<br><font size=2 face="sans-serif">Jan-Willem,</font>
<br>
<br><font size=2 face="sans-serif">Yes - just always set solution and warmstart
- dual and primal.</font>
<br>
<br><font size=2 face="sans-serif">John</font>
<br>
<br>
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<td width=100%><font size=2 face="sans-serif"><b>RE: [Osi] OsiClp WarmStarts</b></font></table>
<br>
<table width=100%>
<tr>
<td><font size=2 color=#e26200 face="sans-serif"><b>Goossens Jan-Willem
</b></font>
<td><font size=2 color=#8f8f8f face="sans-serif">to:</font>
<td><font size=2 face="sans-serif">John J Forrest</font>
<td>
<div align=right><font size=1 face="sans-serif">10/31/2008 12:15 PM</font></div></table>
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<td><font size=1 color=#8f8f8f face="sans-serif">Cc:</font>
<td width=100%><font size=1 face="sans-serif">"osi@list.coin-or.org"</font></table>
<br>
<td>
<div align=right></div></table>
<br></table>
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<br>
<br><font size=2 color=#004080 face="sans-serif">John,</font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif">Thanks for your reply.</font>
<br><font size=2 color=#004080 face="sans-serif">This works! zero iterations
in resolve.</font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif">Just to be sure: you're
saying "not only get/set the WarmStart object, but also get/set the
col solution" ?</font>
<br><font size=2 color=#004080 face="sans-serif">(and make sure to *copy*
the getColSolution() array..)</font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif">Now, is it safe to simply
do this also in the<b> dual</b> algorithm? </font>
<br><font size=2 color=#004080 face="sans-serif">If yes, then I'll simply
always get/set both WarmStart and ColSolution()..</font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif">Again, thanks for you
help.</font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif">Jan-Willem</font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 color=#004080 face="sans-serif"> </font>
<br><font size=2 face="Tahoma"><b>From:</b> osi-bounces@list.coin-or.org
[mailto:osi-bounces@list.coin-or.org] <b>On Behalf Of </b>John J Forrest<b><br>
Sent:</b> 31 October 2008 16:33<b><br>
Cc:</b> osi@list.coin-or.org<b><br>
Subject:</b> Re: [Osi] OsiClp WarmStarts</font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=2 face="Arial"><br>
Jan,</font><font size=3 face="Times New Roman"> <br>
</font><font size=2 face="Arial"><br>
I think the trouble is that OsiClp trusts the current solution as well
as the basis. In Primal it will use the current solution and basis,
which will explain the behavior in Primal. In Dual, I am not
sure what the problem is. Presolve may make a small difference, but
should not make a major difference. Clp itself has more flexibility.</font><font size=3 face="Times New Roman">
<br>
</font><font size=2 face="Arial"><br>
Is it OK with you to use getColSolution(0 and setColSolution()?</font><font size=3 face="Times New Roman">
<br>
</font><font size=2 face="Arial"><br>
John Forrest</font><font size=3 face="Times New Roman"> <br>
</font>
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<td width=100%><font size=2 face="Arial"><b>[Osi] OsiClp WarmStarts</b></font></table>
<br><font size=3 face="Times New Roman"> </font>
<p>
<br>
<table width=100%>
<tr>
<td width=37%><font size=2 color=#e26200 face="Arial"><b>Goossens Jan-Willem
</b></font>
<td width=5%><font size=2 color=#8f8f8f face="Arial">to:</font><font size=3 face="Times New Roman">
</font>
<td width=30%><font size=2 face="Arial">osi@list.coin-or.org</font><font size=3 face="Times New Roman">
</font>
<td width=27%>
<div align=right><font size=1 face="Arial">10/31/2008 06:48 AM</font></div></table>
<br><font size=3 face="Times New Roman"> </font>
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<td width=22%><font size=2 color=#8f8f8f face="Arial">Sent by:</font><font size=3 face="Times New Roman">
</font>
<td width=77%><font size=2 color=#e26200 face="Arial"><b>osi-bounces@list.coin-or.org</b></font></table>
<br>
<td width=1%></table>
<br></table>
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<div align=center>
<br>
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<br><font size=3 face="Times New Roman"><br>
<br>
</font><font size=2 color=#004080 face="Arial"><br>
Hi,</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
I have some questions about WarmStarts using OsiClp. <br>
I'm solving pure LPs and I tried to recreate my real problem using miplib
3.0s "p0548" (See </font><a href=http://www.caam.rice.edu/~bixby/miplib/miplib3.html><font size=2 color=blue face="Arial"><u>http://www.caam.rice.edu/~bixby/miplib/miplib3.html</u></font></a><font size=2 color=#004080 face="Arial">)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
See below for code and output.</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Basically, I (1) solve the problem, store a warm start, (2) change the
objective and resolve, and (3) restore original objecte, load warmstart
and resolve.</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
I was expecting the step (3) to take zero iterations. However, this is
not (always) the case: In this test problem, <br>
Test run 1) if I do NOT set hints concerning DoDualIn*, then indeed (3)
takes zero iterations.</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Test run 2) but if I set HintTry for these to false (so use primal), then
(3) reoptimises (see end of email)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
In my real instances the (3) resolve takes a *lot* of iterations.</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Note that this test problem doesn’t completely represent my real problem:
the real instances show this behaviour even <i>without</i> the DoDual =
false settings, but the resulting iterations are the same.</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
What could be the cause for these reoptimizations?</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
A) different algorithm after warmstart compared to solve warmstart was
based on?</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
B) presolve chooses to remove different rows/columns in resolve?</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
C) something else?</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Or is this simply not what the warmstarts are for?</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Any help would be appreciated.</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Regards,</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Jan-Wilem Goossens</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
————————————————————--</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Here is the test problem</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
OsiClpSolverInterface model;</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
<br>
model.setHintParam(OsiHintParam::OsiDoDualInInitial,
</font><font size=2 color=blue face="Courier New">false</font><font size=2 face="Courier New">);
</font><font size=2 color=#008000 face="Courier New">// comment out</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
model.setHintParam(OsiHintParam::OsiDoDualInResolve,
</font><font size=2 color=blue face="Courier New">false</font><font size=2 face="Courier New">);
</font><font size=2 color=#008000 face="Courier New">// comment out</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
model.setHintParam(OsiHintParam::OsiDoPresolveInInitial);</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
model.setHintParam(OsiHintParam::OsiDoPresolveInResolve);</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=blue face="Courier New">int</font><font size=2 face="Courier New">
status = model.readMps(</font><font size=2 color=#a11f12 face="Courier New">"p0548.mps"</font><font size=2 face="Courier New">,
</font><font size=2 color=blue face="Courier New">true</font><font size=2 face="Courier New">,
</font><font size=2 color=blue face="Courier New">false</font><font size=2 face="Courier New">);</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=2 color=blue face="Courier New">int</font><font size=2 face="Courier New">
n = model.getNumCols();</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=blue face="Courier New">for</font><font size=2 face="Courier New">
(</font><font size=2 color=blue face="Courier New">int</font><font size=2 face="Courier New">
i = 0; i < n; i++) model.setContinuous(i); </font><font size=2 color=#008000 face="Courier New">//
change to LP</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(1) do initial solve of original problem, and store warm start info</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
model.initialSolve();</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
CoinWarmStart *warmStart = model.getWarmStart();</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(2) change the objective function and resolve</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=2 color=blue face="Courier New">const</font><font size=2 face="Courier New">
</font><font size=2 color=blue face="Courier New">double</font><font size=2 face="Courier New">
* objCoefs = model.getObjCoefficients();</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=2 color=blue face="Courier New">double</font><font size=2 face="Courier New">
* oldCoefs = </font><font size=2 color=blue face="Courier New">new</font><font size=2 face="Courier New">
</font><font size=2 color=blue face="Courier New">double</font><font size=2 face="Courier New">[n];</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=2 color=blue face="Courier New">for</font><font size=2 face="Courier New">
(</font><font size=2 color=blue face="Courier New">int</font><font size=2 face="Courier New">
i = 0; i < n; i++) oldCoefs[i] = objCoefs[i];</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=2 color=blue face="Courier New">for</font><font size=2 face="Courier New">
(</font><font size=2 color=blue face="Courier New">int</font><font size=2 face="Courier New">
i = 0; i < n; i++) model.setObjCoeff(i,1.0);</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
model.resolve();</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(3) restore the original problem, and load warm start</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
model.setObjective(oldCoefs);</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
model.setWarmStart(warmStart);</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
model.resolve();</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
OUTPUT:</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><b><br>
Test run 1, with commented out:</b></font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
// model.setHintParam(OsiHintParam::OsiDoDualInInitial,
</font><font size=2 color=blue face="Courier New">false</font><font size=2 face="Courier New">);
</font><font size=2 color=#008000 face="Courier New">// comment out</font><font size=3 face="Times New Roman">
</font><font size=2 face="Courier New"><br>
// model.setHintParam(OsiHintParam::OsiDoDualInResolve,
</font><font size=2 color=blue face="Courier New">false</font><font size=2 face="Courier New">);
</font><font size=2 color=#008000 face="Courier New">// comment out</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(1) do initial solve of original problem, and store warm start info</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0506I Presolve 163 (-13) rows, 543 (-5) columns and 1561 (-150) elements</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 0 Primal inf 38.8018 (12)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 95 Obj 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0000I Optimal - objective value 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0511I After Postsolve, objective 315.255, infeasibilities - dual 0
(0), primal 0 (0)</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0000I Optimal - objective value 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(2) change the objective function and resolve</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0506I Presolve 165 (-11) rows, 543 (-5) columns and 1579 (-132) elements</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 59.3381 Primal inf 0.314674 (1) Dual inf 161381 (290)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 103 Obj 16.571 Primal inf 8.57907 (29)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 165 Obj 26.1669</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0000I Optimal - objective value 26.1669</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0511I After Postsolve, objective 26.1669, infeasibilities - dual 0
(0), primal 0 (0)</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(3) restore the original problem, and load warm start</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0506I Presolve 163 (-13) rows, 543 (-5) columns and 1561 (-150) elements</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 366.255 Primal inf 30.9296 (2) Dual inf 304.123 (2)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0000I Optimal - objective value 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0511I After Postsolve, objective 315.255, infeasibilities - dual 0
(0), primal 0 (0)</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><b><br>
Test run 2, with:</b></font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
model.setHintParam(OsiHintParam::OsiDoDualInInitial,
</font><font size=2 color=blue face="Courier New">false</font><font size=2 face="Courier New">);
<br>
model.setHintParam(OsiHintParam::OsiDoDualInResolve,
</font><font size=2 color=blue face="Courier New">false</font><font size=2 face="Courier New">);
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(1) do initial solve of original problem, and store warm start info</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0506I Presolve 163 (-13) rows, 543 (-5) columns and 1561 (-150) elements</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0028I Crash put 44 variables in basis, 0 dual infeasibilities</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 0 Primal inf 38.8018 (12) Dual inf 5.62868e+012 (120)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 132 Obj 20103.2 Primal inf 1.08159 (1) Dual inf 1.10445e+011
(193)</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 289 Obj 345.667 Dual inf 627.385 (26)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 316 Obj 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0000I Optimal - objective value 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0511I After Postsolve, objective 315.255, infeasibilities - dual 0
(0), primal 0 (0)</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0000I Optimal - objective value 315.255</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(2) change the objective function and resolve</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0506I Presolve 165 (-11) rows, 543 (-5) columns and 1579 (-132) elements</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 0 Obj 69.5868 Dual inf 38838.5 (125)</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0006I 94 Obj 26.1669</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Clp0000I Optimal - objective value 26.1669</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
Coin0511I After Postsolve, objective 26.1669, infeasibilities - dual 0
(0), primal 0 (0)</font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
Coin0506I Presolve 163 (-13) rows, 543 (-5) columns and 1561 (-150) elements</font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><br>
</font><font size=3 face="Times New Roman"> </font><font size=2 face="Courier New"><br>
</font><font size=2 color=#008000 face="Courier New">//
(3) restore the original problem, and load warm start</font><font size=3 face="Times New Roman">
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Clp0006I 0 Obj 1817.67 Dual inf 3514.68 (6)</b></font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><b><br>
Clp0029I End of values pass after 37 iterations</b></font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><b><br>
Clp0006I 37 Obj 1817.67 Dual inf 3515.85 (5)</b></font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><b><br>
Clp0006I 170 Obj 336.741 Dual inf 20.3286 (24)</b></font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><b><br>
Clp0006I 202 Obj 315.255</b></font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><b><br>
Clp0000I Optimal - objective value 315.255</b></font><font size=3 face="Times New Roman">
</font><font size=2 color=#004080 face="Arial"><b><br>
Coin0511I After Postsolve, objective 315.255, infeasibilities - dual 0
(0), primal 0 (0)</b></font><font size=3 face="Times New Roman"> </font><font size=2 color=#004080 face="Arial"><br>
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