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:(b) - f1(x1) ... f1(xs) f2(x1) ... f2(xs) Result Design: 1 2 1 3 2 3 3 3 3 2 3 2 2 2 2 2 2 2 2 3 3 2 3 2 2 2 3 3 2 3 1 1 1 1 2 3 2 1 3 3 2 3 1 1 2 2 1 1 3 3 3 2 1 2 1 1 1 2 3 2 1 1 2 3 3 1 1 2 2 2 3 3 1 1 2 2 2 2 3 1 1 3 1 3 3 3 1 1 3 1 1 2 1 1 3 1 1 1 1 3 1 3 3 3 3 2 2 1 3 1 3 1 2 1 3 2 1 3 2 2 2 2 1 1 2 1 2 3 2 1 3 2 1 3 3 1 1 2 2 2 3 3 1 1 1 2 2 3 3 1 1 2 2 2 2 3 1 2 3 2 1 1 1 3 3 2 2 1 2 2 1 3 3 2 3 1 1 3 1 2 2 1 2 3 2 1 2 2 3 1 1 3 3 2 1 2 1 2 1 3 3 1 3 3 1 3 1 3 1 1 2 2 1 2 3 2 3 1 3 2 1 3 2 1 1 1 2 2 3 2 2 2 1 1 2 3 1 3 1 3 1 2 2 1 3 3 3 2 2 3 1 2 1 2 1 1 1 1 3 1 3 3 3 1 1 1 3 1 1 3 2 1 2 3 2 2 3 2 2 3 2 3 2 3 3 1 1 1 2 3 2 2 2 3 3 3 2 3 3 2 1 1 1 3 1 2 1 3 2 2 1 2 3 3 1 1 2 2 1 1 2 3 1 2 1 3 3 3 2 2 2 1 1 1 1 1 3 2 3 2 2 2 3 1 3 2 2 1 1 1 3 2 2 1 2 3 3 2 3 1 2 1 2 2 1 3 1 1 2 3 3 2 2 1 3 1 2 2 3 3 1 2 3 1 3 2 2 2 1 1 2 1 2 2 1 1 2 1 1 2 1 2 1 2 2 1 1 1 1 2 1 1 1 2 2 2 1 2 2 1 1 1 2 1 1 2 2 3 3 3 1 1 2 2 3 1 2 1 2 1 2 2 2 2 1 2 1 1 1 1 2 2 2 1 2 2 1 2 1 1 1 2 2 1 2 2 1 1 2 2 2 1 3 1 3 3 3 1 2 1 1 2 2 2 1 1 1 3 3 1 2 3 2 3 2 1 1 1 2 3 1 3 2 1 1 3 1 2 2 3 2 2 1 3 3 2 1 1 3 1 2 2 1 2 3 2 1 2 1 3 2 3 3 1 2 2 1 1 3 2 Runs Permutation: 3 2 29 12 21 14 15 18 30 9 35 10 8 16 6 7 19 13 4 1 17 23 24 34 32 11 28 25 33 27 26 36 31 5 22 20 Factors Permutation: 1 2 3 4 7 12 5 13 11 14 10 9 6 15 8 Max Product Det: 5.1188e-013 ============================================ Expanded Matrix: 1 -1 1 -1 1 0 1 1 1 1 0 1 0 0 0 0 -1 2 -1 -1 -1 -1 2 -1 2 2 2 2 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 2 -1 -1 2 -1 2 2 2 -1 -1 2 -1 1 -1 -1 -1 -1 0 1 0 -1 1 1 0 1 -1 -1 0 -1 2 -1 2 -1 -1 -1 2 -1 -1 -1 2 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 0 0 0 1 1 -1 -1 0 -1 -1 -1 -1 2 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 -1 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 0 0 -1 -1 -1 -1 2 -1 -1 2 -1 -1 2 2 1 1 1 -1 -1 0 -1 0 1 0 -1 1 0 -1 1 1 -1 2 -1 2 -1 2 -1 -1 2 -1 -1 -1 1 -1 -1 1 0 0 1 1 -1 -1 -1 0 0 1 1 -1 2 2 -1 -1 -1 -1 -1 2 2 -1 -1 -1 1 -1 1 1 0 0 1 -1 0 1 0 -1 -1 -1 1 1 2 2 -1 -1 2 -1 2 -1 -1 -1 -1 -1 1 1 1 -1 0 0 -1 1 1 0 1 -1 -1 1 -1 0 2 2 -1 -1 -1 2 -1 -1 -1 -1 -1 2 1 1 -1 1 1 0 -1 0 0 1 -1 -1 1 1 0 -1 -1 2 -1 2 2 -1 -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 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 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 0 0 1 -1 0 -1 0 -1 -1 -1 -1 -1 2 2 -1 -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 0 0 1 0 0 1 0 1 0 1 1 -1 2 2 -1 2 2 -1 2 -1 2 -1 -1 1 -1 -1 -1 0 1 0 0 0 1 1 1 0 1 1 0 2 -1 2 2 2 -1 -1 -1 2 -1 -1 2 1 -1 -1 -1 1 -1 0 -1 1 0 0 -1 0 1 1 -1 -1 -1 2 -1 -1 2 2 -1 2 -1 -1 -1 1 -1 1 1 -1 -1 0 1 -1 0 -1 1 1 1 0 0 -1 -1 2 -1 -1 2 -1 -1 -1 -1 2 2 1 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 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 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 1 -1 0 1 -1 1 0 0 0 -1 -1 -1 -1 -1 2 -1 -1 -1 2 2 2 -1 -1 1 1 -1 1 0 -1 -1 0 -1 -1 0 -1 0 -1 0 0 2 -1 -1 2 -1 -1 2 -1 2 -1 2 2 1 -1 -1 -1 -1 0 -1 -1 -1 0 0 0 -1 0 0 -1 -1 2 -1 -1 -1 2 2 2 -1 2 2 -1 1 -1 -1 1 -1 -1 0 0 1 1 1 -1 -1 0 0 1 -1 -1 2 2 -1 -1 -1 -1 -1 2 2 -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 0 0 -1 0 -1 -1 -1 0 0 -1 0 -1 2 2 -1 2 -1 -1 -1 2 2 -1 2 1 1 -1 -1 0 0 0 -1 1 -1 1 1 1 -1 0 -1 2 2 2 -1 -1 -1 -1 -1 -1 -1 2 -1 1 -1 1 1 0 -1 -1 -1 1 1 -1 0 1 0 1 0 2 -1 -1 -1 -1 -1 -1 2 -1 2 -1 2 1 -1 -1 -1 0 1 -1 1 0 -1 -1 1 -1 0 0 1 2 -1 -1 -1 2 -1 -1 -1 -1 2 2 -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 -1 0 0 -1 -1 1 0 -1 -1 2 -1 -1 -1 2 2 -1 -1 -1 2 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.131747 0.914610 4.373448 Top 6 Left 6 Corner: 0.141435 0.817627 4.447960 Top 7 Left 7 Corner: 0.174171 0.807518 5.270007 Top 8 Left 8 Corner: 0.189370 0.777784 5.566315 Top 9 Left 9 Corner: 0.214692 0.797603 6.170061 Top 10 Left 10 Corner: 0.228793 0.787097 6.457902 Top 11 Left 11 Corner: 0.247563 0.792773 6.885403 Top 12 Left 12 Corner: 0.261188 0.776930 7.175659 Top 13 Left 13 Corner: 0.277611 0.758680 7.547957 Top 14 Left 14 Corner: 0.306225 0.747074 8.252083 Top 15 Left 15 Corner: 0.310389 0.707947 8.299951 Top 16 Left 16 Corner: 0.323255 0.700503 8.585772 Top 17 Left 17 Corner: 0.351258 0.721139 9.893204 Top 18 Left 18 Corner: 0.376323 0.714189 11.166506 Top 19 Left 19 Corner: 0.381994 0.706469 11.876116 Top 20 Left 20 Corner: 0.425436 0.749366 13.793923 Top 21 Left 21 Corner: 0.451549 0.759126 15.207480 Top 22 Left 22 Corner: 0.487356 0.781033 16.990171 Top 23 Left 23 Corner: 0.511740 0.787189 18.411777 Top 24 Left 24 Corner: 0.518216 0.768073 19.191596 Top 25 Left 25 Corner: 0.557086 0.795170 21.187119 Top 26 Left 26 Corner: 0.576194 0.794096 22.458421 Top 27 Left 27 Corner: 0.585521 0.783037 23.346603 Top 28 Left 28 Corner: 0.624481 0.805010 25.431217 Top 29 Left 28 Corner: 0.665749 0.828036 27.111794 Top 30 Left 28 Corner: 0.709744 0.853068 28.903429 Top 31 Left 28 Corner: 0.756646 0.879767 30.813461 Top 32 Left 28 Corner: 0.806648 0.908240 32.849715 Top 33 Left 28 Corner: 0.851163 0.928954 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: 5.11876478835128e-013 0.0009658815454281695 3.678751064097166e+036 ============================================ Expanded Matrix for initial design: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 0.000564 0.000000 Top 6 Left 6 Corner: 0.080125 0.539623 2.519842 Top 7 Left 7 Corner: 0.000689 0.003922 0.000000 Top 8 Left 8 Corner: 0.000000 0.000000 0.000000 Top 9 Left 9 Corner: 0.002383 0.010249 0.000000 Top 10 Left 10 Corner: 0.005113 0.019115 0.000000 Top 11 Left 11 Corner: 0.000357 0.001176 0.000000 Top 12 Left 12 Corner: 0.000042 0.000064 0.000000 Top 13 Left 13 Corner: 0.001345 0.003243 0.000000 Top 14 Left 14 Corner: 0.020844 0.054414 0.000000 Top 15 Left 15 Corner: 0.028674 0.061469 0.000000 Top 16 Left 16 Corner: 0.037262 0.071462 0.000000 Top 17 Left 17 Corner: 0.271025 0.551203 7.633427 Top 18 Left 18 Corner: 0.302853 0.584538 8.986459 Top 19 Left 19 Corner: 0.053685 0.110033 1.698038 Top 20 Left 20 Corner: 0.011276 0.021201 0.000000 Top 21 Left 21 Corner: 0.000000 0.021413 0.000000 Top 22 Left 22 Corner: 0.018296 0.027592 0.000000 Top 23 Left 23 Corner: 0.018698 0.033777 0.000000 Top 24 Left 24 Corner: 0.006302 0.009969 0.000000 Top 25 Left 25 Corner: 0.032089 0.049492 1.284321 Top 26 Left 26 Corner: 0.143579 0.206671 5.340511 Top 27 Left 27 Corner: 0.162281 0.230101 5.990057 Top 28 Left 28 Corner: 0.181621 0.236149 7.501427 Top 29 Left 28 Corner: 0.192575 0.249552 7.340784 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