Left 17 Corner: 0.351044 0.747368 14.469672 Top 18 Left 18 Corner: 0.374350 0.760163 14.973587 Top 19 Left 19 Corner: 0.389868 0.742790 16.084295 Top 20 Left 20 Corner: 0.418984 0.752952 16.823540 Top 21 Left 21 Corner: 0.437876 0.754356 18.077895 Top 22 Left 22 Corner: 0.475352 0.773405 19.147137 Top 23 Left 23 Corner: 0.505995 0.795335 20.902684 Top 24 Left 24 Corner: 0.560914 0.854873 22.652984 Top 25 Left 25 Corner: 0.558341 0.808484 23.076636 Top 26 Left 26 Corner: 0.579972 0.805341 23.474728 Top 27 Left 27 Corner: 0.594380 0.795439 24.576623 Top 28 Left 27 Corner: 0.635162 0.818924 26.262897 Top 29 Left 27 Corner: 0.678742 0.844410 28.064871 Top 30 Left 27 Corner: 0.725313 0.871509 29.990483 Top 31 Left 27 Corner: 0.766864 0.891516 31.708560 Top 32 Left 27 Corner: 0.810796 0.912848 33.525061 Top 33 Left 27 Corner: 0.857244 0.935605 35.445625 Top 34 Left 27 Corner: 0.902408 0.955774 37.313085 Top 35 Left 27 Corner: 0.949952 0.977189 39.278932 Top 36 Left 27 Corner: 1.000000 1.000000 41.348350 Det Product: 5.82277940692482e-013 0.00254225244243147 1.70469942911939e+039 ============================================ Expanded Matrix for initial design: 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 -1 -1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 0 2 0 2 0 2 0 2 1 -1 1 -1 1 -1 1 -1 -1 -1 1 0 2 0 2 0 2 0 2 1 -1 1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 2 0 2 0 2 0 2 -1 -1 1 -1 -1 -1 -1 0 2 1 -1 -1 -1 0 2 1 -1 1 -1 -1 -1 0 2 0 2 1 -1 -1 -1 1 0 2 0 2 1 -1 -1 -1 0 2 1 -1 -1 -1 -1 -1 0 2 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1 -1 0 2 1 -1 -1 -1 0 2 0 2 1 -1 -1 -1 -1 -1 0 2 -1 -1 1 -1 -1 -1 -1 1 -1 0 2 -1 -1 1 -1 0 2 1 -1 0 2 -1 -1 1 -1 0 2 -1 -1 1 0 2 0 2 -1 -1 1 -1 0 2 -1 -1 1 -1 -1 -1 1 -1 0 2 -1 -1 1 -1 -1 -1 1 1 -1 1 -1 0 2 -1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 0 2 -1 -1 -1 -1 1 -1 -1 0 2 1 -1 -1 -1 1 -1 0 2 -1 -1 1 -1 1 -1 0 2 -1 -1 0 2 0 2 1 0 2 1 -1 -1 -1 0 2 -1 -1 1 -1 0 2 -1 -1 -1 -1 1 -1 0 2 1 -1 0 2 1 1 -1 -1 -1 0 2 1 -1 0 2 -1 -1 1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 0 2 1 -1 -1 0 2 1 -1 0 2 -1 -1 -1 -1 1 -1 0 2 1 -1 1 -1 0 2 -1 -1 0 2 1 0 2 1 -1 -1 -1 1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 -1 -1 1 -1 0 2 0 2 1 1 -1 -1 -1 0 2 -1 -1 1 -1 1 -1 0 2 -1 -1 0 2 0 2 -1 -1 1 -1 0 2 1 -1 -1 0 2 -1 -1 1 -1 1 -1 1 -1 -1 -1 0 2 0 2 -1 -1 0 2 1 -1 0 2 1 0 2 1 -1 0 2 -1 -1 -1 -1 -1 -1 0 2 1 -1 1 -1 0 2 1 -1 -1 -1 0 2 1 1 -1 -1 -1 1 -1 0 2 0 2 0 2 1 -1 -1 -1 -1 -1 1 -1 -1 -1 0 2 0 2 1 -1 -1 0 2 0 2 1 -1 1 -1 -1 -1 0 2 -1 -1 -1 -1 1 -1 1 -1 0 2 0 2 1 0 2 1 -1 1 -1 -1 -1 -1 -1 0 2 1 -1 0 2 0 2 -1 -1 -1 -1 1 -1 0 2 1 1 -1 -1 -1 -1 -1 0 2 0 2 1 -1 -1 -1 1 -1 1 -1 0 2 0 2 -1 -1 0 2 1 -1 -1 1 -1 0 2 -1 -1 0 2 1 -1 1 -1 -1 -1 1 -1 -1 -1 0 2 0 2 1 -1 1 0 2 -1 -1 1 -1 0 2 1 -1 -1 -1 -1 -1 0 2 -1 -1 0 2 1 -1 1 -1 1 -1 1 1 -1 0 2 -1 -1 1 -1 -1 -1 0 2 0 2 1 -1 0 2 1 -1 -1 -1 -1 -1 1 -1 1 -1 -1 1 -1 0 2 0 2 0 2 -1 -1 -1 -1 1 -1 0 2 1 -1 -1 -1 1 -1 1 -1 1 0 2 -1 -1 1 -1 1 -1 1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 0 2 -1 -1 1 -1 1 1 -1 0 2 -1 -1 -1 -1 -1 -1 1 -1 1 -1 0 2 -1 -1 0 2 1 -1 0 2 1 -1 1 -1 -1 1 -1 1 -1 1 -1 0 2 1 -1 0 2 0 2 -1 -1 0 2 -1 -1 -1 -1 1 -1 1 0 2 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 0 2 1 -1 0 2 0 2 1 -1 1 1 -1 0 2 0 2 0 2 -1 -1 0 2 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 -1 -1 0 2 1 -1 0 2 1 -1 -1 -1 0 2 0 2 1 -1 -1 -1 1 -1 1 0 2 -1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 0 2 1 -1 1 -1 -1 -1 0 2 1 -1 1 1 -1 0 2 1 -1 -1 -1 0 2 -1 -1 0 2 1 -1 -1 -1 -1 -1 0 2 1 -1 1 -1 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000000 0.000000 0.000000 Top 6 Left 6 Corner: 0.000000 0.000000 0.000000 Top 7 Left 7 Corner: 0.000000 0.000000 0.000000 Top 8 Left 8 Corner: 0.000000 0.000000 0.000000 Top 9 Left 9 Corner: 0.000000 0.000000 0.000000 Top 10 Left 10 Corner: 0.000000 0.000000 0.000000 Top 11 Left 11 Corner: 0.000000 0.000966 0.000000 Top 12 Left 12 Corner: 0.000000 0.000000 0.000000 Top 13 Left 13 Corner: 0.000064 0.000158 0.000000 Top 14 Left 14 Corner: 0.000120 0.000296 0.000000 Top 15 Left 15 Corner: 0.000019 0.000050 0.000000 Top 16 Left 16 Corner: 0.000033 0.000076 0.000000 Top 17 Left 17 Corner: 0.000071 0.000155 0.000000 Top 18 Left 18 Corner: 0.000016 0.000029 0.000000 Top 19 Left 19 Corner: 0.000032 0.000071 0.000000 Top 20 Left 20 Corner: 0.000056 0.000094 0.000000 Top 21 Left 21 Corner: 0.000016 0.000031 0.000000 Top 22 Left 22 Corner: 0.000028 0.000049 0.000000 Top 23 Left 23 Corner: 0.000048 0.000066 0.000000 Top 24 Left 24 Corner: 0.000016 0.000022 0.000000 Top 25 Left 25 Corner: 0.000031 0.000041 0.000000 Top 26 Left 26 Corner: 0.000145 0.000211 0.000000 Top 27 Left 27 Corner: 0.000222 0.000308 0.000000 Top 28 Left 27 Corner: 0.000838 0.001082 0.000000 Top 29 Left 27 Corner: 0.003134 0.004320 0.000000 Top 30 Left 27 Corner: 0.003539 0.004323 0.000000 Top 31 Left 27 Corner: 0.014440 0.017893 0.000000 Top 32 Left 27 Corner: 0.055644 0.064741 2.072090 Top 33 Left 27 Corner: 0.057291 0.073856 2.747016 Top 34 Left 27 Corner: 0.248731 0.263147 10.267520 Top 35 Left 27 Corner: 0.949952 0.977278 39.278932 Top 36 Left 27 Corner: 1.000000 1.000000 41.348350 Det Produ27ct: 0 0 0