TA Algorithm to find a lean design Runs n=36, Factors s=15. Initial Design: 1 1 1 2 2 3 3 2 2 3 3 2 2 3 3 2 2 2 2 2 3 3 3 3 2 2 3 3 2 2 1 2 1 3 3 2 2 2 2 3 3 3 3 2 2 2 1 2 3 3 2 2 3 3 2 2 2 2 3 3 1 1 1 2 3 2 3 3 1 3 1 1 2 1 2 2 2 1 2 3 2 3 1 3 1 3 2 1 2 1 1 2 2 3 2 3 2 3 1 3 1 2 1 2 1 2 1 2 3 2 3 2 1 3 1 3 1 2 1 2 1 1 2 2 3 3 2 1 2 2 1 3 1 1 3 2 2 1 2 3 3 2 2 1 1 2 1 3 3 1 1 2 2 3 2 2 3 1 2 2 1 1 3 3 1 2 1 1 3 2 2 3 2 1 1 2 3 1 1 3 1 1 1 3 3 1 1 3 3 1 1 3 3 1 1 2 2 2 3 3 1 1 1 1 3 3 1 1 3 3 1 2 1 1 1 3 3 3 3 1 1 1 1 3 3 2 1 2 1 1 3 3 1 1 3 3 3 3 1 1 1 1 1 3 1 3 1 1 2 1 2 2 3 2 3 2 2 1 3 1 3 1 2 1 2 1 3 2 3 2 1 2 2 1 3 1 3 1 2 1 2 3 2 3 2 2 1 2 1 3 1 3 2 1 2 1 2 3 2 3 1 1 2 3 1 1 3 2 3 3 2 1 2 2 1 2 2 1 3 1 1 3 3 2 2 3 2 1 1 2 1 2 2 1 3 3 1 2 3 3 2 2 1 1 2 2 1 1 1 3 3 1 3 2 2 3 1 2 2 1 1 1 1 1 1 2 2 1 1 2 2 1 1 2 2 2 2 2 1 1 2 2 2 2 1 1 2 2 1 1 1 2 1 2 2 1 1 1 1 2 2 2 2 1 1 2 1 2 2 2 1 1 2 2 1 1 1 1 2 2 1 1 1 1 2 1 2 2 3 2 3 3 1 3 1 2 2 1 1 2 1 2 3 2 3 2 1 3 1 3 1 2 2 2 1 2 1 2 3 2 3 1 3 1 3 2 1 2 2 1 2 1 3 2 3 2 3 1 3 1 1 1 2 1 2 2 1 3 1 1 3 2 3 3 2 2 2 1 1 2 2 1 1 3 3 1 3 2 2 3 1 2 2 2 1 1 2 3 1 1 3 3 2 2 3 2 1 1 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:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 2 1 2 1 1 2 2 3 1 1 3 3 2 3 2 1 1 2 3 3 2 1 1 2 1 3 1 2 2 3 1 2 1 1 3 3 1 1 1 3 3 3 3 1 1 2 2 1 3 2 3 2 1 3 1 3 2 1 1 2 2 2 2 2 3 3 3 2 2 3 3 2 2 3 2 2 1 1 2 3 1 2 1 1 1 2 2 3 3 3 1 2 1 2 1 1 2 2 2 1 1 1 1 2 2 1 1 1 2 2 2 2 2 3 3 3 3 3 2 3 1 2 2 1 2 1 3 3 2 1 3 2 3 2 1 1 1 1 2 1 3 1 3 1 2 3 2 1 2 3 1 1 1 3 3 3 3 3 1 1 1 1 1 3 1 2 2 1 2 1 2 1 3 2 3 2 1 3 3 1 2 1 2 1 1 1 3 1 3 3 3 1 1 3 3 2 2 1 1 2 3 1 2 2 1 2 3 1 3 3 2 2 1 2 3 1 2 3 3 2 3 1 2 1 1 1 2 2 3 2 1 1 2 1 2 3 1 3 3 2 2 1 2 3 3 3 2 3 2 2 2 3 3 2 2 2 1 1 3 1 2 3 2 2 2 3 3 1 1 1 2 1 2 2 2 3 3 1 2 2 1 1 3 1 3 1 2 2 2 1 3 3 1 3 1 2 3 2 2 1 2 2 2 3 1 1 1 3 3 1 1 3 3 1 3 1 2 2 2 3 2 1 1 3 2 1 3 1 3 2 1 1 2 2 2 1 3 3 1 3 2 3 1 1 2 1 1 1 1 1 1 1 1 2 2 2 2 2 1 2 1 1 1 3 2 1 2 1 2 3 1 3 2 3 1 2 2 1 1 3 1 3 2 1 2 1 3 2 2 3 2 1 2 2 2 2 1 2 1 1 1 2 2 1 1 1 2 2 1 3 2 2 3 2 3 1 2 1 1 3 2 1 1 1 2 3 1 3 3 3 1 1 2 2 2 1 2 1 3 2 2 3 3 3 2 2 2 2 3 3 1 1 2 1 1 3 2 2 3 2 1 2 3 3 1 2 2 2 1 2 2 2 1 1 2 2 1 1 2 1 2 2 1 3 1 2 3 1 1 3 1 2 3 2 2 2 1 2 3 3 1 1 2 3 3 2 2 1 2 1 1 1 1 1 3 2 3 2 3 1 2 1 3 1 2 1 2 2 3 1 3 2 2 1 3 2 1 2 1 3 Runs Permutation: 20 21 15 22 2 36 27 1 19 5 13 10 16 30 6 11 4 12 32 35 14 31 9 25 17 34 28 23 24 3 33 26 18 8 29 7 Factors Permutation: 1 2 3 4 9 8 12 5 11 6 7 15 14 13 10 Max Product Det: 2.9792e-013 ============================================ Expanded Matrix: 1 1 -1 1 -1 -1 -1 -1 0 2 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 0 2 -1 -1 -1 -1 0 2 -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 -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 -1 -1 1 -1 0 2 -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 0 2 0 2 1 -1 0 2 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 -1 1 -1 1 -1 0 2 -1 -1 -1 -1 0 2 0 2 0 2 -1 -1 -1 -1 -1 -1 -1 -1 0 2 0 2 1 -1 -1 -1 0 2 0 2 0 2 0 2 0 2 1 -1 1 -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 -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 -1 0 2 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 -1 -1 -1 1 1 1 -1 0 2 -1 -1 0 2 -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 -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 0 2 1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 0 2 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 1 1 -1 0 2 -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 1 -1 1 -1 0 2 1 -1 0 2 0 2 0 2 1 -1 1 -1 0 2 0 2 1 1 -1 -1 1 -1 -1 -1 0 2 1 -1 0 2 0 2 0 2 1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 1 0 2 0 2 1 -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 -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 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 -1 -1 1 -1 0 2 -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 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 0 2 0 2 0 2 0 2 0 2 -1 -1 0 2 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 -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 0 2 0 2 0 2 -1 -1 0 2 -1 -1 -1 -1 -1 -1 0 2 0 2 -1 -1 -1 -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 1 -1 -1 -1 -1 0 2 1 -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 0 2 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 0 2 0 2 1 -1 0 2 -1 -1 0 2 1 -1 1 -1 -1 -1 1 1 1 1 -1 -1 0 2 0 2 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 -1 0 2 1 -1 -1 -1 -1 -1 1 -1 -1 -1 0 2 1 -1 0 2 0 2 1 1 -1 1 1 -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 0 2 1 -1 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 0 2 0 2 -1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.120497 0.836512 4.000000 Top 6 Left 6 Corner: 0.152748 0.916486 5.768998 Top 7 Left 7 Corner: 0.185091 0.921038 6.552103 Top 8 Left 8 Corner: 0.189370 0.860760 7.325683 Top 9 Left 9 Corner: 0.217793 0.873903 7.989967 Top 10 Left 10 Corner: 0.223434 0.809975 8.768655 Top 11 Left 11 Corner: 0.234203 0.784166 8.789439 Top 12 Left 12 Corner: 0.251741 0.761292 9.974775 Top 13 Left 13 Corner: 0.269535 0.742165 10.275781 Top 14 Left 14 Corner: 0.283006 0.729668 11.290655 Top 15 Left 15 Corner: 0.292529 0.710847 11.281793 Top 16 Left 16 Corner: 0.322646 0.728236 12.938395 Top 17 Left 17 Corner: 0.344658 0.727011 13.410001 Top 18 Left 18 Corner: 0.357715 0.717939 14.402134 Top 19 Left 19 Corner: 0.381277 0.718994 14.938420 Top 20 Left 20 Corner: 0.409918 0.741620 16.556756 Top 21 Left 21 Corner: 0.439247 0.751715 17.306995 Top 22 Left 22 Corner: 0.453549 0.746360 18.366988 Top 23 Left 23 Corner: 0.488257 0.763156 19.327874 Top 24 Left 24 Corner: 0.508669 0.767028 20.644071 Top 25 Left 25 Corner: 0.543521 0.784185 21.599850 Top 26 Left 26 Corner: 0.564714 0.785207 22.960952 Top 27 Left 27 Corner: 0.585521 0.783218 23.346603 Top 28 Left 28 Corner: 0.624481 0.805174 25.431217 Top 29 Left 28 Corner: 0.665749 0.828675 27.111794 Top 30 Left 28 Corner: 0.709744 0.853374 28.903429 Top 31 Left 28 Corner: 0.756646 0.880014 30.813461 Top 32 Left 28 Corner: 0.806648 0.908526 32.849715 Top 33 Left 28 Corner: 0.851163 0.929367 34.662559 Top 34 Left 28 Corner: 0.898136 0.951409 36.575447 Top 35 Left 28 Corner: 0.947700 0.974948 38.593899 Top 36 Left 28 Corner: 1.000000 1.000000 40.723742 Det Product: 2.979159624976652e-013 0.001245515566512421 3.24882513975629e+038 ============================================ Expanded Matrix for initial design: 1 -1 -1 -1 0 2 0 2 1 -1 1 -1 0 2 0 2 1 -1 1 -1 0 2 0 2 1 -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 1 -1 0 2 0 2 1 -1 1 -1 1 -1 1 -1 0 2 0 2 0 2 0 2 1 -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 1 -1 0 2 0 2 0 2 0 2 1 -1 1 -1 1 -1 -1 -1 0 2 1 -1 0 2 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 -1 0 2 -1 -1 0 2 1 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 0 2 1 -1 0 2 1 -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 0 2 -1 -1 1 -1 -1 -1 1 -1 -1 -1 0 2 -1 -1 0 2 1 -1 -1 1 0 2 1 -1 1 -1 0 2 -1 -1 0 2 0 2 -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 0 2 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 0 2 0 2 1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 1 -1 1 -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 -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 2 -1 -1 0 2 0 2 1 -1 0 2 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 1 -1 0 2 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 0 2 1 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 0 2 1 -1 0 2 1 -1 1 -1 -1 1 1 -1 -1 -1 -1 -1 1 -1 0 2 1 -1 1 -1 0 2 -1 -1 0 2 0 2 -1 -1 1 1 1 -1 1 -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 -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 -1 1 -1 1 -1 -1 -1 1 -1 0 2 0 2 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 0 2 0 2 -1 -1 -1 -1 0 2 0 2 1 1 1 1 -1 -1 -1 -1 0 2 0 2 0 2 0 2 -1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 1 -1 1 -1 0 2 0 2 -1 -1 -1 -1 -1 -1 -1 -1 0 2 0 2 0 2 0 2 -1 -1 -1 -1 1 1 -1 1 0 2 0 2 -1 -1 -1 -1 0 2 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 0 2 1 -1 0 2 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 0 2 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 1 0 2 -1 -1 0 2 -1 -1 0 2 1 -1 0 2 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 1 -1 0 2 1 -1 -1 -1 1 -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 1 -1 1 -1 0 2 1 1 1 -1 -1 -1 0 2 0 2 -1 -1 -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 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 0 2 -1 -1 1 -1 1 -1 -1 -1 0 2 1 -1 1 -1 0 2 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000000 0.000564 0.000000 Top 6 Left 6 Corner: 0.000339 0.001626 0.000000 Top 7 Left 7 Corner: 0.000692 0.003982 0.000000 Top 8 Left 8 Corner: 0.000021 0.000000 0.000000 Top 9 Left 9 Corner: 0.000063 0.000005 0.000000 Top 10 Left 10 Corner: 0.000006 0.000016 0.000000 Top 11 Left 11 Corner: 0.000000 0.000002 0.000000 Top 12 Left 12 Corner: 0.000000 0.000000 0.000000 Top 13 Left 13 Corner: 0.000003 0.000013 0.000000 Top 14 Left 14 Corner: 0.000011 0.000029 0.000000 Top 15 Left 15 Corner: 0.000263 0.000545 0.000000 Top 16 Left 16 Corner: 0.000054 0.000090 0.000000 Top 17 Left 17 Corner: 0.000713 0.001282 0.000000 Top 18 Left 18 Corner: 0.000915 0.001913 0.000000 Top 19 Left 19 Corner: 0.000203 0.000581 0.000000 Top 20 Left 20 Corner: 0.000056 0.000103 0.000000 Top 21 Left 21 Corner: 0.000466 0.000979 0.000000 Top 22 Left 22 Corner: 0.003961 0.006193 0.000000 Top 23 Left 23 Corner: 0.004840 0.008136 0.000000 Top 24 Left 24 Corner: 0.006708 0.009255 0.000000 Top 25 Left 25 Corner: 0.030477 0.050789 1.257599 Top 26 Left 26 Corner: 0.147723 0.203727 5.632990 Top 27 Left 27 Corner: 0.159013 0.229269 6.383711 Top 28 Left 28 Corner: 0.175381 0.233952 7.466233 Top 29 Left 28 Corner: 0.192117 0.250547 6.997807 Top 30 Left 28 Corner: 0.689096 0.827805 28.062552 Top 31 Left 28 Corner: 0.753046 0.875288 30.666862 Top 32 Left 28 Corner: 0.798402 0.898956 32.513933 Top 33 Left 28 Corner: 0.847114 0.924670 34.497647 Top 34 Left 28 Corner: 0.896068 0.949218 36.491239 Top 35 Left 28 Corner: 0.947700 0.974948 38.593899 Top 36 Left 28 Corner: 1.000000 1.000000 40.723742 Det Product: 0 0 0