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:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 3 1 3 2 3 2 3 1 2 2 1 1 2 2 2 3 1 1 3 3 1 2 1 3 2 3 2 1 1 3 3 1 3 2 3 1 3 3 2 3 3 1 1 2 3 3 2 3 2 1 2 1 1 3 3 3 2 1 3 1 2 3 2 3 1 1 2 1 2 1 2 3 2 3 3 2 1 3 1 1 2 1 3 3 3 3 1 3 2 2 2 3 2 2 3 1 1 3 3 1 2 1 3 3 2 3 3 2 1 1 2 2 1 3 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 3 2 3 2 1 3 3 1 1 3 1 3 1 3 1 3 2 3 2 2 3 1 2 1 2 3 2 2 3 1 3 3 1 1 3 2 1 3 2 3 3 2 1 2 2 1 1 2 3 2 2 1 1 3 2 2 3 2 3 1 3 1 1 2 2 2 3 1 2 1 3 2 3 2 1 3 2 3 3 3 3 2 2 1 1 2 1 1 2 3 1 2 3 3 1 1 1 2 2 3 3 3 3 3 1 3 1 1 3 3 3 3 1 3 3 1 2 2 1 3 1 2 2 3 3 3 1 1 1 3 1 2 2 2 2 1 2 3 3 3 2 3 2 2 2 2 3 3 1 1 3 1 1 2 2 2 1 2 1 1 2 2 2 2 1 2 3 3 2 1 1 2 2 1 3 1 2 3 2 3 1 1 2 2 1 2 3 2 1 2 2 3 2 1 3 3 1 2 1 3 3 2 2 2 1 3 2 1 3 2 2 1 1 1 3 3 2 2 Runs Permutation: 5 12 7 21 25 14 3 16 22 1 9 27 15 26 11 13 18 24 19 6 2 23 10 20 4 8 17 Factors Permutation: 4 1 10 2 8 5 7 9 3 6 12 11 13 Max Product Det: 6.3281e-009 ============================================ Expanded Matrix: 1 1 -1 -1 -1 1 -1 0 2 1 -1 0 2 1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 0 2 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 1 -1 1 0 2 -1 -1 -1 -1 1 -1 1 -1 -1 -1 1 -1 0 2 1 -1 -1 -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 0 2 -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 0 2 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 0 2 -1 -1 1 -1 1 -1 -1 -1 -1 0 2 -1 -1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 0 2 0 2 0 2 1 1 -1 0 2 0 2 1 -1 -1 -1 -1 -1 1 -1 1 -1 -1 -1 0 2 -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 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 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 0 2 1 -1 0 2 0 2 1 -1 -1 -1 0 2 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 1 -1 -1 1 -1 0 2 1 -1 1 -1 0 2 -1 -1 0 2 0 2 -1 -1 -1 -1 0 2 1 -1 1 0 2 0 2 -1 -1 -1 -1 1 -1 0 2 0 2 1 -1 0 2 1 -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 0 2 1 -1 0 2 -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 -1 -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 1 1 -1 1 -1 1 -1 -1 -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 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 0 2 0 2 0 2 0 2 -1 -1 0 2 1 -1 1 -1 1 -1 1 0 2 1 -1 0 2 0 2 0 2 0 2 1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 0 2 0 2 0 2 -1 -1 0 2 -1 -1 -1 -1 0 2 0 2 0 2 0 2 -1 -1 0 2 1 1 -1 1 -1 0 2 -1 -1 -1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 0 2 1 -1 0 2 1 1 -1 -1 -1 -1 -1 0 2 0 2 -1 -1 0 2 1 -1 0 2 -1 -1 0 2 0 2 1 -1 1 0 2 -1 -1 1 -1 1 -1 -1 -1 0 2 -1 -1 1 -1 1 -1 0 2 0 2 0 2 -1 -1 1 1 -1 0 2 -1 -1 1 -1 0 2 0 2 -1 -1 -1 -1 -1 -1 1 -1 1 -1 0 2 0 2 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.138415 0.755082 4.192963 Top 6 Left 6 Corner: 0.216018 0.908560 6.000000 Top 7 Left 7 Corner: 0.208160 0.813921 6.357804 Top 8 Left 8 Corner: 0.276202 0.922634 7.896444 Top 9 Left 9 Corner: 0.304612 0.916702 9.346294 Top 10 Left 10 Corner: 0.308627 0.822201 8.977667 Top 11 Left 11 Corner: 0.317849 0.782679 9.780799 Top 12 Left 12 Corner: 0.353154 0.784063 10.392305 Top 13 Left 13 Corner: 0.348418 0.729512 10.743057 Top 14 Left 14 Corner: 0.394738 0.755522 11.712251 Top 15 Left 15 Corner: 0.415244 0.749947 12.822464 Top 16 Left 16 Corner: 0.458114 0.773480 13.677042 Top 17 Left 17 Corner: 0.491218 0.783380 15.185635 Top 18 Left 18 Corner: 0.531068 0.799718 15.931587 Top 19 Left 19 Corner: 0.537462 0.767244 16.630025 Top 20 Left 20 Corner: 0.597710 0.808640 18.000000 Top 21 Left 21 Corner: 0.600826 0.774575 18.604040 Top 22 Left 22 Corner: 0.683133 0.833686 20.637423 Top 23 Left 23 Corner: 0.682409 0.802413 21.142768 Top 24 Left 24 Corner: 0.782101 0.876270 23.689332 Top 25 Left 25 Corner: 0.802742 0.867754 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: 6.32811304583962e-009 0.0109493615449435 7.0157978388074e+025 ============================================ 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 -1 -1 -1 -1 0 2 0 2 0 2 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 0 2 0 2 0 2 0 2 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 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 0 2 1 -1 -1 0 2 0 2 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 0 2 -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 0 2 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 0 2 1 -1 1 -1 0 2 0 2 -1 -1 0 2 -1 -1 -1 -1 1 -1 1 0 2 -1 -1 0 2 0 2 -1 -1 0 2 -1 -1 0 2 0 2 0 2 -1 -1 0 2 0 2 1 0 2 -1 -1 0 2 0 2 0 2 1 -1 0 2 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 -1 -1 -1 -1 1 -1 0 2 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 1 -1 -1 -1 1 0 2 0 2 1 -1 -1 -1 0 2 1 -1 1 -1 -1 -1 0 2 -1 -1 -1 -1 0 2 1 -1 1 0 2 0 2 1 -1 -1 -1 1 -1 -1 -1 -1 -1 0 2 1 -1 1 -1 1 -1 -1 -1 0 2 1 0 2 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 0 2 1 -1 -1 -1 1 -1 0 2 1 -1 -1 -1 0 2 -1 -1 -1 -1 0 2 1 -1 0 2 1 0 2 1 -1 -1 -1 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 -1 1 -1 -1 -1 1 -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 -1 -1 0 2 1 -1 0 2 0 2 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 0 2 -1 -1 0 2 -1 -1 1 -1 0 2 -1 -1 0 2 1 -1 0 2 -1 -1 0 2 1 1 -1 0 2 -1 -1 0 2 0 2 -1 -1 1 -1 0 2 1 -1 0 2 -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 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 -1 1 -1 0 2 -1 -1 1 1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 -1 -1 1 -1 0 2 0 2 0 2 -1 -1 1 -1 1 1 -1 1 -1 0 2 -1 -1 1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 -1 -1 1 -1 0 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: 0.000000 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 0.000010 0.000000 Top 14 Left 14 Corner: 0.000011 0.000026 0.000000 Top 15 Left 15 Corner: 0.000027 0.000062 0.000000 Top 16 Left 16 Corner: 0.000479 0.000078 0.000000 Top 17 Left 17 Corner: 0.000924 0.001630 0.000000 Top 18 Left 18 Corner: 0.001488 0.001936 0.000000 Top 19 Left 19 Corner: 0.014198 0.022298 0.000000 Top 20 Left 20 Corner: 0.016390 0.022023 0.000000 Top 21 Left 21 Corner: 0.021696 0.025341 0.000000 Top 22 Left 22 Corner: 0.136089 0.144111 3.686976 Top 23 Left 23 Corner: 0.147035 0.178505 4.663095 Top 24 Left 24 Corner: 0.181868 0.200671 0.000000 Top 25 Left 25 Corner: 0.802742 0.867545 24.883422 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