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<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Hi,</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>I’ve been investigating the feasibility of converting
GLPK MathProg problems to FLOPC++. To understand how to convert a MathProg
model to FLOPC++, I started with a simple comparison of FLOPC++ examples/transport.cpp
to GLPK examples/transport.mod. In executing both examples, I seem to get
conflicting optimal solutions:</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal style='margin-left:.5in;text-indent:-.25in'><font size=2
face=Wingdings><span style='font-size:10.0pt;font-family:Wingdings'>n<font
size=1 face="Times New Roman"><span style='font:7.0pt "Times New Roman"'>
</span></font></span></font><font size=2 face=Arial><span style='font-size:
10.0pt;font-family:Arial'>glpsol calculates an optimal solution of 156.375</span></font></p>
<p class=MsoNormal style='margin-left:.5in;text-indent:-.25in'><font size=2
face=Wingdings><span style='font-size:10.0pt;font-family:Wingdings'>n<font
size=1 face="Times New Roman"><span style='font:7.0pt "Times New Roman"'>
</span></font></span></font><font size=2 face=Arial><span style='font-size:
10.0pt;font-family:Arial'>FLOPC++ calculates an optimal solution of 156.15</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>In looking at transport.cpp, it occurred to me that the
problem statement may not exactly match the GLPK transport.mod (in transport.cpp,
transportation links do not seem to be defined for </span></font><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>Seattle</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>-></span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>Topeka</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'> and </span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>San Diego</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>-></span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>New York</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>). To test
weather this accounted for the solution differences, I modified transport.cpp
to add those links (the code is shown below). When the modified transport
problem is executed, the optimal solution is calculated as 153.675. </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Can anyone offer an explanation for the difference in
calculated optimal solutions? It would seem a direct translation of the GLPK transport.mod
would require the additional links added in the code below. But this change
seems to increase the discrepancy with GLPK.</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Thanks in advance for any insights</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>int main() {</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_model::getDefaultModel().setSolver(new
OsiClpSolverInterface);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> enum {</span></font><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>seattle</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>, sandiego, numS};</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> enum {newyork, </span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>chicago</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>, </span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>topeka</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>,numD};</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_set S(numS);
// Sources </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_set D(numD);
// Destinations </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_subset<2> Link(S,D); //
Transportation links (sparse subset of S*D)</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> Link.insert(</span></font><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>seattle</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>,newyork);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> Link.insert(seattle,chicago);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> Link.insert(</span></font><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>seattle</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>,</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>topeka</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> Link.insert(sandiego,newyork);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> Link.insert(sandiego,</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>chicago</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> Link.insert(sandiego,</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>topeka</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_data SUPPLY(S);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_data DEMAND(D);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> SUPPLY(</span></font><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>seattle</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>)=350;
SUPPLY(sandiego)=600;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> DEMAND(newyork)=325; DEMAND(chicago)=300;
DEMAND(topeka)=275;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_data COST(Link);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> COST(Link(</span></font><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>seattle</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>,newyork)) =
2.5;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> COST(Link(seattle,chicago)) = 1.7;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> COST(Link(</span></font><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>seattle</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>,</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>topeka</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>)) = 1.8;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> COST(Link(sandiego,newyork))= 2.5;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> COST(Link(sandiego,</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>chicago</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>))= 1.8;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> COST(Link(sandiego,</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>topeka</span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>)) = 1.4;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> COST(Link) = 90 * COST(Link) / 1000.0;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_variable x(Link);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> x.display("...");</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_constraint supply(S);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> MP_constraint demand(D);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> supply.display("...");</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> supply(S) = sum( Link(S,D), x(Link)
) <= SUPPLY(S);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> demand(D) = sum( Link(S,D), x(Link)
) >= DEMAND(D);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> cout<<"Here"<<endl;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> minimize( sum(Link, COST(Link)*x(Link))
);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>/*</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> assert(MP_model::getDefaultModel()->getNumRows()==5);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> assert(MP_model::getDefaultModel()->getNumCols()==4);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> assert(MP_model::getDefaultModel()->getNumElements()==8);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> assert(MP_model::getDefaultModel()->getObjValue()>=156.14
&& MP_model::getDefaultModel()->getObjValue()<=156.16);</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>*/</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> x.display("Optimal solution:");</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> supply.display("Supply dual
solution");</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> cout<<"Test transport
passed."<<endl;</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>}</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Greg Geiselhart</span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>email: <a href="mailto:geiselha@optonline.net">geiselha@optonline.net</a></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>gmail: <a href="mailto:geiselha@gmail.com">geiselha@gmail.com</a></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> </span></font></p>
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