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:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 2 1 1 1 2 2 1 3 2 2 3 3 1 2 1 1 3 1 2 1 2 2 3 1 1 1 3 3 1 1 1 3 3 3 2 2 2 1 1 3 2 2 2 3 3 3 3 2 2 3 2 1 1 2 1 2 1 3 3 1 2 3 1 2 2 2 3 1 2 1 2 2 2 2 2 3 3 3 2 2 2 2 3 3 3 1 1 1 2 1 2 3 2 3 3 3 1 2 1 1 1 2 2 2 1 2 1 1 2 3 1 3 3 2 1 3 1 2 2 2 1 2 2 1 3 1 3 2 1 2 1 2 3 1 3 2 1 2 2 1 1 1 1 1 3 1 3 3 2 2 3 2 2 1 1 1 2 1 1 2 1 2 2 2 3 1 3 3 3 1 2 2 1 1 2 1 3 1 2 3 2 1 3 2 1 2 3 2 1 2 2 2 1 1 2 2 2 1 1 1 1 2 2 2 2 2 2 1 1 2 1 1 1 2 2 2 2 1 1 2 1 1 2 2 2 2 2 2 3 2 1 3 1 3 1 3 2 1 2 1 1 1 2 1 3 2 1 1 2 2 3 1 3 3 2 2 2 1 2 1 3 1 2 3 2 2 1 3 2 3 1 1 1 1 1 1 1 1 1 3 3 3 1 3 3 1 1 3 1 2 2 1 2 1 2 3 1 2 1 1 3 2 1 2 3 3 1 2 2 2 2 1 1 2 1 3 2 3 2 3 2 1 3 1 2 2 1 1 3 3 3 2 3 2 2 1 1 2 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 2 2 1 2 1 2 1 2 2 1 2 2 2 1 1 2 2 2 1 1 1 1 1 2 1 2 2 1 1 2 3 1 2 3 3 3 1 2 2 1 1 1 2 3 2 1 3 3 1 1 2 3 2 2 1 2 1 2 2 2 3 3 1 1 1 3 3 3 3 1 1 1 2 1 2 2 1 2 3 2 1 3 1 3 1 2 3 2 1 2 2 1 1 2 2 1 2 3 1 3 2 1 3 2 3 1 1 1 1 2 1 3 1 3 1 1 1 2 3 2 2 2 3 1 2 2 1 1 2 2 2 1 2 1 1 3 3 1 3 3 1 2 1 2 2 2 3 3 3 2 2 3 3 3 2 2 2 1 2 2 2 2 3 3 1 3 2 1 2 1 2 1 3 2 2 2 2 1 1 1 3 3 3 1 1 1 1 3 3 1 3 1 1 1 1 1 3 3 2 2 2 3 2 2 3 3 2 3 2 1 2 2 1 1 2 1 3 2 3 2 3 1 2 1 3 2 2 1 1 2 3 2 3 1 2 1 3 2 1 3 1 2 1 1 2 1 2 3 2 2 3 1 2 3 1 1 1 2 3 Runs Permutation: 12 15 2 21 4 5 22 8 19 29 30 28 26 11 36 10 13 34 35 7 25 27 33 24 16 32 6 17 31 3 23 14 1 20 18 9 Factors Permutation: 1 2 3 4 5 8 12 6 7 10 9 14 15 13 16 11 17 Max Product Det: 3.0053e-013 ============================================ Expanded Matrix: 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 -1 1 1 1 -1 -1 -1 -1 -1 -1 -1 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 1 -1 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 -1 0 2 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 -1 1 -1 0 2 0 2 0 2 0 2 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 -1 -1 0 2 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 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 -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 0 2 0 2 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 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 0 2 0 2 0 2 -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 0 2 0 2 0 2 0 2 -1 -1 -1 -1 0 2 -1 -1 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 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 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 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 -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 0 2 -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 0 2 1 -1 0 2 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 0 2 -1 -1 0 2 1 -1 1 -1 1 1 -1 -1 0 2 0 2 0 2 -1 -1 -1 -1 0 2 0 2 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 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 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 -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 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 0 2 1 -1 0 2 0 2 0 2 1 -1 1 -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 0 2 1 -1 1 -1 1 -1 0 2 0 2 1 -1 1 -1 1 -1 0 2 0 2 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 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 0 2 0 2 0 2 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 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 -1 -1 1 -1 0 2 -1 -1 1 -1 -1 -1 0 2 1 -1 -1 1 -1 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 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: 0.168407 0.885380 5.721475 Top 8 Left 8 Corner: 0.177380 0.798602 6.619502 Top 9 Left 9 Corner: 0.201962 0.807850 7.176118 Top 10 Left 10 Corner: 0.213438 0.769343 8.138846 Top 11 Left 11 Corner: 0.235671 0.757773 8.616204 Top 12 Left 12 Corner: 0.256474 0.771444 9.921572 Top 13 Left 13 Corner: 0.278726 0.786268 10.393608 Top 14 Left 14 Corner: 0.308973 0.800170 12.075925 Top 15 Left 15 Corner: 0.321489 0.774195 12.163149 Top 16 Left 16 Corner: 0.342354 0.771817 13.484072 Top 17 Left 17 Corner: 0.354382 0.757123 13.556967 Top 18 Left 18 Corner: 0.372780 0.747596 14.770722 Top 19 Left 19 Corner: 0.402722 0.758210 15.541533 Top 20 Left 20 Corner: 0.410027 0.741794 16.324651 Top 21 Left 21 Corner: 0.433384 0.749257 16.843644 Top 22 Left 22 Corner: 0.455758 0.749129 18.216690 Top 23 Left 23 Corner: 0.478844 0.755660 18.719621 Top 24 Left 24 Corner: 0.507341 0.764023 20.344851 Top 25 Left 25 Corner: 0.541227 0.781279 21.262598 Top 26 Left 26 Corner: 0.558500 0.775516 22.458421 Top 27 Left 27 Corner: 0.591793 0.789205 23.346603 Top 28 Left 28 Corner: 0.618098 0.796391 24.913970 Top 29 Left 29 Corner: 0.655358 0.813670 25.947742 Top 30 Left 30 Corner: 0.684985 0.822944 27.666793 Top 31 Left 30 Corner: 0.731575 0.850324 29.548577 Top 32 Left 30 Corner: 0.781333 0.879732 31.558353 Top 33 Left 30 Corner: 0.832683 0.908884 33.632394 Top 34 Left 30 Corner: 0.887408 0.939893 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: 3.005308237743222e-013 0.00133937165110112 2.033042014298637e+038 ============================================ Expanded Matrix for initial design: 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 -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 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 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 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 -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 -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 -1 -1 1 -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 0 2 -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 -1 -1 0 2 -1 -1 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 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 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 -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 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 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 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 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 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 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 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 -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 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 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 -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 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 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 1 -1 0 2 1 -1 0 2 1 -1 -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 -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 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 -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 0.000619 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: 0.001749 0.000000 0.000000 Top 9 Left 9 Corner: 0.002902 0.011225 0.000000 Top 10 Left 10 Corner: 0.000161 0.000543 0.000000 Top 11 Left 11 Corner: 0.000300 0.000711 0.000000 Top 12 Left 12 Corner: 0.000035 0.000071 0.000000 Top 13 Left 13 Corner: 0.000053 0.000183 0.000000 Top 14 Left 14 Corner: 0.000011 0.000025 0.000000 Top 15 Left 15 Corner: 0.000235 0.000523 0.000000 Top 16 Left 16 Corner: 0.000413 0.000806 0.000000 Top 17 Left 17 Corner: 0.004840 0.010532 0.000000 Top 18 Left 18 Corner: 0.005309 0.010448 0.000000 Top 19 Left 19 Corner: 0.006973 0.015848 0.000000 Top 20 Left 20 Corner: 0.001590 0.002930 0.000000 Top 21 Left 21 Corner: 0.001859 0.004120 0.000000 Top 22 Left 22 Corner: 0.003539 0.004906 0.000000 Top 23 Left 23 Corner: 0.004145 0.006687 0.000000 Top 24 Left 24 Corner: 0.005001 0.009396 0.000000 Top 25 Left 25 Corner: 0.029869 0.046554 1.104504 Top 26 Left 26 Corner: 0.118273 0.184841 5.215083 Top 27 Left 27 Corner: 0.157319 0.221527 5.516886 Top 28 Left 28 Corner: 0.177797 0.213175 6.469667 Top 29 Left 29 Corner: 0.197125 0.254998 2.088866 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 0 0