[Help-glpk] Transforming a Piecewise Linear Functions in a Convex Predicate
Hi, I need to transform a Piecewise Linear Functions in a Convex Predicate. In attachment there is a tex file with the function and my transformation in a convex predicate. Using that convex predicate in a milp, the milp does not found solution. So in attachment there is my .c file with the function that create the MILP and an output with a milp with random valute. The function in the examples is repeated two times, but it does not matter. I don't know where is my mistake. It's impossible for me find it. Thank you for your help. Cheers Simone Piecewise-Linear-Functions.tex Description: Binary data function.c Description: Binary data Maximize obj: 0.5 Z.1 + 0.5 Z.2 Subject To r.1: + 5.6 U.1 -1 Z.1 + 72.8 Y.1.1 <= 56 r.2: -5.6 U.1 + 1 Z.1 -15.8 Y.1.1 <= 1 r.3: + 1 U.1 + 10 Q.1 <= 10 r.4: -1 U.1 + 1 Q.2 <= 0 r.5: - 1 Q.1 - 1 Q.2 - 1 Y.1.1 <= -1 r.6: + 5.6 U.1 -1 Z.1 + 72.8 Y.1.2 <= 56 r.7: -5.6 U.1 + 1 Z.1 -15.8 Y.1.2 <= 1 r.8: + 1 U.1 + 9 Q.3 <= 10 r.9: -1 U.1 + 2 Q.4 <= 0 r.10: - Q.3 - Q.4 - Y.1.2 <= -1 r.11: + 5.6 U.1 -1 Z.1 + 72.8 Y.1.3 <= 56 r.12: -5.6 U.1 + 1 Z.1 -15.8 Y.1.3 <= 1 r.13: -8 Y.1.3 + 1 U.1 <= 2 r.14: + 11.2 U.1 -1 Z.2 + 128.8 Y.1.1 <= 112 r.15: -11.2 U.1 + 1 Z.2 -15.8 Y.1.1 <= 1 r.16: + 1 U.1 + 10 Q.1 <= 10 r.17: -1 U.1 + 1 Q.2 <= 0 r.18: - 1 Q.1 - 1 Q.2 - 1 Y.1.1 <= -1 r.19: + 0 U.1 -1 Z.2 + 28 Y.1.2 <= 0 r.20: + 0 U.1 + 1 Z.2 -27 Y.1.2 <= 1 r.21: + 1 U.1 + 9 Q.3 <= 10 r.22: -1 U.1 + 2 Q.4 <= 0 r.23: - Q.3 - Q.4 - Y.1.2 <= -1 r.24: + 5.6 U.1 -1 Z.2 + 72.8 Y.1.3 <= 56 r.25: -5.6 U.1 + 1 Z.2 -15.8 Y.1.3 <= 1 r.26: -8 Y.1.3 + 1 U.1 <= 2 r.27: Y.1.1 + Y.1.2 + Y.1.3 = 1 Bounds 0 <= Z.1 <= 1 0 <= Z.2 <= 1 0 <= U.1 <= 10 0 <= Y.1.1 <= 1 0 <= Q.1 <= 1 0 <= Q.2 <= 1 0 <= Y.1.2 <= 1 0 <= Q.3 <= 1 0 <= Q.4 <= 1 0 <= Y.1.3 <= 1 Generals Z.1 Z.2 U.1 Integer Y.1.1 Y.1.2 Y.1.3 Q.1 Q.2 Q.3 Q.4 End ___ Help-glpk mailing list Help-glpk@gnu.org http://lists.gnu.org/mailman/listinfo/help-glpk
[Help-glpk] how to defne an array (something like pointer to pointer in C)
Dear All, I am new to glpk and MathProg. I am trying to model a problem in glpk and solve it. The problem is that I don’t know how should I define the following : We have E[i] for each i that is member of N : N is a set that contains A B C D E, So, we have E[A], E[B], E[C], E[D], E[E] The value for each of these members is as follows, for example: E[A]:= AB E[B] := AB BC E[C] := BC CD E[D] := CD DE E[E] := DE The problem is that I don’t know how to define E with the above specifications! I have tested the followings and it didn’t work: 1) param E:= A AB; B AB BC C BC CD D CD DE E DE; 2) param E : if i==A then AB else if i==B then AB BC else if i==C then BC CD else if i==D then CD DE else if i==E then DE; 3) set EA; /*set of edges connected to node A*/ set EB; /*set of edges connected to node B*/ set EC; /*set of edges connected to node C*/ set ED; /*set of edges connected to node D*/ set EE; /*set of edges connected to node E*/ set EA := AB; set EB := AB BC; set EC := BC CD; set ED := CD DE; set EE := DE; and also we have: u can be AB BC CD DE and after defining the E, I have to check something like this: for each I in N, for each u that is in E[i] ….some condition…… I really don’t know how should I solve this problem,how to define E, and it is very essential to solve this problem.. Please do me a favor and help! Many thanks in advance. Regards ___ Help-glpk mailing list Help-glpk@gnu.org http://lists.gnu.org/mailman/listinfo/help-glpk
Re: [Help-glpk] how to defne an array (something like pointer to pointer in C)
Hello Maryam,
you could use the following formulation
set N;
set E{n in N};
display E;
data;
set N:= A B C D E;
set E[A]:= A AB;
set E[B]:= AB BC;
set E[C]:= BC CD;
set E[D]:= CD DE;
set E[E]:= DE;
end;
If you have large data sets consider using the table statement described in
doc\tables.pdf to read the data from a SQL database or from a CSV file.
Best regards
Xypron
Best regards
Xypron
Maryam Ahmadi wrote:
>
> Dear All,
>
> I am new to glpk and MathProg. I am trying to model a problem in glpk
> and solve it. The problem is that I don’t know how should I define the
> following :
> We have E[i] for each i that is member of N :
> N is a set that contains A B C D E,
> So, we have E[A], E[B], E[C], E[D], E[E]
> The value for each of these members is as follows, for example:
> E[A]:= AB
> E[B] := AB BC
> E[C] := BC CD
> E[D] := CD DE
> E[E] := DE
> The problem is that I don’t know how to define E with the above
> specifications!
>
> I have tested the followings and it didn’t work:
> 1)
> param E:=
> A AB;
> B AB BC
> C BC CD
> D CD DE
> E DE;
>
> 2)
> param E :
> if i==A
> then AB
> else if i==B
> then AB BC
> else if i==C
> then BC CD
> else if i==D
> then CD DE
> else if i==E
> then DE;
> 3)
> set EA; /*set of edges connected to node A*/
> set EB; /*set of edges connected to node B*/
> set EC; /*set of edges connected to node C*/
> set ED; /*set of edges connected to node D*/
> set EE; /*set of edges connected to node E*/
> set EA := AB;
> set EB := AB BC;
> set EC := BC CD;
> set ED := CD DE;
> set EE := DE;
>
> and also we have:
> u can be AB BC CD DE
> and after defining the E, I have to check something like this:
> for each I in N, for each u that is in E[i] ….some condition……
>
> I really don’t know how should I solve this problem,how to define E,
> and it is very essential to solve this problem..
> Please do me a favor and help!
> Many thanks in advance.
> Regards
>
>
> ___
> Help-glpk mailing list
> Help-glpk@gnu.org
> http://lists.gnu.org/mailman/listinfo/help-glpk
>
>
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Re: [Help-glpk] Transforming a Piecewise Linear Functions in a Convex Predicate
> I need to transform a Piecewise Linear Functions in a Convex > Predicate. In attachment there is a tex file with the function and my > transformation in a convex predicate. Using that convex predicate in a > milp, the milp does not found solution. So in attachment there is > my .c file with the function that create the MILP and an output with a > milp with random valute. > The function in the examples is repeated two times, but it does not > matter. > I don't know where is my mistake. It's impossible for me find it. Below here is the output from glpsol (mip preprocessing is disabled, debug output is enabled), which shows in details why your mip instance has no integer feasible solution: GLPSOL: GLPK LP/MIP Solver 4.39 Reading problem data from `milp.txt'... 27 rows, 10 columns, 69 non-zeros 10 integer variables, 9 of which are binary 59 lines were read Scaling... A: min|aij| = 1.000e+00 max|aij| = 1.288e+02 ratio = 1.288e+02 GM: min|aij| = 5.546e-01 max|aij| = 1.803e+00 ratio = 3.252e+00 EQ: min|aij| = 3.161e-01 max|aij| = 1.000e+00 ratio = 3.163e+00 Crashing... Size of triangular part = 27 glp_simplex: original LP has 27 rows, 10 columns, 69 non-zeros glp_simplex: presolved LP has 21 rows, 10 columns, 52 non-zeros Scaling... A: min|aij| = 1.000e+00 max|aij| = 1.288e+02 ratio = 1.288e+02 GM: min|aij| = 6.238e-01 max|aij| = 1.603e+00 ratio = 2.570e+00 EQ: min|aij| = 3.977e-01 max|aij| = 1.000e+00 ratio = 2.514e+00 Crashing... Size of triangular part = 21 0: obj = 0.0e+00 infeas = 4.684e+00 (0) *10: obj = 1.0e+00 infeas = 4.926e-16 (0) OPTIMAL SOLUTION FOUND Integer optimization begins... Processing node 1 at level 0 +10: mip = not found yet <= +inf(1; 0) Solving LP relaxation... |10: obj = 1.0e+00 infeas = 0.000e+00 (0) OPTIMAL SOLUTION FOUND Found optimal solution to LP relaxation Local bound is 1.0e+00 There are 6 fractional columns, integer infeasibility is 1.203e+00 branch_drtom: column 7 chosen to branch on branch_drtom: down-branch bound is 1.0e+00 branch_drtom: up-branch is infeasible Up-branch is hopeless +10: mip = not found yet <= 1.0e+00(1; 0) Solving LP relaxation... |11: obj = 1.0e+00 infeas = 0.000e+00 (0) OPTIMAL SOLUTION FOUND Found optimal solution to LP relaxation Local bound is 1.0e+00 There are 3 fractional columns, integer infeasibility is 1.113e+00 branch_drtom: column 4 chosen to branch on branch_drtom: down-branch bound is 1.0e+00 branch_drtom: up-branch bound is 1.0e+00 Branching on column 4, primal value is 6.291208791e-01 Node 2 begins down branch, node 3 begins up branch Processing node 3 at level 1 +11: mip = not found yet <= 1.0e+00(2; 0) Solving LP relaxation... |12: obj = 1.0e+00 infeas = 0.000e+00 (0) PROBLEM HAS NO FEASIBLE SOLUTION LP relaxation has no feasible solution Node 3 fathomed Processing node 2 at level 1 +12: mip = not found yet <= 1.0e+00(1; 1) Solving LP relaxation... |15: obj = 1.0e+00 infeas = 0.000e+00 (0) PROBLEM HAS NO FEASIBLE SOLUTION LP relaxation has no feasible solution Node 2 fathomed Active list is empty! +15: mip = not found yet <= tree is empty(0; 3) PROBLEM HAS NO INTEGER FEASIBLE SOLUTION Time used: 0.0 secs Memory used: 0.1 Mb (57684 bytes) I would suggest you to use the MathProg modeling language. It is much easier than writing a model generator in C. See also: http://lists.gnu.org/archive/html/help-glpk/2008-12/msg00126.html http://lists.gnu.org/archive/html/help-glpk/2007-06/msg5.html Andrew Makhorin ___ Help-glpk mailing list Help-glpk@gnu.org http://lists.gnu.org/mailman/listinfo/help-glpk
Re: [Help-glpk] how to defne an array (something like pointer to pointer in C)
> I am new to glpk and MathProg. I am trying to model a problem in glpk
> and solve it. The problem is that I don’t know how should I define the
> following :
> We have E[i] for each i that is member of N :
> N is a set that contains A B C D E,
> So, we have E[A], E[B], E[C], E[D], E[E]
> The value for each of these members is as follows, for example:
> E[A]:= AB
> E[B] := AB BC
> E[C] := BC CD
> E[D] := CD DE
> E[E] := DE
> The problem is that I don’t know how to define E with the above
> specifications!
> I have tested the followings and it didn’t work:
> 1)
> param E:=
> A AB;
> B AB BC
> C BC CD
> D CD DE
> E DE;
> 2)
> param E :
> if i==A
> then AB
> else if i==B
> then AB BC
> else if i==C
> then BC CD
> else if i==D
> then CD DE
> else if i==E
> then DE;
> 3)
> set EA; /*set of edges connected to node A*/
> set EB; /*set of edges connected to node B*/
> set EC; /*set of edges connected to node C*/
> set ED; /*set of edges connected to node D*/
> set EE; /*set of edges connected to node E*/
> set EA := AB;
> set EB := AB BC;
> set EC := BC CD;
> set ED := CD DE;
> set EE := DE;
> and also we have:
> u can be AB BC CD DE
> and after defining the E, I have to check something like this:
> for each I in N, for each u that is in E[i] ….some condition……
> I really don’t know how should I solve this problem,how to define E,
> and it is very essential to solve this problem..
> Please do me a favor and help!
> Many thanks in advance.
You may try something like this:
set N;
set E{i in N}, dimen 2;
display E;
data;
set N := A B C D E;
set E[A] := (A,B);
set E[B] := (A,B) (B,C);
set E[C] := (B,C) (C,D);
set E[D] := (C,D) (D,E);
set E[E] := (D,E);
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