[AMPL 2579] Problem in using let command

[Vlado15]

Hi all,

I have a decompositin problem to solve. In my .run file, there are
"let" commands, assigning initial values to variables defined in .mod
file. But, the problem occurs as solver (cplexamp) does not take these
initial values into account during its first run. Could somebody help
and explain what it could be wrong?

This is part of .run file with just a master problem.

model proba.mod;
data proba.dat;

option solver cplexamp;
option cplex_options 'mipdisplay 2 mipinterval 100 primal';
option cplex_option 'timelimit=900';

option omit_zero_rows 1;
option display_eps .000001;

problem Master: x2, Ship_pro, Y121, xcon1, xcon2, xcon3, xcon4;
Cut_Point, Cut_Ray;

let Ship_pro := 10000000;

param GAP default Infinity;

printf "\nRE-SOLVING MASTER PROBLEM\n\n";
solve Master;
printf "\n";

And this is part of .mod file with also just a Master problem.

param n>0, integer;

##sets
set Luke := 1..n;
set Luke1 within Luke := 1..n-1;
set Luke2 within Luke := 2..n;
set Luke3 within Luke := 2..n-1;

param pec{Luke};          #pec-lucke takse

var x2{Luke,Luke} binary;
var Ship_pro;

maximize Y121: 100000 - sum{i in Luke, j in Luke}x2[i,j]*pec[j];

subject to

Cut_Point {k in 1..nCUT}:
   if cut_type[k] = "point" then ZZ <= -sum{i in Luke1,j in Luke: j>=i
+1}alfa1[i,j,k]*zr[i,j]*sum{q in i+1..j}x2[i,q]
      -sum{i in Luke2,j in Luke: j<=i-1}beta1[i,j,k]*zr[i,j]*sum{q in
j..i-1}x2[i,q]
      -sum{i in Luke1,j in Luke: j>=i+1}xx1[i,j,k]*zr[i,j]*sum{q in
i..j-1}x2[q,j]
      -sum{i in Luke2,j in Luke: j<=i-1}delta1[i,j,k]*zr[i,j]*sum{q in
j+1..i}x2[q,j]
      +sum{i in 1..n-1,j in i+1..n: j!=i} fi1[i,j,k]*(C+MRS*(1-x2
[i,j]))
      +sum{i in 2..n,j in 1..i-1: j!=i} roi1[i,j,k]*(C+MRS*(1-x2
[i,j]))
      +tau1*(24*maxtt-sum{i in Luke,j in Luke:i!=j}x2[i,j]*(pdt[i]+pat
[j])-(l/v1+l/v2+tl+tb))
      +mi1*(24*mintt-sum{i in Luke,j in Luke:i!=j}x2[i,j]*(pdt[i]+pat
[j])-(l/v1+l/v2+tl+tb))
      +sum{i in Luke}lam1[i,k]*MRS+sum{i in Luke}rog1[i,k]*MRS;
      -(dcc*maxtt+Pout*(l/v1+l/v2)*(scf*fp+scl*lp))-sum{i in Luke, j
in Luke}x2[i,j]*pec[j];

Cut_Ray {k in 1..nCUT}:
   if cut_type[k] = "ray" then
      -sum{i in Luke1,j in Luke: j>=i+1}alfa1[i,j,k]*zr[i,j]*sum{q in i
+1..j}x2[i,q]
      -sum{i in Luke2,j in Luke: j<=i-1}beta1[i,j,k]*zr[i,j]*sum{q in
j..i-1}x2[i,q]
      -sum{i in Luke1,j in Luke: j>=i+1}xx1[i,j,k]*zr[i,j]*sum{q in
i..j-1}x2[q,j]
      -sum{i in Luke2,j in Luke: j<=i-1}delta1[i,j,k]*zr[i,j]*sum{q in
j+1..i}x2[q,j]
      +sum{i in 1..n-1,j in i+1..n: j!=i} fi1[i,j,k]*(C+MRS*(1-x2
[i,j]))
      +sum{i in 2..n,j in 1..i-1: j!=i} roi1[i,j,k]*(C+MRS*(1-x2
[i,j]))
      +tau1*(24*maxtt-sum{i in Luke,j in Luke:i!=j}x2[i,j]*(pdt[i]+pat
[j])-(l/v1+l/v2+tl+tb))
      +mi1*(24*mintt-sum{i in Luke,j in Luke:i!=j}x2[i,j]*(pdt[i]+pat
[j])-(l/v1+l/v2+tl+tb))
      +sum{i in Luke}lam1[i,k]*MRS+sum{i in Luke}rog1[i,k]*MRS>=0;
      -(dcc*maxtt-Pout*(l/v1+l/v2)*(scf*fp+scl*lp))-sum{i in Luke, j
in Luke}x2[i,j]*pec[j]>=0;

xcon1: sum{j in 2..n}x2[1,j]=1;

xcon2: sum{i in 2..n}x2[i,1]=1;

xcon3{q in 2..n-1}:sum{i in 1..q-1}x2[i,q]-sum{j in q+1..n}x2[q,j]=0;

xcon4{q in 2..n-1}:sum{i in q+1..n}x2[i,q]-sum{j in 1..q-1}x2[q,j]=0;

In first run cut_point and cut_ray are of course dropped, but solver
dose not take the initial value of variable Ship_pro into account and
therefore turns the problem infeasible.


Vlado

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[stefano.coniglio]

It may not be as easy. Warm start depends on the solver. If you are
using a simplex solver, a basic solution must be provided.

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[Robert Fourer-2]

The initial value of a variable is sent to the solver, but it is literally
that ... an "initial" value.  The solver may use that value as a hint in
starting its search, but in general it will change that value in the course
of finding an optimal solution.  In particular the initial value has no
effect on whether CPLEX finds the problem to be feasible.

If you want to force CPLEX to keep that variable at its initial value, you
can use "fix Ship_pro := 10000000;" instead.

Bob Fourer
4er@...

> -----Original Message-----
> From: ampl@... [mailto:ampl@...]
> On Behalf Of Vlado15 [marasv@...]
> Sent: Friday, June 05, 2009 4:12 AM
> To: AMPL Modeling Language
> Subject: [AMPL 2579] Problem in using let command
>
>
> Hi all,
>
> I have a decompositin problem to solve. In my .run file, there are
> "let" commands, assigning initial values to variables defined in .mod
> file. But, the problem occurs as solver (cplexamp) does not take these
> initial values into account during its first run. Could somebody help
> and explain what it could be wrong?
>
> This is part of .run file with just a master problem.
>
> model proba.mod;
> data proba.dat;
>
> option solver cplexamp;
> option cplex_options 'mipdisplay 2 mipinterval 100 primal';
> option cplex_option 'timelimit=900';
>
> option omit_zero_rows 1;
> option display_eps .000001;
>
> problem Master: x2, Ship_pro, Y121, xcon1, xcon2, xcon3, xcon4;
> Cut_Point, Cut_Ray;
>
> let Ship_pro := 10000000;
>
> param GAP default Infinity;
>
> printf "\nRE-SOLVING MASTER PROBLEM\n\n";
> solve Master;
> printf "\n";
>
> And this is part of .mod file with also just a Master problem.
>
> param n>0, integer;
>
> ##sets
> set Luke := 1..n;
> set Luke1 within Luke := 1..n-1;
> set Luke2 within Luke := 2..n;
> set Luke3 within Luke := 2..n-1;
>
> param pec{Luke};          #pec-lucke takse
>
> var x2{Luke,Luke} binary;
> var Ship_pro;
>
> maximize Y121: 100000 - sum{i in Luke, j in Luke}x2[i,j]*pec[j];
>
> subject to
>
> Cut_Point {k in 1..nCUT}:
>    if cut_type[k] = "point" then ZZ <= -sum{i in Luke1,j in Luke: j>=i
> +1}alfa1[i,j,k]*zr[i,j]*sum{q in i+1..j}x2[i,q]
>       -sum{i in Luke2,j in Luke: j<=i-1}beta1[i,j,k]*zr[i,j]*sum{q in
> j..i-1}x2[i,q]
>       -sum{i in Luke1,j in Luke: j>=i+1}xx1[i,j,k]*zr[i,j]*sum{q in
> i..j-1}x2[q,j]
>       -sum{i in Luke2,j in Luke: j<=i-1}delta1[i,j,k]*zr[i,j]*sum{q in
> j+1..i}x2[q,j]
>       +sum{i in 1..n-1,j in i+1..n: j!=i} fi1[i,j,k]*(C+MRS*(1-x2
> [i,j]))
>       +sum{i in 2..n,j in 1..i-1: j!=i} roi1[i,j,k]*(C+MRS*(1-x2
> [i,j]))
>       +tau1*(24*maxtt-sum{i in Luke,j in Luke:i!=j}x2[i,j]*(pdt[i]+pat
> [j])-(l/v1+l/v2+tl+tb))
>       +mi1*(24*mintt-sum{i in Luke,j in Luke:i!=j}x2[i,j]*(pdt[i]+pat
> [j])-(l/v1+l/v2+tl+tb))
>       +sum{i in Luke}lam1[i,k]*MRS+sum{i in Luke}rog1[i,k]*MRS;
>       -(dcc*maxtt+Pout*(l/v1+l/v2)*(scf*fp+scl*lp))-sum{i in Luke, j
> in Luke}x2[i,j]*pec[j];
>
> Cut_Ray {k in 1..nCUT}:
>    if cut_type[k] = "ray" then
>       -sum{i in Luke1,j in Luke: j>=i+1}alfa1[i,j,k]*zr[i,j]*sum{q in i
> +1..j}x2[i,q]
>       -sum{i in Luke2,j in Luke: j<=i-1}beta1[i,j,k]*zr[i,j]*sum{q in
> j..i-1}x2[i,q]
>       -sum{i in Luke1,j in Luke: j>=i+1}xx1[i,j,k]*zr[i,j]*sum{q in
> i..j-1}x2[q,j]
>       -sum{i in Luke2,j in Luke: j<=i-1}delta1[i,j,k]*zr[i,j]*sum{q in
> j+1..i}x2[q,j]
>       +sum{i in 1..n-1,j in i+1..n: j!=i} fi1[i,j,k]*(C+MRS*(1-x2
> [i,j]))
>       +sum{i in 2..n,j in 1..i-1: j!=i} roi1[i,j,k]*(C+MRS*(1-x2
> [i,j]))
>       +tau1*(24*maxtt-sum{i in Luke,j in Luke:i!=j}x2[i,j]*(pdt[i]+pat
> [j])-(l/v1+l/v2+tl+tb))
>       +mi1*(24*mintt-sum{i in Luke,j in Luke:i!=j}x2[i,j]*(pdt[i]+pat
> [j])-(l/v1+l/v2+tl+tb))
>       +sum{i in Luke}lam1[i,k]*MRS+sum{i in Luke}rog1[i,k]*MRS>=0;
>       -(dcc*maxtt-Pout*(l/v1+l/v2)*(scf*fp+scl*lp))-sum{i in Luke, j
> in Luke}x2[i,j]*pec[j]>=0;
>
> xcon1: sum{j in 2..n}x2[1,j]=1;
>
> xcon2: sum{i in 2..n}x2[i,1]=1;
>
> xcon3{q in 2..n-1}:sum{i in 1..q-1}x2[i,q]-sum{j in q+1..n}x2[q,j]=0;
>
> xcon4{q in 2..n-1}:sum{i in q+1..n}x2[i,q]-sum{j in 1..q-1}x2[q,j]=0;
>
> In first run cut_point and cut_ray are of course dropped, but solver
> dose not take the initial value of variable Ship_pro into account and
> therefore turns the problem infeasible.
>
>
> Vlado
>

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