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:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 2 3 3 1 2 2 1 2 2 2 1 1 3 3 3 2 1 3 2 1 3 3 2 1 1 2 3 2 3 2 1 1 1 1 1 1 1 1 1 1 2 1 2 3 3 1 1 2 1 3 1 3 1 2 2 2 2 3 1 2 2 1 3 1 2 2 2 3 1 2 3 1 1 2 1 3 2 3 1 3 1 1 3 2 1 3 3 2 1 1 2 1 2 2 3 3 1 3 3 3 3 1 3 3 2 2 3 1 1 1 2 3 2 1 3 3 2 3 2 1 1 2 2 2 2 1 2 2 2 1 1 2 3 2 2 3 2 3 2 2 1 3 1 3 Runs Permutation: 15 17 9 5 1 10 6 12 14 8 7 4 3 11 16 2 13 18 Factors Permutation: 1 3 6 4 5 2 8 7 Max Product Det: 8.2117e-005 ============================================ Expanded Matrix: 1 1 1 -1 1 -1 -1 -1 0 2 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 0 2 -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 -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 1 -1 -1 -1 0 2 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 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 -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 -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 -1 0 2 1 -1 0 2 -1 -1 1 -1 0 2 0 2 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 1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 1 -1 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.238495 0.829503 4.192963 Top 6 Left 6 Corner: 0.302853 0.908560 6.000000 Top 7 Left 7 Corner: 0.365085 0.907008 6.732978 Top 8 Left 8 Corner: 0.382401 0.865498 7.667317 Top 9 Left 9 Corner: 0.426482 0.841108 8.077068 Top 10 Left 10 Corner: 0.450320 0.815118 9.094299 Top 11 Left 11 Corner: 0.485102 0.799125 9.343936 Top 12 Left 12 Corner: 0.515245 0.774899 10.455487 Top 13 Left 13 Corner: 0.602269 0.820921 11.737364 Top 14 Left 14 Corner: 0.624481 0.807367 12.715608 Top 15 Left 15 Corner: 0.693361 0.835420 13.629131 Top 16 Left 16 Corner: 0.746296 0.841181 15.235062 Top 17 Left 16 Corner: 0.871686 0.923611 17.794797 Top 18 Left 16 Corner: 1.000000 1.000000 20.414239 Det Product: 8.21170905998781e-005 0.108052883912187 104921942983831 ============================================ 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 0 2 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 0 2 -1 -1 -1 -1 0 2 0 2 1 -1 1 -1 1 -1 0 2 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 0 2 1 -1 1 -1 -1 -1 0 2 -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 -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 1 -1 1 -1 0 2 1 1 -1 -1 1 -1 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 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 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 -1 -1 1 -1 -1 -1 0 2 1 -1 1 1 1 -1 1 -1 0 2 -1 -1 0 2 1 -1 -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: 0.370107 0.666860 7.474386 Top 11 Left 11 Corner: 0.447657 0.737439 8.622667 Top 12 Left 12 Corner: 0.537285 0.806986 10.902724 Top 13 Left 13 Corner: 0.576194 0.796220 11.229211 Top 14 Left 14 Corner: 0.599337 0.771421 12.203622 Top 15 Left 15 Corner: 0.073184 0.085519 0.000000 Top 16 Left 16 Corner: 0.076937 0.097546 0.000000 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