TA Algorithm to find a lean design Runs n=27, Factors s=13. Initial Design: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 1 1 1 1 3 3 3 3 3 2 2 2 2 1 2 2 3 1 1 2 2 3 1 2 2 3 1 2 2 3 2 2 3 3 1 3 1 1 2 1 2 2 3 3 3 1 1 2 2 3 3 1 1 3 3 2 1 1 3 3 2 1 3 3 2 1 3 3 2 2 2 1 1 3 3 2 2 1 1 3 3 2 3 3 2 2 1 2 1 1 3 2 1 2 2 1 2 1 2 2 2 1 2 2 2 1 2 2 2 3 2 3 3 1 3 1 1 2 1 2 2 3 1 3 1 1 3 2 3 3 2 2 3 1 1 2 2 3 1 2 2 3 1 2 2 3 1 2 3 3 1 2 1 1 2 3 2 2 3 1 3 1 1 2 3 3 3 1 2 2 3 1 3 1 2 3 1 3 2 3 1 3 2 3 1 3 2 3 1 2 1 1 2 3 2 2 3 1 3 3 1 2 3 2 3 1 2 1 3 1 3 3 1 3 1 3 3 3 1 3 3 3 1 3 3 2 1 2 1 1 2 3 2 2 3 1 3 3 3 2 3 2 2 1 2 1 1 3 2 1 2 1 3 2 1 2 3 2 1 2 3 2 1 2 2 1 3 2 3 2 1 3 1 3 2 1 2 3 2 1 3 1 1 3 2 3 3 3 2 1 1 3 3 2 1 3 3 2 1 3 3 2 1 2 1 1 3 2 2 2 1 3 3 3 2 1 3 2 2 1 3 1 1 3 2 Criterion: maximize Det(X(5)'X(5))*...*Det(X(27)'X(27)) Search Type:(b) - f1(x1) ... f1(xs) f2(x1) ... f2(xs) Result Design: 3 2 1 3 2 2 3 2 1 1 3 1 3 3 3 2 1 1 3 1 2 3 1 3 3 2 3 1 3 2 2 3 1 3 1 2 1 3 3 1 1 1 1 3 3 3 2 3 2 2 2 3 1 3 3 3 3 1 1 3 3 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 2 3 3 1 2 1 1 2 2 2 2 3 1 3 1 3 1 1 2 3 3 2 3 2 1 3 3 3 1 1 2 3 2 3 1 3 1 3 2 1 2 3 1 3 3 2 1 2 1 2 2 2 1 3 3 3 1 3 3 2 1 2 3 1 2 1 1 3 2 2 3 1 3 3 2 1 2 3 2 1 3 3 3 1 2 3 1 3 3 2 1 3 2 3 3 2 2 1 1 1 2 2 3 1 2 3 2 2 3 3 1 1 1 2 1 2 3 1 3 2 1 2 2 3 1 3 1 2 2 2 3 2 2 1 3 1 1 3 3 2 3 1 2 2 2 1 1 3 2 3 2 1 3 3 2 1 2 1 2 1 1 3 2 2 3 1 1 1 1 2 2 2 3 2 3 3 3 2 3 1 3 2 3 1 2 2 2 1 3 2 1 2 1 2 3 3 2 1 2 1 3 1 2 2 1 2 2 2 2 1 1 2 2 2 2 1 2 1 3 3 3 1 2 2 2 1 2 2 3 1 2 3 1 2 3 3 2 3 1 1 2 1 2 2 2 3 1 1 2 1 3 2 1 2 2 3 3 2 1 3 1 1 2 3 3 2 1 2 2 Runs Permutation: 27 7 16 3 19 1 21 6 25 18 12 15 24 9 5 23 11 13 8 2 17 22 10 20 14 4 26 Factors Permutation: 2 3 4 1 6 7 5 13 8 10 12 11 9 Max Product Det: 1.9179e-007 ============================================ Expanded Matrix: 1 1 0 -1 1 0 0 1 0 -1 -1 1 -1 1 -1 2 -1 -1 2 2 -1 2 -1 -1 -1 -1 -1 1 1 1 0 -1 -1 1 -1 0 1 -1 1 1 0 -1 -1 2 -1 -1 -1 -1 2 -1 -1 -1 -1 2 1 1 -1 1 0 0 1 -1 1 -1 0 -1 1 1 -1 -1 -1 2 2 -1 -1 -1 -1 2 -1 -1 -1 1 -1 -1 -1 -1 1 1 1 0 1 0 0 0 1 -1 -1 -1 -1 -1 -1 -1 2 -1 2 2 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 0 1 1 -1 0 -1 -1 0 0 -1 -1 -1 -1 2 -1 -1 -1 2 -1 -1 2 2 1 0 0 1 -1 1 -1 1 -1 -1 0 1 1 0 2 2 -1 -1 -1 -1 -1 -1 -1 2 -1 -1 2 1 1 0 -1 1 1 1 -1 -1 0 1 0 1 -1 -1 2 -1 -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 -1 2 -1 2 -1 -1 -1 -1 2 -1 2 1 -1 0 0 0 -1 1 1 1 -1 1 1 0 -1 -1 2 2 2 -1 -1 -1 -1 -1 -1 -1 2 -1 1 0 1 -1 0 -1 -1 1 0 0 1 -1 1 1 2 -1 -1 2 -1 -1 -1 2 2 -1 -1 -1 -1 1 0 -1 0 1 0 -1 1 1 1 -1 0 1 -1 2 -1 2 -1 2 -1 -1 -1 -1 -1 2 -1 -1 1 1 1 0 -1 1 0 1 1 0 0 -1 -1 -1 -1 -1 2 -1 -1 2 -1 -1 2 2 -1 -1 -1 1 0 0 1 -1 0 1 0 0 1 1 -1 -1 -1 2 2 -1 -1 2 -1 2 2 -1 -1 -1 -1 -1 1 0 -1 0 1 -1 1 0 -1 0 0 1 -1 1 2 -1 2 -1 -1 -1 2 -1 2 2 -1 -1 -1 1 -1 0 0 0 1 0 0 -1 1 -1 -1 1 1 -1 2 2 2 -1 2 2 -1 -1 -1 -1 -1 -1 1 0 1 -1 0 0 0 -1 -1 1 0 1 0 -1 2 -1 -1 2 2 2 -1 -1 -1 2 -1 2 -1 1 1 1 0 -1 0 -1 0 -1 -1 1 0 0 1 -1 -1 2 -1 2 -1 2 -1 -1 -1 2 2 -1 1 -1 -1 -1 -1 0 0 0 1 0 1 1 1 0 -1 -1 -1 -1 2 2 2 -1 2 -1 -1 -1 2 1 1 -1 1 0 1 -1 0 0 0 -1 1 0 -1 -1 -1 -1 2 -1 -1 2 2 2 -1 -1 2 -1 1 0 -1 0 1 1 0 -1 0 -1 1 -1 0 0 2 -1 2 -1 -1 2 -1 2 -1 -1 -1 2 2 1 -1 0 0 0 0 -1 -1 0 0 0 0 -1 0 -1 2 2 2 2 -1 -1 2 2 2 2 -1 2 1 -1 1 1 1 -1 0 0 0 -1 0 0 1 -1 -1 -1 -1 -1 -1 2 2 2 -1 2 2 -1 -1 1 0 1 -1 0 1 1 0 1 -1 -1 0 -1 0 2 -1 -1 2 -1 -1 2 -1 -1 -1 2 -1 2 1 0 0 1 -1 -1 0 -1 1 0 -1 0 0 1 2 2 -1 -1 -1 2 -1 -1 2 -1 2 2 -1 1 1 0 -1 1 -1 -1 0 1 1 0 -1 0 0 -1 2 -1 -1 -1 -1 2 -1 -1 2 -1 2 2 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.214798 0.958732 4.192963 Top 6 Left 6 Corner: 0.216018 0.812641 4.160168 Top 7 Left 7 Corner: 0.243533 0.784989 4.645011 Top 8 Left 8 Corner: 0.294871 0.820266 5.583629 Top 9 Left 9 Corner: 0.333333 0.841213 6.276492 Top 10 Left 10 Corner: 0.376449 0.857596 7.056474 Top 11 Left 11 Corner: 0.407032 0.861359 7.601667 Top 12 Left 12 Corner: 0.443018 0.876298 8.248378 Top 13 Left 13 Corner: 0.475943 0.877522 8.838384 Top 14 Left 14 Corner: 0.558785 0.966829 10.353691 Top 15 Left 15 Corner: 0.544123 0.900335 10.827225 Top 16 Left 16 Corner: 0.551075 0.864210 11.671556 Top 17 Left 17 Corner: 0.587016 0.873142 13.136463 Top 18 Left 18 Corner: 0.606021 0.863462 14.241961 Top 19 Left 19 Corner: 0.639962 0.869314 15.712763 Top 20 Left 20 Corner: 0.645711 0.843168 16.491167 Top 21 Left 21 Corner: 0.672154 0.845939 17.789644 Top 22 Left 22 Corner: 0.708784 0.856383 19.377114 Top 23 Left 23 Corner: 0.750816 0.873887 21.142768 Top 24 Left 24 Corner: 0.799339 0.893341 23.128169 Top 25 Left 25 Corner: 0.838804 0.902959 24.883422 Top 26 Left 26 Corner: 0.904744 0.938499 27.465068 Top 27 Left 27 Corner: 1.000000 1.000000 31.011263 Det Product: 1.91785509659702e-007 0.047760748037806 2.51624662134672e+024 ============================================ Expanded Matrix for initial design: 1 -1 -1 -1 -1 -1 -1 -1 -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 0 0 0 1 1 1 1 -1 -1 -1 -1 2 2 2 2 2 -1 -1 -1 -1 1 -1 -1 -1 -1 1 1 1 1 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 2 2 2 1 -1 0 0 1 -1 -1 0 0 1 -1 0 0 1 -1 2 2 -1 -1 -1 2 2 -1 -1 2 2 -1 1 -1 0 0 1 0 0 1 1 -1 1 -1 -1 0 -1 2 2 -1 2 2 -1 -1 -1 -1 -1 -1 2 1 -1 0 0 1 1 1 -1 -1 0 0 1 1 -1 -1 2 2 -1 -1 -1 -1 -1 2 2 -1 -1 -1 1 -1 1 1 0 -1 -1 1 1 0 -1 1 1 0 -1 -1 -1 2 -1 -1 -1 -1 2 -1 -1 -1 2 1 -1 1 1 0 0 0 -1 -1 1 1 0 0 -1 -1 -1 -1 2 2 2 -1 -1 -1 -1 2 2 -1 1 -1 1 1 0 1 1 0 0 -1 0 -1 -1 1 -1 -1 -1 2 -1 -1 2 2 -1 2 -1 -1 -1 1 0 -1 0 0 -1 0 -1 0 0 0 -1 0 0 2 -1 2 2 -1 2 -1 2 2 2 -1 2 2 1 0 -1 0 0 0 1 0 1 1 -1 1 -1 -1 2 -1 2 2 2 -1 2 -1 -1 -1 -1 -1 -1 1 0 -1 0 0 1 -1 1 -1 -1 1 0 1 1 2 -1 2 2 -1 -1 -1 -1 -1 -1 2 -1 -1 1 0 0 1 -1 -1 0 0 1 -1 0 0 1 -1 2 2 -1 -1 -1 2 2 -1 -1 2 2 -1 -1 1 0 0 1 -1 0 1 1 -1 0 -1 -1 0 1 2 2 -1 -1 2 -1 -1 -1 2 -1 -1 2 -1 1 0 0 1 -1 1 -1 -1 0 1 1 1 -1 0 2 2 -1 -1 -1 -1 -1 2 -1 -1 -1 -1 2 1 0 1 -1 1 -1 0 1 -1 1 0 1 -1 1 2 -1 -1 -1 -1 2 -1 -1 -1 2 -1 -1 -1 1 0 1 -1 1 0 1 -1 0 -1 -1 0 1 0 2 -1 -1 -1 2 -1 -1 2 -1 -1 2 -1 2 1 0 1 -1 1 1 -1 0 1 0 1 -1 0 -1 2 -1 -1 -1 -1 -1 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 0 -1 0 -1 -1 0 1 0 0 -1 -1 -1 -1 2 -1 2 -1 -1 2 -1 2 2 1 1 -1 1 1 1 0 1 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 2 -1 2 2 -1 2 -1 -1 1 1 0 -1 0 -1 1 0 -1 0 1 0 -1 0 -1 2 -1 2 -1 -1 2 -1 2 -1 2 -1 2 1 1 0 -1 0 0 -1 1 0 1 0 -1 1 -1 -1 2 -1 2 2 -1 -1 2 -1 2 -1 -1 -1 1 1 0 -1 0 1 0 -1 1 -1 -1 1 0 1 -1 2 -1 2 -1 2 -1 -1 -1 -1 -1 2 -1 1 1 1 0 -1 -1 1 1 0 -1 1 1 0 -1 -1 -1 2 -1 -1 -1 -1 2 -1 -1 -1 2 -1 1 1 1 0 -1 0 -1 -1 1 0 0 0 -1 1 -1 -1 2 -1 2 -1 -1 -1 2 2 2 -1 -1 1 1 1 0 -1 1 0 0 -1 1 -1 -1 1 0 -1 -1 2 -1 -1 2 2 -1 -1 -1 -1 -1 2 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000000 0.000000 0.000000 Top 6 Left 6 Corner: 0.000000 0.000000 0.000000 Top 7 Left 7 Corner: 0.000000 0.000000 0.000000 Top 8 Left 8 Corner: 0.000000 0.000000 0.000000 Top 9 Left 9 Corner: 0.000000 0.000000 0.000000 Top 10 Left 10 Corner: 0.000003 0.000012 0.000000 Top 11 Left 11 Corner: 0.000014 0.000035 0.000000 Top 12 Left 12 Corner: 0.000780 0.002081 0.000000 Top 13 Left 13 Corner: 0.001324 0.000173 0.000000 Top 14 Left 14 Corner: 0.026811 0.054920 0.000000 Top 15 Left 15 Corner: 0.003202 0.006210 0.000000 Top 16 Left 16 Corner: 0.004135 0.005955 0.000000 Top 17 Left 17 Corner: 0.007212 0.012320 0.000000 Top 18 Left 18 Corner: 0.001386 0.001844 0.000000 Top 19 Left 19 Corner: 0.013807 0.022092 0.000000 Top 20 Left 20 Corner: 0.015873 0.021437 0.000000 Top 21 Left 21 Corner: 0.019515 0.026373 0.000000 Top 22 Left 22 Corner: 0.026947 0.032985 0.000000 Top 23 Left 23 Corner: 0.033843 0.039631 0.000000 Top 24 Left 24 Corner: 0.184961 0.198800 5.057262 Top 25 Left 25 Corner: 0.793557 0.858285 23.541152 Top 26 Left 26 Corner: 0.904744 0.938459 27.465068 Top 27 Left 27 Corner: 1.000000 1.000000 31.011263 Det Product: 0 0 0