TA Algorithm to find a lean design Runs n=36, Factors s=13. Initial Design: 1 2 2 3 3 2 2 3 3 2 2 3 3 2 2 2 3 3 3 3 2 2 3 3 2 2 1 3 3 2 2 2 2 3 3 3 3 2 2 2 3 3 2 2 3 3 2 2 2 2 3 3 1 2 3 2 3 3 1 3 1 1 2 1 2 2 2 3 2 3 1 3 1 3 2 1 2 1 1 3 2 3 2 3 1 3 1 2 1 2 1 2 3 2 3 2 1 3 1 3 1 2 1 2 1 2 3 3 2 1 2 2 1 3 1 1 3 2 2 3 3 2 2 1 1 2 1 3 3 1 1 3 2 2 3 1 2 2 1 1 3 3 1 2 3 2 2 3 2 1 1 2 3 1 1 3 1 3 3 1 1 3 3 1 1 3 3 1 1 2 3 3 1 1 1 1 3 3 1 1 3 3 1 1 1 3 3 3 3 1 1 1 1 3 3 2 1 1 3 3 1 1 3 3 3 3 1 1 1 3 1 3 1 1 2 1 2 2 3 2 3 2 3 1 3 1 2 1 2 1 3 2 3 2 1 1 3 1 3 1 2 1 2 3 2 3 2 2 1 3 1 3 2 1 2 1 2 3 2 3 1 3 1 1 3 2 3 3 2 1 2 2 1 2 3 1 1 3 3 2 2 3 2 1 1 2 1 1 3 3 1 2 3 3 2 2 1 1 2 2 1 3 3 1 3 2 2 3 1 2 2 1 1 1 1 2 2 1 1 2 2 1 1 2 2 2 1 1 2 2 2 2 1 1 2 2 1 1 1 2 2 1 1 1 1 2 2 2 2 1 1 2 2 2 1 1 2 2 1 1 1 1 2 2 1 1 2 1 2 2 3 2 3 3 1 3 1 2 1 2 1 2 3 2 3 2 1 3 1 3 1 2 1 2 1 2 3 2 3 1 3 1 3 2 2 1 2 1 3 2 3 2 3 1 3 1 1 1 2 2 1 3 1 1 3 2 3 3 2 2 1 2 2 1 1 3 3 1 3 2 2 3 1 2 1 1 2 3 1 1 3 3 2 2 3 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:(b) - f1(x1) ... f1(xs) f2(x1) ... f2(xs) Result Design: 2 3 3 3 2 3 2 3 2 2 2 3 2 1 2 3 1 3 3 1 2 2 1 3 1 2 1 3 1 2 1 1 2 3 3 2 1 2 3 2 1 1 1 3 1 3 1 3 3 3 1 3 1 1 2 3 1 3 2 2 3 3 1 1 2 2 1 3 1 1 2 2 2 1 2 3 3 3 1 2 3 2 3 1 2 1 1 3 1 3 2 1 3 3 1 1 3 3 1 3 1 1 3 1 2 3 2 3 3 1 1 1 3 1 2 2 2 2 2 1 3 1 3 3 1 1 2 3 2 2 1 1 2 2 1 1 3 3 2 1 3 3 2 2 1 1 3 3 3 1 3 1 1 1 3 3 2 3 2 1 3 2 3 3 1 2 1 1 2 2 2 1 1 1 2 1 3 3 3 2 3 2 1 3 1 2 3 2 1 1 2 2 3 3 1 1 3 3 3 1 1 1 3 1 3 3 1 1 2 1 3 2 3 2 2 3 3 1 2 1 1 1 1 1 2 2 1 1 2 1 2 2 1 2 1 2 3 3 2 2 1 1 3 2 1 1 3 2 1 3 2 1 3 1 1 2 3 2 2 3 2 3 3 2 2 2 3 2 3 3 3 2 2 2 1 3 3 3 1 3 2 2 2 1 2 1 1 3 1 3 1 2 3 2 2 1 2 1 3 1 2 2 2 3 3 3 2 3 2 2 3 3 1 1 2 1 2 3 1 3 3 2 3 2 1 2 2 2 2 1 2 1 2 1 1 1 2 1 1 2 3 1 2 1 3 3 1 1 2 2 3 2 2 1 3 2 1 2 2 3 1 3 3 1 2 2 1 2 2 3 3 3 2 3 1 1 1 1 1 2 3 2 2 3 1 1 3 2 3 1 1 2 2 3 3 2 2 3 2 3 3 2 3 2 3 2 2 2 3 2 1 1 1 3 1 3 1 1 1 1 2 2 2 1 2 1 1 2 2 2 3 2 1 2 1 1 2 2 3 1 3 3 2 2 2 1 1 1 2 1 2 2 2 1 1 1 3 1 1 3 3 2 2 1 3 2 2 1 Runs Permutation: 2 31 7 14 11 34 29 13 22 20 9 16 24 18 35 15 8 25 21 36 4 6 5 3 17 26 23 12 10 19 1 30 27 32 28 33 Factors Permutation: 1 6 7 5 9 11 3 4 2 12 13 10 8 Max Product Det: 1.7283e-012 ============================================ Expanded Matrix: 1 1 1 1 1 0 1 0 1 0 0 0 1 0 -1 -1 -1 2 -1 2 -1 2 2 2 -1 2 1 -1 0 1 -1 1 1 -1 0 0 -1 1 -1 0 2 -1 -1 -1 -1 -1 2 2 -1 -1 -1 2 1 -1 1 -1 0 -1 -1 0 1 1 0 -1 0 1 -1 -1 2 -1 -1 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 0 1 -1 1 0 0 1 1 -1 -1 0 -1 2 -1 -1 -1 2 2 -1 -1 -1 -1 2 1 1 -1 1 -1 -1 0 0 0 -1 0 1 1 1 -1 -1 -1 -1 2 2 2 -1 2 -1 -1 -1 1 -1 0 1 0 1 -1 0 -1 -1 1 -1 1 0 2 -1 2 -1 -1 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 0 1 1 -1 -1 -1 1 -1 0 0 0 -1 2 -1 -1 -1 -1 -1 -1 -1 2 2 2 1 1 0 -1 1 -1 1 1 -1 -1 0 1 0 0 2 -1 -1 -1 -1 -1 -1 -1 2 -1 2 2 1 -1 -1 0 0 -1 -1 1 1 0 -1 1 1 0 -1 2 2 -1 -1 -1 -1 2 -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 0 -1 1 0 1 1 -1 0 -1 -1 0 -1 2 -1 -1 2 -1 -1 -1 2 -1 -1 2 1 1 0 -1 -1 -1 0 -1 1 1 1 0 1 0 2 -1 -1 -1 2 -1 -1 -1 -1 2 -1 2 1 -1 1 -1 0 1 0 -1 -1 0 0 1 1 -1 -1 -1 2 -1 2 -1 -1 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 0 1 0 0 1 1 -1 0 -1 -1 -1 -1 2 -1 2 2 -1 -1 -1 2 -1 -1 1 -1 -1 -1 0 0 -1 -1 0 -1 0 0 -1 0 -1 -1 2 2 -1 -1 2 -1 2 2 -1 2 1 -1 0 1 1 0 0 -1 -1 1 0 -1 -1 1 2 -1 -1 2 2 -1 -1 -1 2 -1 -1 -1 1 1 -1 1 0 -1 1 -1 -1 0 1 0 0 1 -1 -1 2 -1 -1 -1 -1 2 -1 2 2 -1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 -1 -1 2 2 2 -1 2 -1 -1 -1 2 2 1 1 -1 1 1 1 -1 1 0 0 0 -1 0 -1 -1 -1 -1 -1 -1 -1 2 2 2 -1 2 -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 0 0 0 1 1 1 0 1 0 0 1 1 2 2 2 -1 -1 -1 2 -1 2 2 -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 0 0 0 -1 0 -1 0 -1 -1 -1 0 -1 2 2 2 -1 2 -1 2 -1 -1 -1 2 -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 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 0 -1 0 0 1 1 1 0 1 -1 -1 -1 2 -1 2 2 -1 -1 -1 2 -1 -1 -1 -1 1 -1 -1 0 1 0 0 1 -1 -1 1 0 1 -1 -1 2 -1 2 2 -1 -1 -1 -1 2 -1 -1 1 -1 0 0 1 1 0 0 1 0 1 1 0 1 2 2 -1 -1 2 2 -1 2 -1 -1 2 -1 1 1 1 0 0 0 1 0 -1 -1 -1 1 -1 1 -1 2 2 2 -1 2 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 0 0 0 -1 0 -1 -1 0 0 -1 -1 -1 2 2 2 -1 2 -1 -1 2 2 1 1 1 0 -1 0 -1 -1 0 0 1 -1 1 1 -1 2 -1 2 -1 -1 2 2 -1 -1 -1 -1 1 1 0 0 -1 -1 -1 0 -1 0 0 0 -1 -1 2 2 -1 -1 -1 2 -1 2 2 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 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.148550 0.958732 4.192963 Top 6 Left 6 Corner: 0.173340 0.896281 4.762203 Top 7 Left 7 Corner: 0.186015 0.842200 5.012694 Top 8 Left 8 Corner: 0.193383 0.819955 5.136323 Top 9 Left 9 Corner: 0.208547 0.777588 5.477045 Top 10 Left 10 Corner: 0.237366 0.776527 6.178009 Top 11 Left 11 Corner: 0.257813 0.783983 6.660898 Top 12 Left 12 Corner: 0.286288 0.769691 7.351267 Top 13 Left 13 Corner: 0.301243 0.749306 7.695181 Top 14 Left 14 Corner: 0.308827 0.752258 7.853835 Top 15 Left 15 Corner: 0.336623 0.774231 9.175759 Top 16 Left 16 Corner: 0.357685 0.765479 10.360080 Top 17 Left 17 Corner: 0.379532 0.773847 11.597773 Top 18 Left 18 Corner: 0.385390 0.769713 12.351052 Top 19 Left 19 Corner: 0.403246 0.760188 13.485773 Top 20 Left 20 Corner: 0.442734 0.797027 15.385066 Top 21 Left 21 Corner: 0.449797 0.779200 16.182228 Top 22 Left 22 Corner: 0.478352 0.796883 17.760922 Top 23 Left 23 Corner: 0.502271 0.795518 19.193815 Top 24 Left 24 Corner: 0.538916 0.816677 21.144962 Top 25 Left 25 Corner: 0.543073 0.791977 21.831828 Top 26 Left 26 Corner: 0.570997 0.794997 23.474728 Top 27 Left 26 Corner: 0.611734 0.819174 25.149506 Top 28 Left 26 Corner: 0.655378 0.845317 26.943770 Top 29 Left 26 Corner: 0.694409 0.864409 28.548409 Top 30 Left 26 Corner: 0.735765 0.884800 30.248614 Top 31 Left 26 Corner: 0.776060 0.902317 31.905212 Top 32 Left 26 Corner: 0.818561 0.921662 33.652535 Top 33 Left 26 Corner: 0.861250 0.940144 35.407552 Top 34 Left 26 Corner: 0.906165 0.959901 37.254096 Top 35 Left 26 Corner: 0.951927 0.979310 39.135446 Top 36 Left 26 Corner: 1.000000 1.000000 41.111804 Det Product: 1.728293271337053e-012 0.002577134026724592 1.159379902322952e+037 ============================================ Expanded Matrix for initial design: 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 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 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 0 0 1 1 0 0 0 0 1 1 -1 -1 2 2 -1 -1 2 2 2 2 -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 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 0 1 -1 1 -1 0 -1 0 -1 -1 2 -1 2 -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 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 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 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 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 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 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 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 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 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 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 0 0 -1 -1 0 -1 -1 -1 -1 2 -1 -1 2 2 -1 -1 2 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 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 0 0 0 0 -1 -1 0 0 -1 -1 -1 -1 2 2 2 2 -1 -1 2 2 -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 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 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 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 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 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 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 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 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 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: 0.000067 0.000432 0.000000 Top 6 Left 6 Corner: 0.000001 0.000003 0.000000 Top 7 Left 7 Corner: 0.000005 0.000027 0.000000 Top 8 Left 8 Corner: 0.000000 0.000000 0.000000 Top 9 Left 9 Corner: 0.000059 0.000256 0.000000 Top 10 Left 10 Corner: 0.000166 0.000628 0.000000 Top 11 Left 11 Corner: 0.000333 0.001103 0.000000 Top 12 Left 12 Corner: 0.000760 0.001449 0.000000 Top 13 Left 13 Corner: 0.017864 0.041944 0.000000 Top 14 Left 14 Corner: 0.237694 0.614042 6.044838 Top 15 Left 15 Corner: 0.249774 0.582271 6.808412 Top 16 Left 16 Corner: 0.036126 0.065024 1.000000 Top 17 Left 17 Corner: 0.044638 0.090446 1.205560 Top 18 Left 18 Corner: 0.007700 0.015473 0.000000 Top 19 Left 19 Corner: 0.009287 0.020786 0.000000 Top 20 Left 20 Corner: 0.002112 0.003596 0.000000 Top 21 Left 21 Corner: 0.002463 0.005276 0.000000 Top 22 Left 22 Corner: 0.003842 0.006361 0.000000 Top 23 Left 23 Corner: 0.022338 0.038853 0.000000 Top 24 Left 24 Corner: 0.029553 0.045609 1.068296 Top 25 Left 25 Corner: 0.133980 0.202108 5.223303 Top 26 Left 26 Corner: 0.570997 0.792250 23.474728 Top 27 Left 26 Corner: 0.611734 0.817008 25.149506 Top 28 Left 26 Corner: 0.655378 0.843623 26.943770 Top 29 Left 26 Corner: 0.694409 0.862974 28.548409 Top 30 Left 26 Corner: 0.735765 0.883941 30.248614 Top 31 Left 26 Corner: 0.776060 0.902099 31.905212 Top 32 Left 26 Corner: 0.818561 0.921713 33.652535 Top 33 Left 26 Corner: 0.861250 0.940144 35.407552 Top 34 Left 26 Corner: 0.906165 0.959949 37.254096 Top 35 Left 26 Corner: 0.951927 0.979310 39.135446 Top 36 Left 26 Corner: 1.000000 1.000000 41.111804 Det Product: 2.8287e-062+2.062e-060i 0+0i 0+0i