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problem with no superbasic variables(simple model)
Posted: Fri Oct 12, 2018 3:32 pm
by piglet
Dear all,
I establish a model recently. The code runs successfully but the solution is infeasible. GAMS shows that there are no superbasic variables. This is a quite simple model but I don't know what the problems is after checking for several time. Could anyone help me?
Thanks for your prompt attention.
Set
i 'nodenumber' /1,11*13/;
Parameter
Sl(i) 'load capacity'
/1 900
11 300
12 200
13 400/
uav /0.5/
Positive Variable
Sd(i) 'compensate compacity'
u(i) 'node voltage'
ud(i) 'compensate voltage'
Variable
z 'total cost';
Binary Variable sigma(i)'install or not';
u.UP(i)=1.05;
u.LO('1')=0.3;
u.LO('11')=0.3;
u.LO('12')=0.8;
u.LO('13')=0.71;
Equation
v1
v2
v3
v4
v5
compacity(i);
v1..u('1')=e=uav+sigma('1')*ud('1');
v2..u('11')=e=u('1')+sigma('11')*ud('11');
v3..u('12')=e=u('1')+sigma('12')*ud('12');
v4..u('13')=e=u('1')+sigma('13')*ud('13');
compacity(i)..Sd(i)=e=sigma(i)*ud(i)*Sl(i)/u(i);
v5..z=e=sum(i,Sd(i));
Model beiqi/all/;
solve beiqi using rminlp minimizing z;
Re: problem with no superbasic variables(simple model)
Posted: Mon Oct 15, 2018 4:43 pm
by bussieck
You probably solved the non-convex model with a local solver (CONOPT) that gets stuck. The model is small enough to ask a global solver if the model is truly infeasible or if you need to pay more attention in setting a good starting point for your local solver. It turns out the latter is true. I solved with global solver Couenne and got the following solution (just solve summary and variable section):
Code: Select all
S O L V E S U M M A R Y
MODEL beiqi OBJECTIVE z
TYPE RMINLP DIRECTION MINIMIZE
SOLVER COUENNE FROM LINE 40
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 1 Optimal
**** OBJECTIVE VALUE 193.3099
RESOURCE USAGE, LIMIT 0.546 1000.000
ITERATION COUNT, LIMIT 0 2000000000
EVALUATION ERRORS 0 0
...
---- VAR Sd compensate compacity
LOWER LEVEL UPPER
1 . . +INF
11 . . +INF
12 . 75.0000 +INF
13 . 118.3099 +INF
---- VAR u node voltage
LOWER LEVEL UPPER
1 0.3000 0.5000 1.0500
11 0.3000 0.5000 1.0500
12 0.8000 0.8000 1.0500
13 0.7100 0.7100 1.0500
---- VAR ud compensate voltage
LOWER LEVEL UPPER
1 . 81129.3556 +INF
11 . 61375.9878 +INF
12 . 173.1841 +INF
13 . 145.2858 +INF
LOWER LEVEL UPPER
---- VAR z -INF 193.3099 +INF
z total cost
---- VAR sigma install or not
LOWER LEVEL UPPER
1 . . 1.0000
11 . . 1.0000
12 . 0.0017 1.0000
13 . 0.0014 1.0000
-Michael
Re: problem with no superbasic variables(simple model)
Posted: Wed Oct 17, 2018 3:39 am
by piglet
bussieck wrote: ↑5 years ago
You probably solved the non-convex model with a local solver (CONOPT) that gets stuck. The model is small enough to ask a global solver if the model is truly infeasible or if you need to pay more attention in setting a good starting point for your local solver. It turns out the latter is true. I solved with global solver Couenne and got the following solution (just solve summary and variable section):
Code: Select all
S O L V E S U M M A R Y
MODEL beiqi OBJECTIVE z
TYPE RMINLP DIRECTION MINIMIZE
SOLVER COUENNE FROM LINE 40
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 1 Optimal
**** OBJECTIVE VALUE 193.3099
RESOURCE USAGE, LIMIT 0.546 1000.000
ITERATION COUNT, LIMIT 0 2000000000
EVALUATION ERRORS 0 0
...
---- VAR Sd compensate compacity
LOWER LEVEL UPPER
1 . . +INF
11 . . +INF
12 . 75.0000 +INF
13 . 118.3099 +INF
---- VAR u node voltage
LOWER LEVEL UPPER
1 0.3000 0.5000 1.0500
11 0.3000 0.5000 1.0500
12 0.8000 0.8000 1.0500
13 0.7100 0.7100 1.0500
---- VAR ud compensate voltage
LOWER LEVEL UPPER
1 . 81129.3556 +INF
11 . 61375.9878 +INF
12 . 173.1841 +INF
13 . 145.2858 +INF
LOWER LEVEL UPPER
---- VAR z -INF 193.3099 +INF
z total cost
---- VAR sigma install or not
LOWER LEVEL UPPER
1 . . 1.0000
11 . . 1.0000
12 . 0.0017 1.0000
13 . 0.0014 1.0000
-Michael
Thanks for your prompt reply. At the beginning of the model, the sigma(i) is defined as a binary variable. However, sigma(12)、sigma(13) turn out to be 0.0017 and 0.0014 in the solution.
Re: problem with no superbasic variables(simple model)
Posted: Wed Oct 17, 2018 9:17 am
by bussieck
Your solve statement solves the model as an RMINLP (see
https://www.gams.com/latest/docs/UG_Mod ... odel_types). This relaxes the integral requirement. If you solve as MINLP you get:
Code: Select all
S O L V E S U M M A R Y
MODEL beiqi OBJECTIVE z
TYPE MINLP DIRECTION MINIMIZE
SOLVER COUENNE FROM LINE 40
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 1 Optimal
**** OBJECTIVE VALUE 193.3099
...
---- VAR sigma install or not
LOWER LEVEL UPPER
1 . . 1.0000
11 . . 1.0000
12 . 1.0000 1.0000
13 . 1.0000 1.0000
-Michael