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Here we provide some examples to illustrates our proposal
The objective function for this case
The variable x31 is the constant imposed to obtain the GED value.
The first part that focues on x_0,0 : meaning node 0 of g1 matched to node 0 of g2.
- 45.2221125911041 *x_0,0 ^2 + 30 x_0,0 * x_2,1 + 30 x_0,0 * x_2,2
+ 30 x_0,0 * x_2,3 + 30 x_0,0 * x_2,4 + 30 x_0,0 * x_3,1
+ 30 x_0,0 * x_3,2 + 30 x_0,0 * x_3,3 + 30 x_0,0 * x_3,4
+ 30 x_0,0 * x_4,1 + 30 x_0,0 * x_4,2 + 30 x_0,0 * x_4,3
+ 30 x_0,0 * x_4,4
\ENCODING=ISO-8859-1
\Problem name: ILOG.CPLEX
Maximize
obj: x31 + [ - 45.2221125911041 x_0,0 ^2 + 30 x_0,0 * x_2,1 + 30 x_0,0 * x_2,2
+ 30 x_0,0 * x_2,3 + 30 x_0,0 * x_2,4 + 30 x_0,0 * x_3,1
+ 30 x_0,0 * x_3,2 + 30 x_0,0 * x_3,3 + 30 x_0,0 * x_3,4
+ 30 x_0,0 * x_4,1 + 30 x_0,0 * x_4,2 + 30 x_0,0 * x_4,3
+ 30 x_0,0 * x_4,4 - 210.691694306393 x_0,1 ^2 + 30 x_0,1 * x_2,0
+ 30 x_0,1 * x_2,4 + 30 x_0,1 * x_2,5 + 30 x_0,1 * x_3,0
+ 30 x_0,1 * x_3,4 + 30 x_0,1 * x_3,5 + 30 x_0,1 * x_4,0
+ 30 x_0,1 * x_4,4 + 30 x_0,1 * x_4,5 + 30 x_0,2 * x_2,0
+ 30 x_0,2 * x_2,4 + 30 x_0,2 * x_3,0 + 30 x_0,2 * x_3,4
+ 30 x_0,2 * x_4,0 + 30 x_0,2 * x_4,4 + 30 x_0,3 * x_2,0
+ 30 x_0,3 * x_3,0 + 30 x_0,3 * x_4,0 - 30.6845983929533 x_0,4 ^2
+ 30 x_0,4 * x_2,0 + 30 x_0,4 * x_2,1 + 30 x_0,4 * x_2,2
+ 30 x_0,4 * x_3,0 + 30 x_0,4 * x_3,1 + 30 x_0,4 * x_3,2
+ 30 x_0,4 * x_4,0 + 30 x_0,4 * x_4,1 + 30 x_0,4 * x_4,2
+ 30 x_0,5 * x_2,1 + 30 x_0,5 * x_3,1 + 30 x_0,5 * x_4,1
+ 30 x_1,0 * x_2,1 + 30 x_1,0 * x_2,2 + 30 x_1,0 * x_2,3
+ 30 x_1,0 * x_2,4 + 30 x_1,0 * x_3,1 + 30 x_1,0 * x_3,2
+ 30 x_1,0 * x_3,3 + 30 x_1,0 * x_3,4 + 30 x_1,1 * x_2,0
+ 30 x_1,1 * x_2,4 + 30 x_1,1 * x_2,5 + 30 x_1,1 * x_3,0
+ 30 x_1,1 * x_3,4 + 30 x_1,1 * x_3,5 - 410.529423483708 x_1,2 ^2
+ 30 x_1,2 * x_2,0 + 30 x_1,2 * x_2,4 + 30 x_1,2 * x_3,0
+ 30 x_1,2 * x_3,4 + 30 x_1,3 * x_2,0 + 30 x_1,3 * x_3,0
+ 30 x_1,4 * x_2,0 + 30 x_1,4 * x_2,1 + 30 x_1,4 * x_2,2
+ 30 x_1,4 * x_3,0 + 30 x_1,4 * x_3,1 + 30 x_1,4 * x_3,2
+ 30 x_1,5 * x_2,1 + 30 x_1,5 * x_3,1 - 293.178613210699 x_2,2 ^2
- 198.977571895752 x_3,2 ^2 - 277.595891589949 x_4,3 ^2
- 226.020935420823 x_4,5 ^2 ] / 2
The constraints
The sum of the rows
Subject To
c1: x_0,0 + x_0,1 + x_0,2 + x_0,3 + x_0,4 + x_0,5 <= 1
c3: x_1,0 + x_1,1 + x_1,2 + x_1,3 + x_1,4 + x_1,5 <= 1
c5: x_2,0 + x_2,1 + x_2,2 + x_2,3 + x_2,4 + x_2,5 <= 1
c6: x_3,0 + x_3,1 + x_3,2 + x_3,3 + x_3,4 + x_3,5 <= 1
c7: x_4,0 + x_4,1 + x_4,2 + x_4,3 + x_4,4 + x_4,5 <= 1
The sum of the columns
c8: x_0,0 + x_1,0 + x_2,0 + x_3,0 + x_4,0 <= 1
c9: x_0,1 + x_1,1 + x_2,1 + x_3,1 + x_4,1 <= 1
c10: x_0,2 + x_1,2 + x_2,2 + x_3,2 + x_4,2 <= 1
c11: x_0,3 + x_1,3 + x_2,3 + x_3,3 + x_4,3 <= 1
c12: x_0,4 + x_1,4 + x_2,4 + x_3,4 + x_4,4 <= 1
c13: x_0,5 + x_1,5 + x_2,5 + x_3,5 + x_4,5 <= 1
Domain constraints
Bounds
0 <= x_0,0 <= 1
0 <= x_0,1 <= 1
0 <= x_0,2 <= 1
0 <= x_0,3 <= 1
0 <= x_0,4 <= 1
0 <= x_0,5 <= 1
0 <= x_1,0 <= 1
0 <= x_1,1 <= 1
0 <= x_1,2 <= 1
0 <= x_1,3 <= 1
0 <= x_1,4 <= 1
0 <= x_1,5 <= 1
0 <= x_2,0 <= 1
0 <= x_2,1 <= 1
0 <= x_2,2 <= 1
0 <= x_2,3 <= 1
0 <= x_2,4 <= 1
0 <= x_2,5 <= 1
0 <= x_3,0 <= 1
0 <= x_3,1 <= 1
0 <= x_3,2 <= 1
0 <= x_3,3 <= 1
0 <= x_3,4 <= 1
0 <= x_3,5 <= 1
0 <= x_4,0 <= 1
0 <= x_4,1 <= 1
0 <= x_4,2 <= 1
0 <= x_4,3 <= 1
0 <= x_4,4 <= 1
0 <= x_4,5 <= 1
x31 = -675
Binaries
x_0,0 x_0,1 x_0,2 x_0,3 x_0,4 x_0,5 x_1,0 x_1,1 x_1,2 x_1,3 x_1,4
x_1,5 x_2,0 x_2,1 x_2,2 x_2,3 x_2,4 x_2,5 x_3,0 x_3,1 x_3,2 x_3,3
x_3,4 x_3,5 x_4,0 x_4,1 x_4,2 x_4,3 x_4,4 x_4,5
End
The solution in details (please expand)
The solution in details (please expand)
<?xml version = "1.0" encoding="UTF-8" standalone="yes"?>
<CPLEXSolution version="1.2">
<header
problemName="ILOG.CPLEX"
solutionName="incumbent"
solutionIndex="-1"
objectiveValue="-615"
solutionTypeValue="3"
solutionTypeString="primal"
solutionStatusValue="101"
solutionStatusString="integer optimal solution"
solutionMethodString="mip"
primalFeasible="1"
dualFeasible="1"
MIPNodes="13"
MIPIterations="929"
writeLevel="1"/>
<quality
epInt="1e-05"
epRHS="1e-06"
maxIntInfeas="0"
maxPrimalInfeas="0"
maxX="675"
maxSlack="1"/>
<linearConstraints>
<constraint name="c1" index="0" slack="0"/>
<constraint name="c3" index="1" slack="0"/>
<constraint name="c5" index="2" slack="0"/>
<constraint name="c6" index="3" slack="0"/>
<constraint name="c7" index="4" slack="0"/>
<constraint name="c8" index="5" slack="0"/>
<constraint name="c9" index="6" slack="0"/>
<constraint name="c10" index="7" slack="0"/>
<constraint name="c11" index="8" slack="1"/>
<constraint name="c12" index="9" slack="0"/>
<constraint name="c13" index="10" slack="0"/>
</linearConstraints>
<variables>
<variable name="x_0,0" index="0" value="0"/>
<variable name="x_0,1" index="1" value="0"/>
<variable name="x_0,2" index="2" value="1"/>
<variable name="x_0,3" index="3" value="0"/>
<variable name="x_0,4" index="4" value="0"/>
<variable name="x_0,5" index="5" value="0"/>
<variable name="x_1,0" index="6" value="0"/>
<variable name="x_1,1" index="7" value="1"/>
<variable name="x_1,2" index="8" value="0"/>
<variable name="x_1,3" index="9" value="0"/>
<variable name="x_1,4" index="10" value="0"/>
<variable name="x_1,5" index="11" value="0"/>
<variable name="x_2,0" index="12" value="1"/>
<variable name="x_2,1" index="13" value="0"/>
<variable name="x_2,2" index="14" value="0"/>
<variable name="x_2,3" index="15" value="0"/>
<variable name="x_2,4" index="16" value="0"/>
<variable name="x_2,5" index="17" value="0"/>
<variable name="x_3,0" index="18" value="0"/>
<variable name="x_3,1" index="19" value="0"/>
<variable name="x_3,2" index="20" value="0"/>
<variable name="x_3,3" index="21" value="0"/>
<variable name="x_3,4" index="22" value="0"/>
<variable name="x_3,5" index="23" value="1"/>
<variable name="x_4,0" index="24" value="0"/>
<variable name="x_4,1" index="25" value="0"/>
<variable name="x_4,2" index="26" value="0"/>
<variable name="x_4,3" index="27" value="0"/>
<variable name="x_4,4" index="28" value="1"/>
<variable name="x_4,5" index="29" value="0"/>
<variable name="x31" index="30" value="-675"/>
</variables>
</CPLEXSolution>
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