binary variable at not binary level in optimal solution

Hi,



I am solving a MIP problem with CPLEX and I am getting as solution status:



“Fixed MIP status(1): optimal



Proven optimal solution.

“

In some cases, though, I find non integer values for some of my integer variables, for example for variable y (defined as binary variable) I sometimes get:



“---- 267 VARIABLE y.L 1 if the selected process k is selected or 0 otherwise



2 1.000, 12 1.000, 21 1.433039E-7, 22 1.000

33 1.000

“



Any advice?



I attached the full log file below.



Thanks

Alberto



Reading data…

Starting Cplex…

Tried aggregator 3 times.

MIP Presolve eliminated 2677 rows and 2391 columns.

MIP Presolve modified 147 coefficients.

Aggregator did 206 substitutions.

Reduced MIP has 284 rows, 242 columns, and 1018 nonzeros.

Reduced MIP has 98 binaries, 0 generals, 0 SOSs, and 0 indicators.

Probing fixed 18 vars, tightened 68 bounds.

Probing time = 0.00 sec.

Tried aggregator 1 time.

MIP Presolve eliminated 42 rows and 39 columns.

MIP Presolve modified 38 coefficients.

Reduced MIP has 242 rows, 203 columns, and 886 nonzeros.

Reduced MIP has 80 binaries, 0 generals, 0 SOSs, and 0 indicators.

Presolve time = 0.02 sec.

Probing fixed 3 vars, tightened 12 bounds.

Probing time = 0.00 sec.

Clique table members: 1287.

MIP emphasis: balance optimality and feasibility.

MIP search method: dynamic search.

Parallel mode: none, using 1 thread.

Tried aggregator 1 time.

LP Presolve eliminated 7 rows and 6 columns.

Aggregator did 2 substitutions.

Reduced LP has 233 rows, 195 columns, and 859 nonzeros.

Presolve time = 0.00 sec.

Initializing dual steep norms . . .



Iteration log . . .

Iteration: 1 Dual objective = 86889.713025

Iteration: 62 Dual objective = 21115.461946

Initializing dual steep norms . . .

Root relaxation solution time = 0.00 sec.



Nodes Cuts/

Node Left Objective IInf Best Integer Best Bound ItCnt Gap



0 0 20888.4162 18 20888.4162 89

  • 0+    0                        20609.4369    20888.4162       89    1.35%
    

0 0 20618.3028 6 20609.4369 Cuts: 90 137 0.04%

  • 0+    0                        20609.4370    20618.3028      137    0.04%
    

0 0 cutoff 20609.4370 20618.3028 143 0.04%

Elapsed real time = 0.09 sec. (tree size = 0.00 MB, solutions = 2)



Clique cuts applied: 10

Implied bound cuts applied: 17

Flow cuts applied: 18

Gomory fractional cuts applied: 4



Root node processing (before b&c):

Real time = 0.09

Sequential b&c:

Real time = 0.00


Total (root+branch&cut) = 0.09 sec.

MIP status(101): integer optimal solution

Fixing integer variables, and solving final LP…

Tried aggregator 1 time.

LP Presolve eliminated 3138 rows and 2810 columns.

Aggregator did 29 substitutions.

All rows and columns eliminated.

Presolve time = 0.00 sec.

Fixed MIP status(1): optimal



Proven optimal solution.



MIP Solution: 20609.436961 (143 iterations, 0 nodes)

Final Solve: 20609.436940 (0 iterations)



Best possible: 20609.436961

Absolute gap: 0.000000

Relative gap: 0.000000



— Restarting execution

— Model2.gms(250) 2 Mb

— Reading solution for model Model2

— Model2.gms(250) 3 Mb

— Executing after solve: elapsed 0:00:02.005

— Model2.gms(279) 3 Mb


To post to this group, send email to gamsworld@googlegroups.com.
To unsubscribe from this group, send email to gamsworld+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/gamsworld?hl=en.

Hi,
I think u have not written two additional equation which are required
for a variable to behave as a binary variable.
Merely defining the variable as a binary variable does not ensure that
the variable will work as binary variable.

On Apr 2, 5:27 pm, Alberto Quaglia wrote:

Hi,

I am solving a MIP problem with CPLEX and I am getting as solution status:

"Fixed MIP status(1): optimal

Proven optimal solution.
"
In some cases, though, I find non integer values for some of my integer variables, for example for variable y (defined as binary variable) I sometimes get:

"---- 267 VARIABLE y.L 1 if the selected process k is selected or 0 otherwise

2 1.000, 12 1.000, 21 1.433039E-7, 22 1.000
33 1.000
"

Any advice?

I attached the full log file below.

Thanks
Alberto

Reading data…
Starting Cplex…
Tried aggregator 3 times.
MIP Presolve eliminated 2677 rows and 2391 columns.
MIP Presolve modified 147 coefficients.
Aggregator did 206 substitutions.
Reduced MIP has 284 rows, 242 columns, and 1018 nonzeros.
Reduced MIP has 98 binaries, 0 generals, 0 SOSs, and 0 indicators.
Probing fixed 18 vars, tightened 68 bounds.
Probing time = 0.00 sec.
Tried aggregator 1 time.
MIP Presolve eliminated 42 rows and 39 columns.
MIP Presolve modified 38 coefficients.
Reduced MIP has 242 rows, 203 columns, and 886 nonzeros.
Reduced MIP has 80 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec.
Probing fixed 3 vars, tightened 12 bounds.
Probing time = 0.00 sec.
Clique table members: 1287.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: none, using 1 thread.
Tried aggregator 1 time.
LP Presolve eliminated 7 rows and 6 columns.
Aggregator did 2 substitutions.
Reduced LP has 233 rows, 195 columns, and 859 nonzeros.
Presolve time = 0.00 sec.
Initializing dual steep norms . . .

Iteration log . . .
Iteration: 1 Dual objective = 86889.713025
Iteration: 62 Dual objective = 21115.461946
Initializing dual steep norms . . .
Root relaxation solution time = 0.00 sec.

    Nodes                                         Cuts/

Node Left Objective IInf Best Integer Best Bound ItCnt Gap

  0     0    20888.4162    18                  20888.4162       89
  • 0+    0                        20609.4369    20888.4162       89    1.35%
    0     0    20618.3028     6    20609.4369      Cuts: 90      137    0.04%
    
  • 0+    0                        20609.4370    20618.3028      137    0.04%
    0     0        cutoff          20609.4370    20618.3028      143    0.04%
    

Elapsed real time = 0.09 sec. (tree size = 0.00 MB, solutions = 2)

Clique cuts applied: 10
Implied bound cuts applied: 17
Flow cuts applied: 18
Gomory fractional cuts applied: 4

Root node processing (before b&c):
Real time = 0.09
Sequential b&c:
Real time = 0.00
-------
Total (root+branch&cut) = 0.09 sec.
MIP status(101): integer optimal solution
Fixing integer variables, and solving final LP…
Tried aggregator 1 time.
LP Presolve eliminated 3138 rows and 2810 columns.
Aggregator did 29 substitutions.
All rows and columns eliminated.
Presolve time = 0.00 sec.
Fixed MIP status(1): optimal

Proven optimal solution.

MIP Solution: 20609.436961 (143 iterations, 0 nodes)
Final Solve: 20609.436940 (0 iterations)

Best possible: 20609.436961
Absolute gap: 0.000000
Relative gap: 0.000000

— Restarting execution
— Model2.gms(250) 2 Mb
— Reading solution for model Model2
— Model2.gms(250) 3 Mb
— Executing after solve: elapsed 0:00:02.005
— Model2.gms(279) 3 Mb

\

Hi,

Thanks for your answer, which equations are you referring to?

-----Original Message-----
From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of dharmender yadav
Sent: 3. april 2012 12:04
To: gamsworld
Subject: Re: binary variable at not binary level in optimal solution

Hi,
I think u have not written two additional equation which are required
for a variable to behave as a binary variable.
Merely defining the variable as a binary variable does not ensure that
the variable will work as binary variable.

On Apr 2, 5:27 pm, Alberto Quaglia wrote:

Hi,

I am solving a MIP problem with CPLEX and I am getting as solution status:

"Fixed MIP status(1): optimal

Proven optimal solution.
"
In some cases, though, I find non integer values for some of my integer variables, for example for variable y (defined as binary variable) I sometimes get:

"---- 267 VARIABLE y.L 1 if the selected process k is selected or 0 otherwise

2 1.000, 12 1.000, 21 1.433039E-7, 22 1.000
33 1.000
"

Any advice?

I attached the full log file below.

Thanks
Alberto

Reading data…
Starting Cplex…
Tried aggregator 3 times.
MIP Presolve eliminated 2677 rows and 2391 columns.
MIP Presolve modified 147 coefficients.
Aggregator did 206 substitutions.
Reduced MIP has 284 rows, 242 columns, and 1018 nonzeros.
Reduced MIP has 98 binaries, 0 generals, 0 SOSs, and 0 indicators.
Probing fixed 18 vars, tightened 68 bounds.
Probing time = 0.00 sec.
Tried aggregator 1 time.
MIP Presolve eliminated 42 rows and 39 columns.
MIP Presolve modified 38 coefficients.
Reduced MIP has 242 rows, 203 columns, and 886 nonzeros.
Reduced MIP has 80 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec.
Probing fixed 3 vars, tightened 12 bounds.
Probing time = 0.00 sec.
Clique table members: 1287.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: none, using 1 thread.
Tried aggregator 1 time.
LP Presolve eliminated 7 rows and 6 columns.
Aggregator did 2 substitutions.
Reduced LP has 233 rows, 195 columns, and 859 nonzeros.
Presolve time = 0.00 sec.
Initializing dual steep norms . . .

Iteration log . . .
Iteration: 1 Dual objective = 86889.713025
Iteration: 62 Dual objective = 21115.461946
Initializing dual steep norms . . .
Root relaxation solution time = 0.00 sec.

    Nodes                                         Cuts/

Node Left Objective IInf Best Integer Best Bound ItCnt Gap

  0     0    20888.4162    18                  20888.4162       89
  • 0+    0                        20609.4369    20888.4162       89    1.35%
    0     0    20618.3028     6    20609.4369      Cuts: 90      137    0.04%
    
  • 0+    0                        20609.4370    20618.3028      137    0.04%
    0     0        cutoff          20609.4370    20618.3028      143    0.04%
    

Elapsed real time = 0.09 sec. (tree size = 0.00 MB, solutions = 2)

Clique cuts applied: 10
Implied bound cuts applied: 17
Flow cuts applied: 18
Gomory fractional cuts applied: 4

Root node processing (before b&c):
Real time = 0.09
Sequential b&c:
Real time = 0.00
-------
Total (root+branch&cut) = 0.09 sec.
MIP status(101): integer optimal solution
Fixing integer variables, and solving final LP…
Tried aggregator 1 time.
LP Presolve eliminated 3138 rows and 2810 columns.
Aggregator did 29 substitutions.
All rows and columns eliminated.
Presolve time = 0.00 sec.
Fixed MIP status(1): optimal

Proven optimal solution.

MIP Solution: 20609.436961 (143 iterations, 0 nodes)
Final Solve: 20609.436940 (0 iterations)

Best possible: 20609.436961
Absolute gap: 0.000000
Relative gap: 0.000000

— Restarting execution
— Model2.gms(250) 2 Mb
— Reading solution for model Model2
— Model2.gms(250) 3 Mb
— Executing after solve: elapsed 0:00:02.005
— Model2.gms(279) 3 Mb

\