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:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 3 3 1 3 1 2 2 2 2 1 1 3 3 3 3 2 2 2 1 3 1 1 1 1 2 2 1 1 1 3 3 2 3 3 2 3 1 3 2 3 2 3 2 1 2 3 3 1 2 3 3 2 1 3 1 1 2 3 1 2 1 1 3 2 1 3 1 1 2 1 2 3 3 3 2 3 1 1 2 3 1 1 1 2 2 2 2 2 2 2 2 1 1 2 3 1 3 3 1 2 1 3 3 2 1 3 1 1 1 2 3 2 1 3 2 1 2 2 3 3 2 3 3 2 1 3 Runs Permutation: 3 2 5 1 18 7 4 15 12 16 9 8 14 13 11 10 6 17 Factors Permutation: 3 2 1 6 5 7 4 Max Product Det: 6.0629e-005 ============================================ Expanded Matrix: 1 1 -1 1 -1 -1 -1 1 -1 -1 -1 0 2 0 2 1 0 2 0 2 -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 -1 -1 -1 -1 -1 0 2 0 2 -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 -1 0 2 1 -1 0 2 1 -1 1 0 2 -1 -1 0 2 1 -1 1 -1 -1 -1 0 2 1 1 -1 1 -1 0 2 -1 -1 1 -1 -1 -1 -1 -1 1 0 2 1 -1 -1 -1 0 2 -1 -1 -1 -1 1 -1 1 0 2 -1 -1 1 -1 -1 -1 -1 -1 0 2 -1 -1 1 0 2 1 -1 1 -1 1 -1 0 2 1 -1 -1 -1 1 -1 -1 0 2 1 -1 -1 -1 -1 -1 -1 -1 0 2 1 0 2 0 2 0 2 0 2 0 2 0 2 0 2 1 -1 -1 -1 -1 0 2 1 -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 0 2 1 -1 0 2 1 -1 -1 1 -1 0 2 -1 -1 0 2 0 2 1 -1 1 1 -1 0 2 1 -1 1 -1 0 2 -1 -1 1 -1 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.207622 0.755082 4.192963 Top 6 Left 6 Corner: 0.283064 0.827037 5.241483 Top 7 Left 7 Corner: 0.338990 0.873600 6.902460 Top 8 Left 8 Corner: 0.366310 0.858165 6.981707 Top 9 Left 9 Corner: 0.400970 0.815050 8.201858 Top 10 Left 10 Corner: 0.464979 0.821852 9.017218 Top 11 Left 11 Corner: 0.485994 0.808501 9.969970 Top 12 Left 12 Corner: 0.532952 0.800078 10.455487 Top 13 Left 13 Corner: 0.570997 0.796947 11.737364 Top 14 Left 15 Corner: 0.616949 0.800135 12.203622 Top 15 Left 15 Corner: 0.698827 0.842005 14.386230 Top 16 Left 15 Corner: 0.787493 0.887728 16.211520 Top 17 Left 15 Corner: 0.887408 0.940314 18.268399 Top 18 Left 15 Corner: 1.000000 1.000000 20.586250 Det Product: 6.06287432685097e-005 0.0909188765237828 102582062239887 ============================================ Expanded Matrix for initial design: 1 -1 -1 -1 -1 -1 -1 -1 -1 0 2 0 2 -1 -1 1 -1 -1 0 2 0 2 1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 -1 1 -1 0 2 -1 -1 1 -1 0 2 1 0 2 -1 -1 0 2 0 2 1 -1 1 -1 -1 -1 1 0 2 0 2 1 -1 -1 -1 -1 -1 0 2 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 0 2 0 2 1 1 -1 0 2 -1 -1 0 2 -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 -1 0 2 0 2 -1 -1 1 -1 1 -1 -1 0 2 -1 -1 -1 -1 1 -1 1 -1 0 2 1 -1 -1 1 -1 0 2 1 -1 -1 -1 0 2 -1 -1 1 0 2 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 0 2 0 2 0 2 0 2 0 2 0 2 0 2 1 0 2 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 1 1 -1 0 2 1 -1 1 -1 0 2 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 0 2 1 -1 0 2 1 -1 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000149 0.000512 0.000000 Top 6 Left 6 Corner: 0.000742 0.001901 0.000000 Top 7 Left 7 Corner: 0.312241 0.806451 6.357804 Top 8 Left 8 Corner: 0.348386 0.792550 6.640092 Top 9 Left 9 Corner: 0.500000 1.000000 10.227532 Top 10 Left 10 Corner: 0.015117 0.000000 0.000000 Top 11 Left 11 Corner: 0.476773 0.781793 9.780799 Top 12 Left 12 Corner: 0.029208 0.044894 0.000000 Top 13 Left 13 Corner: 0.044519 0.050510 0.000000 Top 14 Left 15 Corner: 0.054013 0.062406 1.000000 Top 15 Left 15 Corner: 0.007537 0.008997 0.000000 Top 16 Left 15 Corner: 0.077437 0.094496 1.502116 Top 17 Left 15 Corner: 0.887408 0.940314 18.268399 Top 18 Left 15 Corner: 1.000000 1.000000 20.586250 Det Product: 1.5799e-018 0 0