TA Algorithm to find a lean design Runs n=18, Factors s=8. Initial Design: 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 3 3 3 3 3 3 1 2 1 1 2 2 3 3 1 2 2 2 3 3 1 1 1 2 3 3 1 1 2 2 1 3 1 2 1 3 2 3 1 3 2 3 2 1 3 1 1 3 3 1 3 2 1 2 2 1 1 3 3 2 2 1 2 1 2 1 1 3 3 2 2 1 3 2 2 1 1 3 2 2 1 2 3 1 3 2 2 2 2 3 1 2 1 3 2 2 3 1 2 3 2 1 2 3 1 3 2 3 1 2 2 3 2 1 3 1 2 3 2 3 3 2 1 2 3 1 Criterion: maximize Det(X(5)'X(5))*...*Det(X(18)'X(18)) Search Type:(b) - f1(x1) ... f1(xs) f2(x1) ... f2(xs) Result Design: 1 3 3 3 1 3 3 3 1 1 1 1 1 1 1 1 2 1 1 3 1 3 2 2 2 3 1 2 3 1 2 3 2 2 3 1 3 3 1 2 1 1 3 2 3 1 3 2 2 2 2 1 1 1 3 3 1 2 1 2 2 3 3 1 2 2 3 3 2 1 2 1 1 2 1 3 3 2 1 3 1 3 2 1 3 3 2 1 2 1 2 2 2 3 1 3 2 3 1 1 2 2 3 2 2 3 3 2 1 2 1 1 1 1 3 1 2 2 2 3 1 2 2 2 1 2 2 2 2 1 2 3 3 2 3 1 1 3 2 3 2 1 1 2 Runs Permutation: 3 1 10 18 17 7 11 5 14 8 9 13 15 12 4 2 16 6 Factors Permutation: 3 1 8 4 2 5 6 7 Max Product Det: 0.00021671 ============================================ Expanded Matrix: 1 -1 1 1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 -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 2 2 1 1 1 -1 0 1 -1 0 1 -1 -1 2 -1 -1 2 -1 1 1 0 1 -1 1 1 -1 0 2 -1 -1 -1 -1 -1 2 1 -1 -1 1 0 1 -1 1 0 -1 -1 2 -1 -1 -1 2 1 1 0 0 -1 -1 -1 1 1 2 2 -1 -1 -1 -1 -1 1 -1 0 -1 0 0 1 1 -1 2 -1 2 2 -1 -1 -1 1 1 0 1 1 0 -1 0 -1 2 -1 -1 2 -1 2 -1 1 -1 0 -1 1 1 0 -1 1 2 -1 -1 -1 2 -1 -1 1 -1 1 0 -1 1 1 0 -1 -1 2 -1 -1 -1 2 -1 1 1 -1 0 0 0 1 -1 1 -1 2 2 2 -1 -1 -1 1 1 1 -1 -1 0 0 1 0 -1 -1 -1 2 2 -1 2 1 1 1 1 0 -1 0 -1 -1 -1 -1 2 -1 2 -1 -1 1 -1 -1 1 -1 0 0 0 1 -1 -1 -1 2 2 2 -1 1 -1 0 0 0 -1 0 0 0 2 2 2 -1 2 2 2 1 1 -1 0 1 1 0 1 -1 -1 2 -1 -1 2 -1 -1 1 -1 1 0 1 0 -1 -1 0 -1 2 -1 2 -1 -1 2 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.297100 0.916885 4.192963 Top 6 Left 6 Corner: 0.333333 0.841688 4.578857 Top 7 Left 7 Corner: 0.374275 0.810775 5.042937 Top 8 Left 8 Corner: 0.424288 0.849025 5.634626 Top 9 Left 9 Corner: 0.452012 0.839637 5.935573 Top 10 Left 10 Corner: 0.530705 0.876167 7.708411 Top 11 Left 11 Corner: 0.540980 0.841622 8.533520 Top 12 Left 12 Corner: 0.574848 0.825532 9.713222 Top 13 Left 13 Corner: 0.599859 0.812811 10.743057 Top 14 Left 14 Corner: 0.662697 0.848062 12.475345 Top 15 Left 15 Corner: 0.714300 0.854625 14.040724 Top 16 Left 16 Corner: 0.746296 0.841181 15.235062 Top 17 Left 16 Corner: 0.871686 0.923761 17.794797 Top 18 Left 16 Corner: 1.000000 1.000000 20.414239 Det Product: 0.000216714019637102 0.124296157425816 21546971260814.3 ============================================ Expanded Matrix for initial design: 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 -1 2 2 2 2 2 2 1 -1 -1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 0 -1 -1 0 0 1 1 2 -1 -1 2 2 -1 -1 1 -1 0 0 0 1 1 -1 -1 2 2 2 -1 -1 -1 -1 1 -1 0 1 1 -1 -1 0 0 2 -1 -1 -1 -1 2 2 1 -1 1 -1 0 -1 1 0 1 -1 -1 2 -1 -1 2 -1 1 -1 1 0 1 0 -1 1 -1 -1 2 -1 2 -1 -1 -1 1 -1 1 1 -1 1 0 -1 0 -1 -1 -1 -1 2 -1 2 1 1 -1 -1 1 1 0 0 -1 -1 -1 -1 -1 2 2 -1 1 1 -1 0 -1 -1 1 1 0 -1 2 -1 -1 -1 -1 2 1 1 -1 1 0 0 -1 -1 1 -1 -1 2 2 -1 -1 -1 1 1 0 -1 0 1 -1 1 0 2 -1 2 -1 -1 -1 2 1 1 0 0 1 -1 0 -1 1 2 2 -1 -1 2 -1 -1 1 1 0 1 -1 0 1 0 -1 2 -1 -1 2 -1 2 -1 1 1 1 -1 1 0 1 -1 0 -1 -1 -1 2 -1 -1 2 1 1 1 0 -1 1 -1 0 1 -1 2 -1 -1 -1 2 -1 1 1 1 1 0 -1 0 1 -1 -1 -1 2 -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: 0.012581 0.018478 0.000000 Top 11 Left 11 Corner: 0.424844 0.693677 6.701564 Top 12 Left 12 Corner: 0.029170 0.038157 0.000000 Top 13 Left 13 Corner: 0.040016 0.048693 0.000000 Top 14 Left 14 Corner: 0.587147 0.753696 11.053109 Top 15 Left 15 Corner: 0.073575 0.081520 1.242601 Top 16 Left 16 Corner: 0.090443 0.099260 1.746329 Top 17 Left 16 Corner: 0.871686 0.923611 17.794797 Top 18 Left 16 Corner: 1.000000 1.000000 20.414239 Det Product: 0 0 0