Reputation: 203
Optimisation in GAMS
I have a problem with my GAMS-code and the implementation of the GAMS-code in Ruby. I know that GAMS is not the most popular program, but maybe someone can help me. I have a model, where I try to allocate children optimally to kindergartens. This is a basic example of the code:
Sets
i Child
j Kindergarten
l Links
LI(l,i), LJ(l,j);
Parameters
a(j) accessibility
C(j) Capacity of Kindergartens
ch Capacity for handicapped children
d(i,j) distance
da(i) distance average
h(i) handicapped children
p(i,j) preferences
s(i,j) siblings;
Binary Variables
x(i,j) 1 if child i is allocated to kindergarten j;
Free Variables
ZFW Zielfunktionswert;
*----- Iclude -----
$include ...
da(i) = sum(j, d(i,j)) / card(j);
*----- Deklaration -----
Equations
ZF objective function
Zuordnung every child is assigned to one kindergarten
Kapa the capacity of the kindergarten must be maintained
Behin handicapped children are only assigned to suitable kindergartens;
ZF.. ZFW =E= sum((i,j), x(i,j) * (p(i,j)/s(i,j)) * (d(i,j)/da(i)));
Zuordnung(i).. sum(j, x(i,j)) =E= 1;
Kapa(j).. sum(i, x(i,j) * (1 - h(i))) + sum(i, x(i,j) * h(i) * ch) =L= C(j);
Behin(i,j).. x(i,j) * h(i) =L= a(j);
Model KiGaOpt /all/;
Solve KiGaOpt using MIP minimizing ZFW;
display x.l;
I have also a include file, where I define the parameters. My problem is, that I want to implement this in Ruby and I wanna use links (l) instaed of loops for the relation between i and j. I know, that I have to replace all i's and j's in dependence of l. But everytime I try this, I receive an error message. I have written it to this form, where I have replaced each time, when a parameter is dependent on i and j, with a l. But I have problems with the rest.
Sets
i Child
j Kindergarten
l Links
LI(l,i), LJ(l,j);
Parameters
a(j) accessibility
C(j) Capacity of Kindergartens
ch Capacity for handicapped children
d(l) distance
da(i) distance average
h(i) handicapped children
p(l) preferences
s(l) siblings;
Binary Variables
x(l) 1 if child i is allocated to kindergarten j;
Free Variables
ZFW Zielfunktionswert;
*----- Iclude -----
$include ...
da(i) = sum(l$LI(l,i), d(l)) / card(j);
*----- Deklaration -----
Equations
ZF objective function
Zuordnung every child is assigned to one kindergarten
Kapa the capacity of the kindergarten must be maintained
Behin handicapped children are only assigned to suitable kindergartens;
ZF.. ZFW =E= sum(l, x(l) * (p(l)/s(l)) * (d(l)/da(i)));
Zuordnung(i).. sum(l$LI(l,i), x(l)) =E= 1;
Kapa(j).. sum(l$LJ(l,j), x(l) * (1 - h(i))) + sum(l$LJ(l,j), x(l) * h(i) * ch) =L= C(j);
Behin(i,j).. x(l) * h(i) =L= a(j);
Model KiGaOpt /all/;
Solve KiGaOpt using MIP minimizing ZFW;
display x.l;
My include file looks as follow:
Sets
i /i1*i5/
j /j1*j2/
l /l1*l10/;
LI(l,i) = no;
LJ(l,j) = no;
LI( 'l1', 'i1') = yes;
LJ( 'l1', 'j1') = yes;
LI( 'l2', 'i1') = yes;
LJ( 'l2', 'j2') = yes;
LI( 'l3', 'i2') = yes;
LJ( 'l3', 'j1') = yes;
LI( 'l4', 'i2') = yes;
LJ( 'l4', 'j2') = yes;
LI( 'l5', 'i3') = yes;
LJ( 'l5', 'j1') = yes;
LI( 'l6', 'i3') = yes;
LJ( 'l6', 'j2') = yes;
LI( 'l7', 'i4') = yes;
LJ( 'l7', 'j1') = yes;
LI( 'l8', 'i4') = yes;
LJ( 'l8', 'j2') = yes;
LI( 'l9', 'i5') = yes;
LJ( 'l9', 'j1') = yes;
LI( 'l10', 'i5') = yes;
LJ( 'l10', 'j2') = yes;
Parameters
a(j)
/j1 1
j2 0/
h(i)
/i1 1
i2 0
i3 0
i4 0
i5 1/
C(j)
/j1 100
j2 100/
ch /2/;
Table p(i,j)
j1 j2
i1 10 1
i2 10 1
i3 10 1
i4 10 1
i5 10 1 ;
Table d(i,j)
j1 j2
i1 1 4
i2 2 1
i3 1 1
i4 1 2
i5 2 10.2 ;
Table s(i,j)
j1 j2
i1 5 1
i2 1 1
i3 1 1
i4 1 1
i5 1 1 ;
Can someone help me to rearrange my model and my include data?
Thank you!
Upvotes: 0
Views: 390
Answers (4)
Reputation: 203
this is my model:
Sets
i Child
j Kindergarten
l Links
LI(l,i), LJ(l,j);
Parameters
a(j) accessibility
C(j) Capacity of Kindergartens
ch Capacity for handicapped children
d(l) distance
da(i) distance average
h(i) handicapped children
p(l) preferences
s(l) siblings;
Binary Variables
x(l) 1 if child i is allocated to kindergarten j;
Free Variables
ZFW objective function value;
*----- Iclude -----
$include
da(i) = sum(l$LI(l,i), d(l)) / card(j);
*----- Deklaration -----
Equations
ZF objective function
Zuordnung every child is assigned to one kindergarten
Kapa the capacity of the kindergarten must be maintained
Behin handicapped children are only assigned to suitable kindergartens
Inklus equal distribution of handicapped children;
ZF.. ZFW =E= sum(LI(l,i), x(l) * (p(l)/s(l)) * (d(l)/da(i)));
Zuordnung(i).. sum(l$LI(l,i), x(l)) =E= 1;
Kapa(j).. sum(LI(l,i)$LJ(l,j), x(l) * (1 - h(i))) + sum(LI(l,i)$LJ(l,j), x(l) * h(i) * ch) =L= C(j);
Behin(l).. x(l) *sum(LI(l,i),h(i)) =L= sum(LJ(l,j),a(j))
Inklus(j).. sum(i, x(i,j)) =L= (card(h)/card(a) +1) * (1+TI) ;
Model KiGaOpt /all/;
Solve KiGaOpt using MIP minimizing ZFW;
display x.l;
and this is my include file:
*Instanzen
Sets
i /i1*i5/
j /j1*j2/
l /l1*l10/;
LI(l,i) = no;
LJ(l,j) = no;
LI( 'l1', 'i1') = yes;
LJ( 'l1', 'j1') = yes;
LI( 'l2', 'i1') = yes;
LJ( 'l2', 'j2') = yes;
LI( 'l3', 'i2') = yes;
LJ( 'l3', 'j1') = yes;
LI( 'l4', 'i2') = yes;
LJ( 'l4', 'j2') = yes;
LI( 'l5', 'i3') = yes;
LJ( 'l5', 'j1') = yes;
LI( 'l6', 'i3') = yes;
LJ( 'l6', 'j2') = yes;
LI( 'l7', 'i4') = yes;
LJ( 'l7', 'j1') = yes;
LI( 'l8', 'i4') = yes;
LJ( 'l8', 'j2') = yes;
LI( 'l9', 'i5') = yes;
LJ( 'l9', 'j1') = yes;
LI( 'l10', 'i5') = yes;
LJ( 'l10', 'j2') = yes;
Parameters
a(j)
/j1 1
j2 0/
h(i)
/i1 1
i2 0
i3 0
i4 0
i5 1/
C(j)
/j1 100
j2 100/
ch /2/
p(l) /l1 10
l2 10
l3 10
l4 10
l5 10
l6 1
l7 1
l8 1
l9 1
l10 1/
d(l) /l1 1
l2 2
l3 1
l4 1
l5 2
l6 4
l7 1
l8 1
l9 2
l10 10.2/
s(l) /l1 5
l2 1
l3 1
l4 1
l5 1
l6 1
l7 1
l8 1
l9 1
l10 1/
TI /0.5/;
Thank you very much for your help!
Best regards
Upvotes: 0
Reputation: 2292
I do not completely understand, why you went for the LI/LJ approach, but you actually should to use these maps in your equations to control i and j (these are often uncontrolled). So changing the equations in the following way gets rid of all compilation errors and solves the model:
ZF.. ZFW =E= sum(LI(l,i), x(l) * (p(l)/s(l)) * (d(l)/da(i)));
Zuordnung(i).. sum(l$LI(l,i), x(l)) =E= 1;
Kapa(j).. sum(LI(l,i)$LJ(l,j), x(l) * (1 - h(i))) + sum(LI(l,i)$LJ(l,j), x(l) * h(i) * ch) =L= C(j);
Behin(l).. x(l) *sum(LI(l,i),h(i)) =L= sum(LJ(l,j),a(j));
Best regards, Lutz
Upvotes: 0
Reputation: 203
This is my new include file. I tried to include it in the model code above.
Sets
i /i1*i5/
j /j1*j2/
l /l1*l10/;
LI(l,i) = no;
LJ(l,j) = no;
LI( 'l1', 'i1') = yes;
LJ( 'l1', 'j1') = yes;
LI( 'l2', 'i1') = yes;
LJ( 'l2', 'j2') = yes;
LI( 'l3', 'i2') = yes;
LJ( 'l3', 'j1') = yes;
LI( 'l4', 'i2') = yes;
LJ( 'l4', 'j2') = yes;
LI( 'l5', 'i3') = yes;
LJ( 'l5', 'j1') = yes;
LI( 'l6', 'i3') = yes;
LJ( 'l6', 'j2') = yes;
LI( 'l7', 'i4') = yes;
LJ( 'l7', 'j1') = yes;
LI( 'l8', 'i4') = yes;
LJ( 'l8', 'j2') = yes;
LI( 'l9', 'i5') = yes;
LJ( 'l9', 'j1') = yes;
LI( 'l10', 'i5') = yes;
LJ( 'l10', 'j2') = yes;
Parameters
a(j)
/j1 1
j2 0/
h(i)
/i1 1
i2 0
i3 0
i4 0
i5 1/
C(j)
/j1 100
j2 100/
ch /2/
p(l) /l1 10
l2 10
l3 10
l4 10
l5 10
l6 1
l7 1
l8 1
l9 1
l10 1/
d(l) /l1 1
l2 2
l3 1
l4 1
l5 2
l6 4
l7 1
l8 1
l9 2
l10 10.2/
s(l) /l1 5
l2 1
l3 1
l4 1
l5 1
l6 1
l7 1
l8 1
l9 1
l10 1/;
Upvotes: 0
Reputation: 2292
If I run your model, the first errors I get are about naming/declaration conflicts between your main model and the include file. For example, in you main model you have
Parameters
...
d(l) distance
...
p(l) preferences
s(l) siblings;
And then in the include file I see
Table p(i,j)
... ;
Table d(i,j)
... ;
Table s(i,j)
... ;
You cannot have the same symbol name with different argument lists (which is also mentioned in the error message: "**** 184 Domain list redefined"), so this is the first thing you need to resolve. Afterwards one could check how to proceed.
Good luck, Lutz
Upvotes: 0
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