TA Algorithm to find a lean design Runs n=18, Factors s=7. Initial Design: 1 1 1 1 2 2 1 1 2 2 3 3 1 3 1 3 3 2 1 3 2 2 1 2 2 3 3 1 2 2 3 1 1 2 3 2 3 1 3 2 1 2 3 1 3 3 3 2 2 3 2 1 2 1 1 1 3 3 2 1 2 3 3 1 1 3 2 2 1 3 1 2 1 1 3 3 2 1 3 2 3 1 2 1 2 1 1 3 1 3 3 2 2 2 2 2 2 2 2 3 3 1 3 1 1 3 1 2 1 1 1 2 3 2 3 3 2 3 1 3 3 1 2 3 2 3 Criterion: maximize Det(X(5)'X(5))*...*Det(X(18)'X(18)) Search Type:(b) - f1(x1) ... f1(xs) f2(x1) ... f2(xs) Result Design: 3 1 3 2 1 1 3 2 3 2 1 1 3 3 1 2 3 3 2 3 3 3 3 1 3 2 2 3 1 1 1 1 2 1 2 3 2 3 1 3 2 1 2 3 3 2 2 1 1 2 1 1 3 1 2 1 2 2 1 1 3 1 3 1 2 2 3 1 1 1 1 1 2 2 3 2 3 3 2 1 2 1 3 2 2 2 2 2 2 2 2 3 1 2 1 2 3 1 3 3 2 3 3 1 2 2 1 3 3 3 3 2 1 3 3 1 1 2 2 1 3 1 2 3 3 1 Runs Permutation: 15 2 7 18 1 3 5 8 11 16 4 6 14 12 9 17 10 13 Factors Permutation: 2 7 3 1 6 4 5 Max Product Det: 0.00017132 ============================================ Expanded Matrix: 1 1 -1 1 0 -1 -1 1 -1 -1 -1 2 -1 -1 -1 1 0 1 0 -1 -1 1 1 2 -1 2 -1 -1 -1 -1 1 -1 0 1 1 0 1 1 -1 2 -1 -1 2 -1 -1 1 1 1 -1 1 0 0 1 -1 -1 -1 -1 2 2 -1 1 -1 -1 -1 -1 0 -1 0 -1 -1 -1 -1 2 -1 2 1 1 0 1 -1 1 0 -1 -1 2 -1 -1 -1 2 -1 1 0 1 1 0 0 -1 -1 2 -1 -1 2 2 -1 -1 1 0 -1 -1 1 -1 0 -1 2 -1 -1 -1 -1 2 -1 1 0 0 -1 -1 1 -1 1 2 2 -1 -1 -1 -1 -1 1 -1 0 0 1 -1 -1 -1 -1 2 2 -1 -1 -1 -1 1 -1 -1 0 0 1 0 1 -1 -1 2 2 -1 2 -1 1 1 0 -1 0 -1 1 0 -1 2 -1 2 -1 -1 2 1 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 -1 0 -1 0 1 -1 -1 -1 2 -1 2 -1 -1 1 1 1 0 1 1 -1 0 -1 -1 2 -1 -1 -1 2 1 0 -1 1 1 1 1 0 2 -1 -1 -1 -1 -1 2 1 -1 1 1 -1 -1 0 0 -1 -1 -1 -1 -1 2 2 1 -1 1 -1 0 1 1 -1 -1 -1 -1 2 -1 -1 -1 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.299536 0.931980 3.898060 Top 6 Left 6 Corner: 0.332789 0.936824 4.272659 Top 7 Left 7 Corner: 0.354779 0.901221 4.511237 Top 8 Left 8 Corner: 0.407748 0.876770 5.147357 Top 9 Left 9 Corner: 0.445247 0.840592 6.314824 Top 10 Left 10 Corner: 0.480132 0.814880 7.474386 Top 11 Left 11 Corner: 0.523176 0.833702 8.789439 Top 12 Left 12 Corner: 0.569234 0.840322 10.190288 Top 13 Left 13 Corner: 0.594449 0.822697 11.229211 Top 14 Left 15 Corner: 0.642832 0.819564 12.715608 Top 15 Left 15 Corner: 0.698827 0.840843 14.386230 Top 16 Left 15 Corner: 0.787493 0.887028 16.211520 Top 17 Left 15 Corner: 0.887408 0.940151 18.268399 Top 18 Left 15 Corner: 1.000000 1.000000 20.586250 Det Product: 0.000171324139189963 0.156527066063319 20476030213176.7 ============================================ Expanded Matrix for initial design: 1 -1 -1 -1 -1 0 0 -1 -1 -1 -1 -1 2 2 -1 1 -1 0 0 1 1 -1 1 -1 2 2 -1 -1 -1 -1 1 -1 1 1 0 -1 1 0 -1 -1 -1 2 -1 -1 2 1 0 -1 0 0 1 1 -1 2 -1 2 2 -1 -1 -1 1 0 0 1 -1 -1 0 1 2 2 -1 -1 -1 2 -1 1 0 1 -1 1 0 -1 0 2 -1 -1 -1 2 -1 2 1 1 -1 1 1 1 0 0 -1 -1 -1 -1 -1 2 2 1 1 0 -1 0 -1 -1 -1 -1 2 -1 2 -1 -1 -1 1 1 1 0 -1 0 1 1 -1 -1 2 -1 2 -1 -1 1 -1 -1 1 0 0 -1 1 -1 -1 -1 2 2 -1 -1 1 -1 0 -1 -1 1 1 0 -1 2 -1 -1 -1 -1 2 1 -1 1 0 1 -1 0 -1 -1 -1 2 -1 -1 2 -1 1 0 -1 -1 1 -1 1 1 2 -1 -1 -1 -1 -1 -1 1 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 0 1 1 -1 1 -1 -1 2 -1 -1 -1 -1 -1 -1 1 1 -1 0 -1 -1 -1 0 -1 -1 2 -1 -1 -1 2 1 1 0 1 1 0 1 -1 -1 2 -1 -1 2 -1 -1 1 1 1 -1 0 1 0 1 -1 -1 -1 2 -1 2 -1 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000102 0.000400 0.000000 Top 6 Left 6 Corner: 0.000000 0.000000 0.000000 Top 7 Left 7 Corner: 0.201662 0.520960 2.564254 Top 8 Left 8 Corner: 0.003094 0.007278 0.000000 Top 9 Left 9 Corner: 0.007915 0.015831 0.000000 Top 10 Left 10 Corner: 0.012638 0.018494 0.000000 Top 11 Left 11 Corner: 0.019143 0.032872 0.000000 Top 12 Left 12 Corner: 0.027841 0.040426 0.000000 Top 13 Left 13 Corner: 0.045388 0.002587 0.000000 Top 14 Left 15 Corner: 0.050093 0.061449 1.024412 Top 15 Left 15 Corner: 0.007692 0.008077 0.000000 Top 16 Left 15 Corner: 0.071794 0.089501 1.427373 Top 17 Left 15 Corner: 0.887408 0.940314 18.268399 Top 18 Left 15 Corner: 1.000000 1.000000 20.586250 Det Product: 0 0 0