TA Algorithm to find a lean design Runs n=36, Factors s=13. Initial Design: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 2 2 2 2 3 3 3 3 1 2 2 2 2 3 3 3 3 1 1 1 1 1 3 3 3 3 1 1 1 1 2 2 2 2 1 1 1 2 3 1 2 3 3 1 2 2 3 1 2 2 3 1 2 3 1 1 2 3 3 1 1 3 3 1 2 3 1 2 2 3 1 1 2 1 1 1 3 2 1 3 2 3 2 1 3 2 1 2 2 1 3 2 1 3 1 3 2 1 3 1 3 3 2 1 3 2 1 2 1 3 2 1 1 1 2 3 1 3 2 1 3 3 2 1 2 2 2 3 1 2 1 3 2 1 1 3 2 3 2 3 1 2 3 2 1 3 2 2 1 3 1 2 1 2 3 2 1 1 3 2 3 3 2 1 2 2 3 1 3 2 2 1 3 1 1 3 2 2 3 1 2 1 3 3 2 1 2 2 1 3 2 1 2 1 3 3 3 1 2 2 1 2 3 2 2 3 2 1 1 1 2 3 3 2 3 1 2 3 1 3 2 2 2 3 1 1 3 1 2 2 1 2 2 3 3 1 2 1 1 3 3 2 2 2 3 3 1 1 2 3 2 2 1 1 3 2 3 1 1 2 2 3 1 3 3 2 2 1 2 1 3 2 1 2 3 3 1 3 1 2 2 3 2 1 3 2 3 1 1 2 1 2 3 3 3 3 2 1 3 1 2 2 3 2 3 1 1 3 1 3 2 2 2 1 1 3 2 3 1 3 3 2 1 3 3 3 2 2 1 3 1 2 1 3 3 2 1 1 1 3 3 2 1 2 3 2 3 1 3 3 3 2 3 2 2 1 2 1 1 3 2 1 1 1 3 1 3 3 2 3 2 2 3 3 2 2 2 1 2 1 1 3 1 3 3 3 1 3 1 2 3 2 3 1 2 2 3 1 3 2 1 2 3 1 3 1 2 3 3 1 2 3 3 2 3 1 2 1 2 3 1 1 2 3 3 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: 3 1 1 3 1 2 2 1 1 2 2 3 3 1 3 1 3 2 2 3 2 3 2 1 1 2 1 1 3 1 2 1 3 3 2 2 2 3 2 3 3 1 1 3 2 1 3 2 2 3 2 1 3 3 3 3 1 3 3 3 3 3 3 3 3 2 2 3 3 3 1 3 2 1 1 2 1 3 1 1 2 2 3 3 2 1 3 3 1 3 2 1 2 2 3 1 2 1 3 2 1 1 3 3 2 3 3 1 1 3 2 1 3 2 2 1 1 2 1 2 3 3 1 1 2 3 2 3 3 1 1 3 3 2 2 2 1 2 1 3 2 3 1 2 1 1 3 2 3 2 3 2 1 3 1 2 2 3 2 1 3 2 3 1 1 1 3 3 2 2 2 1 2 2 2 1 1 3 3 3 1 3 2 2 1 2 2 3 3 3 1 2 1 3 1 3 2 3 2 2 1 2 1 2 1 3 3 1 1 2 2 1 1 3 3 2 2 3 3 1 1 1 3 2 2 1 1 2 3 1 2 3 1 3 3 3 2 3 2 1 1 1 2 3 2 1 2 3 1 2 2 3 2 3 3 3 1 2 1 1 1 3 1 2 3 3 3 1 2 1 2 2 3 3 2 1 1 1 3 1 2 3 1 2 3 2 1 2 3 3 3 3 1 1 1 2 3 2 2 3 1 3 2 3 3 1 2 2 2 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 2 2 2 2 3 1 3 2 3 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 3 3 1 2 3 1 2 3 1 2 1 2 3 1 1 3 1 2 2 2 3 1 3 3 3 2 2 1 2 1 3 1 3 2 1 2 3 1 2 1 3 3 1 2 3 3 3 2 2 1 2 1 2 1 2 3 1 3 1 3 2 2 3 2 3 3 2 1 1 1 3 3 1 1 2 2 3 2 3 1 3 2 2 3 1 3 1 1 2 3 1 1 2 1 1 3 2 1 3 3 2 2 3 3 2 3 2 3 2 2 1 1 1 2 1 Runs Permutation: 8 23 17 32 3 31 33 10 11 26 15 13 34 18 20 22 9 5 21 28 25 4 29 35 1 19 2 6 30 14 36 24 7 27 12 16 Factors Permutation: 10 7 4 3 13 9 2 8 12 1 5 11 6 Max Product Det: 1.4529e-012 ============================================ Expanded Matrix: 1 1 -1 -1 1 -1 0 0 -1 -1 0 0 1 1 -1 -1 -1 -1 -1 2 2 -1 -1 2 2 -1 -1 1 -1 1 -1 1 0 0 1 0 1 0 -1 -1 0 -1 -1 -1 -1 2 2 -1 2 -1 2 -1 -1 2 1 -1 -1 1 -1 0 -1 1 1 0 0 0 1 0 -1 -1 -1 -1 2 -1 -1 -1 2 2 2 -1 2 1 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 1 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 1 1 1 -1 1 0 -1 -1 0 -1 1 2 2 -1 -1 -1 -1 -1 2 -1 -1 2 -1 -1 1 -1 -1 0 0 1 1 0 -1 1 1 -1 1 0 -1 -1 2 2 -1 -1 2 -1 -1 -1 -1 -1 2 1 -1 0 0 1 -1 0 -1 1 0 -1 -1 1 1 -1 2 2 -1 -1 2 -1 -1 2 -1 -1 -1 -1 1 0 1 1 -1 -1 1 0 -1 1 0 0 -1 -1 2 -1 -1 -1 -1 -1 2 -1 -1 2 2 -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 -1 1 -1 1 1 0 0 0 -1 0 -1 1 0 1 -1 -1 -1 -1 2 2 2 -1 2 -1 -1 2 -1 -1 1 0 -1 -1 1 0 1 0 1 0 -1 1 -1 0 2 -1 -1 -1 2 -1 2 -1 2 -1 -1 -1 2 1 0 1 0 -1 1 0 1 -1 -1 -1 1 1 0 2 -1 2 -1 -1 2 -1 -1 -1 -1 -1 -1 2 1 0 0 -1 0 0 0 -1 -1 1 1 1 -1 1 2 2 -1 2 2 2 -1 -1 -1 -1 -1 -1 -1 1 0 0 -1 0 0 1 1 1 -1 0 -1 1 -1 2 2 -1 2 2 -1 -1 -1 -1 2 -1 -1 -1 1 1 0 1 0 0 -1 0 -1 0 -1 1 1 -1 -1 2 -1 2 2 -1 2 -1 2 -1 -1 -1 -1 1 -1 0 0 -1 -1 1 1 0 0 1 1 -1 -1 -1 2 2 -1 -1 -1 -1 2 2 -1 -1 -1 -1 1 -1 1 0 0 -1 -1 0 1 -1 0 1 -1 1 -1 -1 2 2 -1 -1 2 -1 -1 2 -1 -1 -1 1 1 1 0 1 0 -1 -1 -1 0 1 0 -1 0 -1 -1 2 -1 2 -1 -1 -1 2 -1 2 -1 2 1 1 -1 0 0 1 0 1 1 1 -1 0 -1 -1 -1 -1 2 2 -1 2 -1 -1 -1 -1 2 -1 -1 1 -1 1 -1 0 1 1 1 -1 0 -1 0 0 1 -1 -1 -1 2 -1 -1 -1 -1 2 -1 2 2 -1 1 1 0 -1 -1 -1 1 -1 0 1 -1 0 1 0 -1 2 -1 -1 -1 -1 -1 2 -1 -1 2 -1 2 1 -1 0 1 1 1 1 -1 -1 -1 0 1 0 0 -1 2 -1 -1 -1 -1 -1 -1 -1 2 -1 2 2 1 1 -1 1 0 1 1 -1 0 0 0 -1 -1 1 -1 -1 -1 2 -1 -1 -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 0 0 0 0 1 -1 1 0 1 -1 -1 -1 -1 2 2 2 2 -1 -1 -1 2 -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 2 2 2 2 -1 2 2 2 2 2 2 2 2 1 0 -1 1 1 -1 0 1 -1 0 1 -1 0 -1 2 -1 -1 -1 -1 2 -1 -1 2 -1 -1 2 -1 1 0 1 -1 -1 1 -1 0 0 0 1 -1 1 1 2 -1 -1 -1 -1 -1 2 2 2 -1 -1 -1 -1 1 1 0 0 -1 0 -1 1 -1 1 0 -1 0 1 -1 2 2 -1 2 -1 -1 -1 -1 2 -1 2 -1 1 -1 0 -1 1 1 -1 0 1 1 1 0 0 -1 -1 2 -1 -1 -1 -1 2 -1 -1 -1 2 2 -1 1 0 -1 0 -1 0 1 -1 1 -1 1 0 0 1 2 -1 2 -1 2 -1 -1 -1 -1 -1 2 2 -1 1 0 1 1 0 -1 -1 -1 1 1 -1 -1 0 0 2 -1 -1 2 -1 -1 -1 -1 -1 -1 -1 2 2 1 1 0 1 -1 1 0 0 1 -1 1 -1 -1 0 -1 2 -1 -1 -1 2 2 -1 -1 -1 -1 -1 2 1 1 -1 -1 0 -1 -1 1 0 -1 1 1 0 0 -1 -1 -1 2 -1 -1 -1 2 -1 -1 -1 2 2 1 1 1 0 1 0 1 0 0 -1 -1 -1 0 -1 -1 -1 2 -1 2 -1 2 2 -1 -1 -1 2 -1 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.180745 0.940863 4.704316 Top 6 Left 6 Corner: 0.183141 0.891119 4.702669 Top 7 Left 7 Corner: 0.195900 0.883395 4.981987 Top 8 Left 8 Corner: 0.204740 0.841261 5.169214 Top 9 Left 9 Corner: 0.228283 0.828431 5.731257 Top 10 Left 10 Corner: 0.238146 0.791148 5.952016 Top 11 Left 11 Corner: 0.251795 0.808144 6.269976 Top 12 Left 12 Corner: 0.253197 0.759000 6.285550 Top 13 Left 13 Corner: 0.284137 0.762781 7.035328 Top 14 Left 14 Corner: 0.302128 0.764196 7.464154 Top 15 Left 15 Corner: 0.317525 0.746180 8.424349 Top 16 Left 16 Corner: 0.335030 0.744688 9.461081 Top 17 Left 17 Corner: 0.358442 0.749867 10.695151 Top 18 Left 18 Corner: 0.382071 0.754645 11.971962 Top 19 Left 19 Corner: 0.409018 0.764618 13.389985 Top 20 Left 20 Corner: 0.438375 0.774238 14.927878 Top 21 Left 21 Corner: 0.450241 0.762529 15.888451 Top 22 Left 22 Corner: 0.460372 0.750156 16.781202 Top 23 Left 23 Corner: 0.486257 0.759997 18.257143 Top 24 Left 24 Corner: 0.515770 0.768507 19.897792 Top 25 Left 25 Corner: 0.570150 0.812901 22.551602 Top 26 Left 26 Corner: 0.559378 0.776561 22.641179 Top 27 Left 27 Corner: 0.594380 0.794906 24.576623 Top 28 Left 27 Corner: 0.635162 0.818635 26.262897 Top 29 Left 27 Corner: 0.678742 0.844701 28.064871 Top 30 Left 27 Corner: 0.725313 0.872000 29.990483 Top 31 Left 27 Corner: 0.766864 0.891698 31.708560 Top 32 Left 27 Corner: 0.810796 0.913096 33.525061 Top 33 Left 27 Corner: 0.857244 0.935749 35.445625 Top 34 Left 27 Corner: 0.902408 0.955958 37.313085 Top 35 Left 27 Corner: 0.949952 0.977300 39.278932 Top 36 Left 27 Corner: 1.000000 1.000000 41.348350 Det Product: 1.45287944954753e-012 0.00195581418436622 5.03363401255715e+036 ============================================ 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 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 2 2 2 2 2 2 2 2 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 0 0 0 0 1 1 1 1 -1 -1 -1 -1 -1 2 2 2 2 -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 -1 -1 -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 -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 0 0 1 -1 0 1 -1 -1 0 1 1 -1 -1 2 2 -1 -1 2 -1 -1 -1 2 -1 -1 -1 -1 1 1 1 -1 0 1 -1 0 0 1 -1 -1 0 -1 -1 -1 -1 2 -1 -1 2 2 -1 -1 -1 2 -1 1 -1 -1 1 0 -1 1 0 1 0 -1 1 0 -1 -1 -1 -1 2 -1 -1 2 -1 2 -1 -1 2 -1 1 0 0 -1 1 0 -1 1 -1 1 0 -1 1 -1 2 2 -1 -1 2 -1 -1 -1 -1 2 -1 -1 -1 1 1 1 0 -1 1 0 -1 0 -1 1 0 -1 -1 -1 -1 2 -1 -1 2 -1 2 -1 -1 2 -1 -1 1 -1 0 1 -1 1 0 -1 1 1 0 -1 0 0 -1 2 -1 -1 -1 2 -1 -1 -1 2 -1 2 2 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 1 -1 0 1 0 -1 1 0 0 -1 1 -1 0 -1 -1 2 -1 2 -1 -1 2 2 -1 -1 -1 2 1 -1 0 1 0 -1 -1 1 0 1 1 0 -1 0 -1 2 -1 2 -1 -1 -1 2 -1 -1 2 -1 2 1 0 1 -1 1 0 0 -1 1 -1 -1 1 0 0 2 -1 -1 -1 2 2 -1 -1 -1 -1 -1 2 2 1 1 -1 0 -1 1 1 0 -1 0 0 -1 1 0 -1 -1 2 -1 -1 -1 2 -1 2 2 -1 -1 2 1 -1 0 -1 1 1 1 -1 0 0 -1 0 1 0 -1 2 -1 -1 -1 -1 -1 2 2 -1 2 -1 2 1 0 1 0 -1 -1 -1 0 1 1 0 1 -1 0 2 -1 2 -1 -1 -1 2 -1 -1 2 -1 -1 2 1 1 -1 1 0 0 0 1 -1 -1 1 -1 0 0 -1 -1 -1 2 2 2 -1 -1 -1 -1 -1 2 2 1 -1 0 0 1 1 -1 0 -1 -1 1 1 0 0 -1 2 2 -1 -1 -1 2 -1 -1 -1 -1 2 2 1 0 1 1 -1 -1 0 1 0 0 -1 -1 1 0 2 -1 -1 -1 -1 2 -1 2 2 -1 -1 -1 2 1 1 -1 -1 0 0 1 -1 1 1 0 0 -1 0 -1 -1 -1 2 2 -1 -1 -1 -1 2 2 -1 2 1 -1 1 0 -1 0 1 1 -1 1 -1 0 0 1 -1 -1 2 -1 2 -1 -1 -1 -1 -1 2 2 -1 1 0 -1 1 0 1 -1 -1 0 -1 0 1 1 1 2 -1 -1 2 -1 -1 -1 2 -1 2 -1 -1 -1 1 1 0 -1 1 -1 0 0 1 0 1 -1 -1 1 -1 2 -1 -1 -1 2 2 -1 2 -1 -1 -1 -1 1 -1 1 0 0 0 -1 -1 1 0 1 -1 1 1 -1 -1 2 2 2 -1 -1 -1 2 -1 -1 -1 -1 1 0 -1 1 1 1 0 0 -1 1 -1 0 -1 1 2 -1 -1 -1 -1 2 2 -1 -1 -1 2 -1 -1 1 1 0 -1 -1 -1 1 1 0 -1 0 1 0 1 -1 2 -1 -1 -1 -1 -1 2 -1 2 -1 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 -1 -1 1 -1 1 1 0 1 0 0 1 2 -1 -1 -1 -1 -1 -1 -1 2 -1 2 2 -1 1 1 0 0 0 -1 0 -1 -1 1 -1 1 1 1 -1 2 2 2 -1 2 -1 -1 -1 -1 -1 -1 -1 1 -1 1 -1 0 1 0 1 -1 0 0 1 -1 1 -1 -1 -1 2 -1 2 -1 -1 2 2 -1 -1 -1 1 0 -1 0 1 -1 1 -1 0 1 1 -1 0 1 2 -1 2 -1 -1 -1 -1 2 -1 -1 -1 2 -1 1 1 0 1 -1 0 -1 0 1 -1 -1 0 1 1 -1 2 -1 -1 2 -1 2 -1 -1 -1 2 -1 -1 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 0.000001 0.000000 Top 12 Left 12 Corner: 0.000000 0.000000 0.000000 Top 13 Left 13 Corner: 0.000003 0.000009 0.000000 Top 14 Left 14 Corner: 0.000009 0.000022 0.000000 Top 15 Left 15 Corner: 0.000192 0.000504 0.000000 Top 16 Left 16 Corner: 0.000280 0.000837 0.000000 Top 17 Left 17 Corner: 0.000488 0.001039 0.000000 Top 18 Left 18 Corner: 0.000136 0.000280 0.000000 Top 19 Left 19 Corner: 0.000170 0.000421 0.000000 Top 20 Left 20 Corner: 0.000312 0.000565 0.000000 Top 21 Left 21 Corner: 0.000086 0.000166 0.000000 Top 22 Left 22 Corner: 0.000124 0.000238 0.000000 Top 23 Left 23 Corner: 0.000196 0.000285 0.000000 Top 24 Left 24 Corner: 0.000069 0.000107 0.000000 Top 25 Left 25 Corner: 0.000115 0.000159 0.000000 Top 26 Left 26 Corner: 0.000117 0.000173 0.000000 Top 27 Left 27 Corner: 0.000242 0.000290 0.000000 Top 28 Left 27 Corner: 0.000839 0.001102 0.000000 Top 29 Left 27 Corner: 0.003259 0.004196 0.000000 Top 30 Left 27 Corner: 0.003654 0.004055 0.000000 Top 31 Left 27 Corner: 0.013925 0.015444 0.000000 Top 32 Left 27 Corner: 0.050332 0.064957 2.414632 Top 33 Left 27 Corner: 0.059505 0.067492 2.548822 Top 34 Left 27 Corner: 0.249648 0.259495 10.267192 Top 35 Left 27 Corner: 0.949952 0.977278 39.278932 Top 36 Left 27 Corner: 1.000000 1.000000 41.348350 Det Product: 0 0 0