TA Algorithm to find a lean design Runs n=36, Factors s=17. Initial Design: 1 1 1 1 1 2 2 3 3 2 2 3 3 2 2 3 3 2 2 2 1 1 2 2 3 3 3 3 2 2 3 3 2 2 1 2 1 2 2 3 3 2 2 2 2 3 3 3 3 2 2 2 1 2 2 2 3 3 2 2 3 3 2 2 2 2 3 3 1 1 1 2 1 2 3 2 3 3 1 3 1 1 2 1 2 2 2 1 1 2 2 3 2 3 1 3 1 3 2 1 2 1 1 2 2 1 1 3 2 3 2 3 1 3 1 2 1 2 1 2 1 2 2 1 3 2 3 2 1 3 1 3 1 2 1 2 1 1 2 1 2 2 3 3 2 1 2 2 1 3 1 1 3 2 2 1 2 1 2 3 3 2 2 1 1 2 1 3 3 1 1 2 2 2 2 3 2 2 3 1 2 2 1 1 3 3 1 2 1 1 1 2 3 2 2 3 2 1 1 2 3 1 1 3 1 1 1 1 1 3 3 1 1 3 3 1 1 3 3 1 1 2 2 2 1 1 3 3 1 1 1 1 3 3 1 1 3 3 1 2 1 2 2 1 1 3 3 3 3 1 1 1 1 3 3 2 1 2 2 2 1 1 3 3 1 1 3 3 3 3 1 1 1 1 1 2 1 3 1 3 1 1 2 1 2 2 3 2 3 2 2 1 1 2 3 1 3 1 2 1 2 1 3 2 3 2 1 2 2 1 1 1 3 1 3 1 2 1 2 3 2 3 2 2 1 2 2 1 1 3 1 3 2 1 2 1 2 3 2 3 1 1 2 1 2 3 1 1 3 2 3 3 2 1 2 2 1 2 2 1 2 1 3 1 1 3 3 2 2 3 2 1 1 2 1 2 2 2 2 1 3 3 1 2 3 3 2 2 1 1 2 2 1 1 1 2 1 3 3 1 3 2 2 3 1 2 2 1 1 1 1 1 1 1 1 2 2 1 1 2 2 1 1 2 2 2 2 2 1 1 1 1 2 2 2 2 1 1 2 2 1 1 1 2 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 2 1 2 2 2 2 2 1 1 2 2 1 1 1 1 2 2 1 1 1 2 1 1 2 1 2 2 3 2 3 3 1 3 1 2 2 1 1 2 1 2 1 2 3 2 3 2 1 3 1 3 1 2 2 1 1 2 1 2 1 2 3 2 3 1 3 1 3 2 1 2 2 1 2 1 2 1 3 2 3 2 3 1 3 1 1 1 2 1 2 1 2 2 1 3 1 1 3 2 3 3 2 2 2 1 2 1 1 2 2 1 1 3 3 1 3 2 2 3 1 2 2 2 2 2 1 1 2 3 1 1 3 3 2 2 3 2 1 1 1 2 2 1 1 2 1 3 3 1 2 3 3 2 Criterion: maximize Det(X(5)'X(5))*...*Det(X(36)'X(36)) Search Type:(b) - f1(x1) ... f1(xs) f2(x1) ... f2(xs) Result Design: 1 1 1 1 1 1 1 1 1 2 2 1 2 1 2 2 2 2 2 1 1 2 1 3 3 2 2 3 2 1 1 1 3 2 1 2 2 1 1 3 1 3 1 1 1 2 2 2 3 3 2 2 1 2 2 2 1 1 3 1 3 3 3 3 1 3 1 1 1 2 1 2 2 1 1 1 3 1 3 1 1 3 3 3 3 2 2 1 2 1 3 2 1 2 1 3 3 2 1 2 3 1 2 1 1 1 2 3 1 1 3 2 3 2 3 2 1 2 1 1 1 1 1 1 3 3 3 3 1 1 3 1 3 1 1 1 1 2 2 2 2 2 3 1 1 2 2 3 1 2 3 3 1 1 2 2 1 1 2 3 2 3 3 3 1 1 1 2 2 1 1 2 1 2 2 3 3 3 2 3 2 3 3 2 2 2 2 2 2 1 1 2 2 1 1 3 3 1 3 2 2 2 1 3 2 2 1 2 1 1 3 2 3 2 1 1 3 2 3 1 2 1 2 2 1 1 1 2 1 2 2 2 3 3 3 1 1 3 2 2 1 2 1 2 1 3 1 3 2 2 1 3 1 2 3 1 2 2 2 2 1 2 3 3 1 1 2 3 1 2 2 3 1 1 1 1 1 2 2 2 2 3 3 2 3 2 3 3 3 2 1 1 1 2 2 3 3 2 1 2 1 2 1 3 1 3 2 1 2 2 1 3 1 2 2 2 1 3 1 1 3 2 3 2 2 1 1 2 3 2 2 1 1 2 1 3 3 3 2 1 1 1 1 2 1 1 3 2 1 1 3 3 2 2 1 2 3 1 1 1 2 1 2 1 3 2 2 1 1 3 3 2 3 1 2 2 2 1 1 3 3 1 1 3 1 1 3 1 1 3 3 1 1 2 1 2 3 2 3 1 2 3 1 1 2 2 1 3 1 1 2 1 2 1 3 1 2 3 1 2 2 3 3 2 1 2 1 2 2 1 1 2 3 3 3 2 1 2 2 1 3 1 2 1 2 2 2 3 3 2 3 2 2 2 2 3 2 3 3 2 2 2 1 1 1 1 2 2 1 2 2 1 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 2 2 1 1 1 1 2 1 2 2 2 2 2 1 2 1 1 1 1 2 1 2 2 1 1 1 2 1 3 2 1 3 3 2 2 1 1 3 1 2 2 1 1 1 2 1 2 2 1 3 1 3 1 3 2 3 2 2 1 2 2 1 2 3 1 1 1 3 2 3 3 2 1 2 1 1 2 1 2 2 1 2 3 1 2 3 3 1 1 3 2 2 2 2 1 1 2 2 3 3 2 3 3 2 3 3 2 2 1 2 2 2 2 3 1 2 2 3 3 1 2 3 1 1 2 Runs Permutation: 25 18 19 16 15 10 24 13 11 7 3 30 22 31 34 35 1 12 20 6 17 29 14 9 21 32 4 26 27 28 5 36 8 33 2 23 Factors Permutation: 1 2 3 4 5 7 6 14 10 12 8 15 13 11 9 16 17 Max Product Det: 3.9695e-013 ============================================ Expanded Matrix: 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 0 -1 0 0 0 -1 -1 -1 -1 2 2 -1 2 -1 2 2 2 1 1 1 -1 -1 1 -1 1 1 0 0 1 0 -1 -1 -1 1 0 -1 -1 -1 2 2 -1 2 -1 -1 -1 -1 2 1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 0 0 0 1 1 0 -1 -1 -1 -1 -1 -1 2 2 2 -1 -1 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 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 -1 1 -1 1 0 -1 0 -1 1 1 0 -1 0 1 -1 -1 2 -1 2 -1 -1 -1 2 -1 2 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 0 1 0 1 0 -1 0 -1 -1 -1 -1 -1 2 -1 2 -1 2 -1 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 0 1 -1 -1 0 0 1 -1 0 1 1 -1 2 -1 -1 -1 2 2 -1 -1 2 -1 -1 -1 1 -1 1 1 -1 -1 0 1 0 1 1 1 -1 -1 -1 0 0 -1 2 -1 2 -1 -1 -1 -1 -1 -1 2 2 -1 1 -1 1 -1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 -1 -1 -1 2 -1 2 -1 -1 2 2 2 2 1 1 1 -1 -1 1 0 -1 -1 1 1 -1 1 0 0 0 -1 1 2 -1 -1 -1 -1 -1 -1 2 2 2 -1 -1 1 1 1 -1 1 -1 -1 1 0 1 0 -1 -1 1 0 1 -1 0 -1 -1 2 -1 2 -1 -1 -1 2 -1 -1 2 1 -1 1 1 -1 -1 -1 0 -1 0 0 0 1 1 1 -1 -1 1 -1 2 -1 2 2 2 -1 -1 -1 -1 -1 -1 1 1 1 -1 1 -1 0 -1 1 -1 1 0 0 -1 1 -1 0 1 2 -1 -1 -1 -1 2 2 -1 -1 -1 2 -1 1 -1 1 1 1 1 -1 0 1 1 -1 -1 0 1 -1 0 0 1 -1 2 -1 -1 -1 -1 2 -1 -1 2 2 -1 1 -1 -1 -1 -1 -1 0 0 0 0 1 1 0 1 0 1 1 1 2 2 2 2 -1 -1 2 -1 2 -1 -1 -1 1 1 -1 -1 -1 1 0 1 1 0 -1 0 -1 0 -1 1 -1 1 2 -1 -1 2 -1 2 -1 2 -1 -1 -1 -1 1 1 -1 1 1 -1 1 -1 0 0 0 -1 1 -1 -1 1 0 1 -1 -1 2 2 2 -1 -1 -1 -1 -1 2 -1 1 1 1 -1 -1 1 1 0 0 -1 -1 0 -1 1 1 1 0 -1 -1 2 2 -1 -1 2 -1 -1 -1 -1 2 -1 1 -1 -1 -1 1 -1 -1 1 0 -1 -1 1 1 0 0 -1 0 1 -1 -1 2 -1 -1 -1 -1 2 2 -1 2 -1 1 -1 -1 -1 1 -1 0 -1 1 0 0 -1 -1 1 1 0 1 -1 2 -1 -1 2 2 -1 -1 -1 -1 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 0 1 -1 0 1 -1 -1 0 0 -1 1 -1 2 -1 -1 2 -1 -1 -1 2 2 -1 -1 1 -1 -1 1 -1 1 -1 1 -1 0 1 -1 0 0 1 1 0 -1 -1 -1 -1 2 -1 -1 2 2 -1 -1 2 -1 1 1 -1 1 1 -1 -1 0 1 1 1 0 -1 0 0 -1 1 -1 -1 2 -1 -1 -1 2 -1 2 2 -1 -1 -1 1 1 -1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 -1 -1 2 -1 2 2 2 2 -1 2 -1 -1 1 1 1 1 -1 -1 -1 -1 0 0 -1 0 0 -1 0 0 -1 -1 -1 -1 2 2 -1 2 2 -1 2 2 -1 -1 1 -1 1 -1 1 1 0 0 0 -1 0 -1 0 0 -1 -1 -1 -1 2 2 2 -1 2 -1 2 2 -1 -1 -1 -1 1 1 -1 1 1 1 0 0 -1 0 -1 -1 -1 -1 0 -1 0 0 2 2 -1 2 -1 -1 -1 -1 2 -1 2 2 1 -1 -1 -1 1 -1 1 0 -1 1 1 0 0 -1 -1 1 -1 0 -1 2 -1 -1 -1 2 2 -1 -1 -1 -1 2 1 1 -1 -1 -1 1 -1 0 0 -1 1 -1 1 -1 1 0 1 0 -1 2 2 -1 -1 -1 -1 -1 -1 2 -1 2 1 1 -1 1 1 -1 0 1 -1 -1 -1 1 0 1 1 0 -1 0 2 -1 -1 -1 -1 -1 2 -1 -1 2 -1 2 1 -1 -1 1 -1 1 0 -1 0 1 -1 0 1 1 -1 -1 1 0 2 -1 2 -1 -1 2 -1 -1 -1 -1 -1 2 1 1 1 1 -1 -1 0 0 1 1 0 1 1 0 1 1 0 0 2 2 -1 -1 2 -1 -1 2 -1 -1 2 2 1 -1 1 1 1 1 1 -1 0 0 1 1 -1 0 1 -1 -1 0 -1 -1 2 2 -1 -1 -1 2 -1 -1 -1 2 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.130675 0.940863 4.704316 Top 6 Left 6 Corner: 0.150801 0.904806 5.428835 Top 7 Left 7 Corner: 0.174957 0.849140 5.943977 Top 8 Left 8 Corner: 0.190413 0.787292 6.194082 Top 9 Left 9 Corner: 0.222455 0.797944 6.995968 Top 10 Left 10 Corner: 0.243574 0.796214 7.455839 Top 11 Left 11 Corner: 0.264285 0.799480 7.912863 Top 12 Left 12 Corner: 0.276420 0.763576 8.125055 Top 13 Left 13 Corner: 0.291634 0.744581 8.439594 Top 14 Left 14 Corner: 0.314067 0.758180 8.968113 Top 15 Left 15 Corner: 0.333635 0.764457 9.417136 Top 16 Left 16 Corner: 0.350749 0.755825 9.800349 Top 17 Left 17 Corner: 0.342473 0.707846 9.483905 Top 18 Left 18 Corner: 0.362656 0.707390 9.963309 Top 19 Left 19 Corner: 0.391867 0.727045 11.325819 Top 20 Left 20 Corner: 0.396671 0.705983 12.000000 Top 21 Left 21 Corner: 0.408362 0.697341 12.874448 Top 22 Left 22 Corner: 0.428932 0.698185 14.040229 Top 23 Left 23 Corner: 0.461209 0.712740 15.623110 Top 24 Left 24 Corner: 0.487951 0.724791 17.056516 Top 25 Left 25 Corner: 0.513778 0.737747 18.485998 Top 26 Left 26 Corner: 0.558500 0.772891 20.638474 Top 27 Left 27 Corner: 0.585521 0.777895 22.178143 Top 28 Left 28 Corner: 0.611780 0.783154 23.710505 Top 29 Left 29 Corner: 0.668490 0.824465 26.467689 Top 30 Left 30 Corner: 0.684985 0.823789 27.666793 Top 31 Left 30 Corner: 0.731575 0.850908 29.548577 Top 32 Left 30 Corner: 0.781333 0.879863 31.558353 Top 33 Left 30 Corner: 0.832683 0.909009 33.632394 Top 34 Left 30 Corner: 0.887408 0.939975 35.842744 Top 35 Left 30 Corner: 0.942023 0.969096 38.048682 Top 36 Left 30 Corner: 1.000000 1.000000 40.390385 Det Product: 3.969520631708044e-013 0.0006807098338122992 3.458085244132165e+036 ============================================ Expanded Matrix for initial design: 1 -1 -1 -1 -1 -1 0 0 1 1 0 0 1 1 0 0 1 1 2 2 -1 -1 2 2 -1 -1 2 2 -1 -1 1 1 1 1 -1 -1 0 0 1 1 1 1 0 0 1 1 0 0 2 2 -1 -1 -1 -1 2 2 -1 -1 2 2 1 -1 1 -1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 -1 -1 2 2 2 2 -1 -1 -1 -1 2 2 1 1 -1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 -1 -1 2 2 -1 -1 2 2 2 2 -1 -1 1 -1 -1 -1 1 -1 0 1 0 1 1 -1 1 -1 -1 0 -1 0 2 -1 2 -1 -1 -1 -1 -1 -1 2 -1 2 1 1 1 -1 -1 1 0 1 0 1 -1 1 -1 1 0 -1 0 -1 2 -1 2 -1 -1 -1 -1 -1 2 -1 2 -1 1 -1 1 1 -1 -1 1 0 1 0 1 -1 1 -1 0 -1 0 -1 -1 2 -1 2 -1 -1 -1 -1 2 -1 2 -1 1 1 -1 1 1 -1 1 0 1 0 -1 1 -1 1 -1 0 -1 0 -1 2 -1 2 -1 -1 -1 -1 -1 2 -1 2 1 -1 -1 1 -1 1 0 1 1 0 -1 0 0 -1 1 -1 -1 1 2 -1 -1 2 -1 2 2 -1 -1 -1 -1 -1 1 1 1 -1 1 -1 0 1 1 0 0 -1 -1 0 -1 1 1 -1 2 -1 -1 2 2 -1 -1 2 -1 -1 -1 -1 1 -1 1 1 1 1 1 0 0 1 -1 0 0 -1 -1 1 1 -1 -1 2 2 -1 -1 2 2 -1 -1 -1 -1 -1 1 1 -1 -1 -1 1 1 0 0 1 0 -1 -1 0 1 -1 -1 1 -1 2 2 -1 2 -1 -1 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 -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 -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 -1 0 0 1 0 1 -1 -1 -1 -1 -1 2 -1 2 2 -1 2 -1 1 1 1 -1 -1 1 1 -1 1 -1 0 -1 0 -1 1 0 1 0 -1 -1 -1 -1 2 -1 2 -1 -1 2 -1 2 1 -1 1 1 -1 -1 -1 1 -1 1 -1 0 -1 0 1 0 1 0 -1 -1 -1 -1 -1 2 -1 2 -1 2 -1 2 1 1 -1 1 1 -1 -1 1 -1 1 0 -1 0 -1 0 1 0 1 -1 -1 -1 -1 2 -1 2 -1 2 -1 2 -1 1 -1 -1 1 -1 1 1 -1 -1 1 0 1 1 0 -1 0 0 -1 -1 -1 -1 -1 2 -1 -1 2 -1 2 2 -1 1 1 1 -1 1 -1 1 -1 -1 1 1 0 0 1 0 -1 -1 0 -1 -1 -1 -1 -1 2 2 -1 2 -1 -1 2 1 -1 1 1 1 1 -1 1 1 -1 0 1 1 0 0 -1 -1 0 -1 -1 -1 -1 2 -1 -1 2 2 -1 -1 2 1 1 -1 -1 -1 1 -1 1 1 -1 1 0 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 2 2 -1 -1 2 2 -1 1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 2 2 -1 -1 2 2 -1 -1 2 2 1 1 1 1 -1 -1 -1 -1 0 0 0 0 -1 -1 0 0 -1 -1 -1 -1 2 2 2 2 -1 -1 2 2 -1 -1 1 -1 1 -1 1 1 0 0 -1 -1 -1 -1 0 0 0 0 -1 -1 2 2 -1 -1 -1 -1 2 2 2 2 -1 -1 1 1 -1 1 1 1 0 0 -1 -1 0 0 -1 -1 -1 -1 0 0 2 2 -1 -1 2 2 -1 -1 -1 -1 2 2 1 -1 -1 -1 1 -1 -1 0 -1 0 0 1 0 1 1 -1 1 -1 -1 2 -1 2 2 -1 2 -1 -1 -1 -1 -1 1 1 1 -1 -1 1 -1 0 -1 0 1 0 1 0 -1 1 -1 1 -1 2 -1 2 -1 2 -1 2 -1 -1 -1 -1 1 -1 1 1 -1 -1 0 -1 0 -1 0 1 0 1 -1 1 -1 1 2 -1 2 -1 2 -1 2 -1 -1 -1 -1 -1 1 1 -1 1 1 -1 0 -1 0 -1 1 0 1 0 1 -1 1 -1 2 -1 2 -1 -1 2 -1 2 -1 -1 -1 -1 1 -1 -1 1 -1 1 -1 0 0 -1 1 -1 -1 1 0 1 1 0 -1 2 2 -1 -1 -1 -1 -1 2 -1 -1 2 1 1 1 -1 1 -1 -1 0 0 -1 -1 1 1 -1 1 0 0 1 -1 2 2 -1 -1 -1 -1 -1 -1 2 2 -1 1 -1 1 1 1 1 0 -1 -1 0 1 -1 -1 1 1 0 0 1 2 -1 -1 2 -1 -1 -1 -1 -1 2 2 -1 1 1 -1 -1 -1 1 0 -1 -1 0 -1 1 1 -1 0 1 1 0 2 -1 -1 2 -1 -1 -1 -1 2 -1 -1 2 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000000 0.000619 0.000000 Top 6 Left 6 Corner: 0.111111 0.666667 4.000000 Top 7 Left 7 Corner: 0.000959 0.004657 0.000000 Top 8 Left 8 Corner: 0.086949 0.420448 2.828427 Top 9 Left 9 Corner: 0.080125 0.349132 2.519842 Top 10 Left 10 Corner: 0.004480 0.016881 0.000000 Top 11 Left 11 Corner: 0.007652 0.024251 0.000000 Top 12 Left 12 Corner: 0.011454 0.027392 0.000000 Top 13 Left 13 Corner: 0.015384 0.037453 0.000000 Top 14 Left 14 Corner: 0.018871 0.047631 0.000000 Top 15 Left 15 Corner: 0.027411 0.059240 0.000000 Top 16 Left 16 Corner: 0.034690 0.069595 0.000000 Top 17 Left 17 Corner: 0.215830 0.443262 5.976868 Top 18 Left 18 Corner: 0.280404 0.541209 7.703588 Top 19 Left 19 Corner: 0.289071 0.531206 8.354792 Top 20 Left 20 Corner: 0.056217 0.087176 1.736250 Top 21 Left 21 Corner: 0.055939 0.105138 1.905578 Top 22 Left 22 Corner: 0.073858 0.118605 2.341168 Top 23 Left 23 Corner: 0.084321 0.135316 2.708402 Top 24 Left 24 Corner: 0.096785 0.147218 3.440331 Top 25 Left 25 Corner: 0.102330 0.159401 3.904296 Top 26 Left 26 Corner: 0.121043 0.182985 4.594955 Top 27 Left 27 Corner: 0.147058 0.211611 5.477893 Top 28 Left 28 Corner: 0.172624 0.211278 6.677798 Top 29 Left 29 Corner: 0.199426 0.252156 7.538350 Top 30 Left 30 Corner: 0.644394 0.774049 26.027323 Top 31 Left 30 Corner: 0.709568 0.824702 28.659718 Top 32 Left 30 Corner: 0.760097 0.855778 30.700605 Top 33 Left 30 Corner: 0.832683 0.908883 33.632394 Top 34 Left 30 Corner: 0.883931 0.936332 35.702297 Top 35 Left 30 Corner: 0.942023 0.969096 38.048682 Top 36 Left 30 Corner: 1.000000 1.000000 40.390385 Det Product: 0+0i -7.8018e-027+1.0265e-026i 0+0i