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:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 1 3 1 1 3 2 3 3 1 1 2 2 2 2 3 2 2 3 1 1 1 3 3 1 2 2 2 1 1 3 3 1 1 3 3 1 3 3 1 2 2 3 2 3 2 3 1 2 1 1 3 1 1 1 3 1 3 3 2 1 3 2 2 2 1 1 2 2 3 3 3 2 3 2 3 2 3 2 2 2 2 1 1 2 2 1 1 2 1 1 2 1 1 1 2 2 2 1 2 1 2 1 2 1 1 1 3 3 1 1 3 3 2 2 1 2 2 1 2 3 3 2 1 2 2 3 3 1 1 1 2 3 1 3 1 3 1 2 3 2 2 1 2 2 2 1 2 1 3 2 3 3 1 1 2 3 1 1 2 1 2 3 3 2 3 1 1 3 2 1 2 2 1 1 1 1 2 2 1 2 2 1 2 3 3 1 1 3 1 3 1 3 1 3 1 2 2 1 1 2 3 3 3 2 2 3 1 1 2 3 1 1 3 1 2 2 2 2 1 3 3 1 2 1 2 1 1 3 2 1 3 3 3 2 2 3 2 3 2 1 3 1 1 2 2 3 1 1 3 1 3 1 2 2 1 2 3 3 2 1 1 3 3 2 2 2 2 3 3 2 3 3 2 2 1 2 2 1 2 3 3 3 3 2 1 1 1 3 2 2 3 3 2 2 1 1 3 1 1 2 2 2 3 3 2 3 2 3 2 3 2 3 2 3 3 2 2 3 3 2 2 3 2 2 3 1 3 2 3 2 2 1 3 2 1 1 1 3 1 2 3 2 3 1 1 3 1 2 2 1 3 2 2 3 3 2 3 1 1 1 1 3 2 2 2 1 3 3 1 2 2 2 1 1 2 3 3 1 1 2 2 1 3 1 1 2 2 3 3 3 2 1 2 1 2 1 2 3 1 3 3 2 3 1 3 3 1 1 1 3 1 3 1 3 1 3 2 1 3 1 3 2 1 2 2 3 3 1 2 1 1 1 3 3 3 3 1 1 3 1 1 3 2 1 1 2 2 1 2 1 2 1 2 1 2 1 2 1 1 2 2 1 1 3 3 2 3 3 Runs Permutation: 21 12 16 6 19 1 28 25 23 9 18 32 29 27 14 36 22 31 8 17 3 34 11 2 4 7 5 10 24 33 30 13 20 15 26 35 Factors Permutation: 1 2 3 4 5 12 7 8 10 13 11 9 6 Max Product Det: 3.1164e-013 ============================================ Expanded Matrix: 1 -1 1 -1 -1 -1 -1 -1 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 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 -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 -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 0 2 0 2 0 2 -1 -1 1 -1 0 2 0 2 1 -1 1 -1 1 -1 0 2 1 -1 0 2 1 -1 0 2 1 -1 0 2 1 1 0 2 0 2 -1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 0 2 -1 -1 -1 -1 0 2 1 -1 -1 -1 -1 -1 0 2 0 2 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 1 -1 0 2 0 2 -1 -1 0 2 0 2 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 -1 -1 1 -1 -1 -1 0 2 1 -1 0 2 0 2 -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 0 2 1 -1 1 -1 -1 -1 0 2 -1 -1 0 2 1 -1 1 -1 0 2 1 -1 -1 -1 -1 -1 1 -1 0 2 1 -1 0 2 0 2 -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 -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 0 2 1 -1 -1 -1 -1 -1 1 1 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 -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 0 2 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 -1 -1 0 2 0 2 -1 -1 0 2 1 -1 1 -1 0 2 -1 -1 1 -1 1 -1 1 -1 0 2 0 2 0 2 0 2 1 -1 1 -1 0 2 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 -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 1 -1 0 2 1 -1 0 2 1 -1 0 2 1 -1 1 1 1 -1 1 -1 0 2 0 2 1 -1 1 -1 0 2 0 2 1 -1 0 2 0 2 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 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 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 0 2 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 0 2 0 2 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 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 0 2 -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 0 2 0 2 -1 -1 0 2 -1 -1 0 2 -1 -1 0 2 -1 -1 0 2 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 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.119247 0.834624 4.192963 Top 6 Left 6 Corner: 0.151427 0.908560 6.000000 Top 7 Left 7 Corner: 0.166667 0.853751 6.147409 Top 8 Left 8 Corner: 0.184923 0.833376 7.415586 Top 9 Left 9 Corner: 0.209758 0.812637 7.945140 Top 10 Left 10 Corner: 0.207622 0.751627 8.385925 Top 11 Left 11 Corner: 0.233409 0.772138 8.991753 Top 12 Left 12 Corner: 0.253361 0.766190 10.282530 Top 13 Left 13 Corner: 0.271818 0.759379 10.594706 Top 14 Left 14 Corner: 0.294668 0.761289 12.000000 Top 15 Left 15 Corner: 0.311582 0.751343 12.249280 Top 16 Left 16 Corner: 0.304674 0.688733 12.439376 Top 17 Left 17 Corner: 0.319036 0.680175 12.624938 Top 18 Left 18 Corner: 0.353287 0.710725 14.453029 Top 19 Left 19 Corner: 0.373976 0.716846 14.875933 Top 20 Left 20 Corner: 0.406680 0.734655 16.663956 Top 21 Left 21 Corner: 0.435427 0.745817 17.393110 Top 22 Left 22 Corner: 0.466671 0.764635 19.147137 Top 23 Left 23 Corner: 0.508593 0.798020 20.386272 Top 24 Left 24 Corner: 0.538453 0.809664 22.116370 Top 25 Left 25 Corner: 0.543073 0.784688 21.831828 Top 26 Left 26 Corner: 0.570997 0.791491 23.474728 Top 27 Left 26 Corner: 0.611734 0.816618 25.149506 Top 28 Left 26 Corner: 0.655378 0.843625 26.943770 Top 29 Left 26 Corner: 0.694409 0.862796 28.548409 Top 30 Left 26 Corner: 0.735765 0.883769 30.248614 Top 31 Left 26 Corner: 0.776060 0.902099 31.905212 Top 32 Left 26 Corner: 0.818561 0.921505 33.652535 Top 33 Left 26 Corner: 0.861250 0.939994 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: 3.116425626194018e-013 0.00131118164076449 6.352158476815454e+038 ============================================ Expanded Matrix for initial design: 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 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 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 0 2 0 2 1 -1 1 -1 0 2 0 2 0 2 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 0 2 -1 -1 0 2 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 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 0 2 -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 0 2 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 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 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 0 2 -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 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 -1 -1 0 2 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 0 2 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 0 2 0 2 -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 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 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 0 2 0 2 -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 0 2 0 2 -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 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 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 0 2 -1 -1 0 2 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 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 0 2 1 -1 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 1 -1 0 2 1 -1 1 -1 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 -1 -1 -1 -1 0 2 1 -1 -1 -1 -1 -1 1 -1 1 -1 0 2 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 0 2 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000069 0.000426 0.000000 Top 6 Left 6 Corner: 0.000001 0.000004 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: 0.000000 0.000000 0.000000 Top 11 Left 11 Corner: 0.000000 0.000000 0.000000 Top 12 Left 12 Corner: 0.000000 0.000000 0.000000 Top 13 Left 13 Corner: 0.000004 0.000015 0.000000 Top 14 Left 14 Corner: 0.000010 0.000026 0.000000 Top 15 Left 15 Corner: 0.000243 0.000561 0.000000 Top 16 Left 16 Corner: 0.000053 0.000098 0.000000 Top 17 Left 17 Corner: 0.000094 0.000191 0.000000 Top 18 Left 18 Corner: 0.000149 0.000277 0.000000 Top 19 Left 19 Corner: 0.000207 0.000598 0.000000 Top 20 Left 20 Corner: 0.000363 0.000719 0.000000 Top 21 Left 21 Corner: 0.002672 0.005211 0.000000 Top 22 Left 22 Corner: 0.017093 0.031546 0.000000 Top 23 Left 23 Corner: 0.023631 0.038663 0.000000 Top 24 Left 24 Corner: 0.029102 0.046401 1.069360 Top 25 Left 25 Corner: 0.135531 0.204475 5.457957 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: -7.9377e-101+1.1997e-100i 0+0i 0+0i