A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">  Correlation structure </td><td align="center"><span style="width: 9.2875004px;"><svg height="12.175" id="M151" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 9.2875004 12.175" width="9.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M516 277q0 -126 -140 -231q-36 -27 -75.5 -42.5t-63.5 -15.5q-38 0 -73 43q-10 -44 -18 -106q-18 -134 -32 -151q-12 -16 -40 -25t-46 -10l-5 14q22 38 84 406q16 92 44.5 146.5t88.5 95.5q68 47 136 47q63 0 101.5 -47.5t38.5 -123.5zM432 259q0 61 -27 101t-79 40
t-82 -49t-49 -148l-24 -127q42 -36 88 -36q79 0 126 61.5t47 157.5z" id="x1D70C"></path></g>
</svg></span></td><td align="center">Nonreheated determinant </td><td align="center">Reheated determinant </td><td align="center">Ratio </td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left"> Nearest neighbor</td><td align="center"> 0.4 </td><td align="center">74276 </td><td align="center"> 97284 </td><td align="center"> 1.3098 </td></tr><tr><td align="left"> Circular </td><td align="center"> 0.4 </td><td align="center"> 65894 </td><td align="center"> 87291 </td><td align="center">1.3247 </td></tr><tr><td align="left"> Autoregress </td><td align="center"> 0.4 </td><td align="center"> 45234 </td><td align="center"> 68548 </td><td align="center"> 1.5154 </td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

2-way polynomial regression with <svg height="11.125" id="M150" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 44.400002 11.125" width="44.400002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" id="x1D45B"></path></g><g transform="matrix(.017,-0,0,-.017,13.305,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,28.008,10.862)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,36.168,10.862)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>; compare reheated simulated annealing with nonreheated simulated annealing.

Journal of Applied Mathematics

tab6

Table 6

Table 6: A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations 