# Re: [gecode-users] Cost optimization problem

```Dear Christian,

```
When I transform all the code from float variables to integer variables (in
changing the constraints from 1 to 100 for example), that works perfectly.
So maybe my implementation for float variables is not good. I will try to
find why.

Best regards,

SD

-----Message d'origine-----
De : Christian Schulte [mailto:cschu...@kth.se]
Envoyé : jeudi 15 septembre 2016 17:03
À : 'Sebastien Delmotte'; users@gecode.org
Objet : RE: [gecode-users] Cost optimization problem

Hi,

Sorry but I think this is really a modelling issue and not a Gecode issue,
as you have already figured out 3).

Cheers
Christian

--
Christian Schulte, www.gecode.org/~schulte
Professor of Computer Science, KTH, cschu...@kth.se
Expert Researcher, SICS, cschu...@sics.se

-----Original Message-----
From: users-boun...@gecode.org [mailto:users-boun...@gecode.org] On Behalf
Of Sebastien Delmotte
Sent: Tuesday, September 13, 2016 14:55
To: users@gecode.org
Subject: [gecode-users] Cost optimization problem

Dear All,

I have a problem with using Gecode to solve an optimization problem.

Problem description:
- I have a recipe with two sub-components. Each component has a coefficient
corresponding to its amount in the recipe. So the sum of the sub-components
coefficients must be equal to 1;
- Each of the two sub-components is composed of several raw materials. Each
raw material has a coefficient corresponding to its amount in its
sub-component. So, for each sub-component, the sum of the raw materials
coefficients is equal to 1;
- At the recipe level, I have some constraints on the raw materials amount
(e.g. raw material 1 must be in a given interval). The amount of each raw
material in the recipe is equal to the product of the coefficient of this
raw material by the coefficient of its sub-component
- I have to minimize the cost of the recipe accounting for the cost of each
raw materials. This cost is equal to the sum of the product of each raw
material coefficient by its unit cost.

Code

#include <gecode/driver.hh>
#include <gecode/int.hh>
#include <gecode/minimodel.hh>
using namespace Gecode;
class Tests : public FloatMinimizeScript  {
protected:
FloatVarArray _rms_in_sub_c_1; // raw mat in sub-comp1
FloatVarArray _rms_in_sub_c_2; // raw mat in sub-comp2
FloatVarArray _sub_c; // 2 sub-comp
FloatVar _cost; // cost
public:
Tests(const Options& o)
:FloatMinimizeScript(o),_rms_in_sub_c_1(*this,4,0,1),_rms_in_sub_c_2(*this,3
,0,1),_sub_c(*this,2,0,1),_cost(*this,0,1000)
{
//sum of raw mat in sub-comp =1
FloatVar all_rms_sub1 = expr(*this,sum(_rms_in_sub_c_1));
rel(*this,all_rms_sub1 ,FRT_EQ,1);
FloatVar all_rms_sub2 = expr(*this,sum(_rms_in_sub_c_2));
rel(*this,all_rms_sub2 ,FRT_EQ,1);
// sum of sub-comp =1
FloatVar sm = expr(*this,sum(_sub_c));
rel(*this,sm ,FRT_EQ,1);
// Global constraints on raw mat in recipe FloatVar rm_0_sub_coef1=
expr(*this,_rms_in_sub_c_1[0]*_sub_c[0]);
rel(*this,rm_0_sub_coef1,FRT_GQ,0);
FloatVar rm_1_sub_coef1= expr(*this,_rms_in_sub_c_1[1]*_sub_c[0]);
rel(*this,rm_1_sub_coef1,FRT_GQ,0);
FloatVar rm_2_sub_coef1= expr(*this,_rms_in_sub_c_1[2]*_sub_c[0]);
rel(*this,rm_2_sub_coef1,FRT_GQ,0);
FloatVar rm_3_sub_coef1= expr(*this,_rms_in_sub_c_1[3]*_sub_c[0]);
rel(*this,rm_3_sub_coef1,FRT_GQ,0);
FloatVar rm_0_sub_coef2= expr(*this,_rms_in_sub_c_2[0]*_sub_c[1]);
rel(*this,rm_0_sub_coef2,FRT_GQ,0);
FloatVar rm_1_sub_coef2= expr(*this,_rms_in_sub_c_2[1]*_sub_c[1]);
rel(*this,rm_1_sub_coef2,FRT_GQ,0);
FloatVar rm_2_sub_coef2= expr(*this,_rms_in_sub_c_2[2]*_sub_c[1]);
rel(*this,rm_2_sub_coef2,FRT_GQ,0);

// Cost
_cost = expr(*this,_sub_c[0]*(_rms_in_sub_c_1[0]*12 +_rms_in_sub_c_1[1]*14 +
_rms_in_sub_c_1[2] * 22 +_rms_in_sub_c_1[3] * 17 )
+_sub_c[1]*(_rms_in_sub_c_2[0]*9 +_rms_in_sub_c_2[1]*2 +
+_rms_in_sub_c_2[2]
* 18 ));
FloatVarArgs all;
for(int i = 0; i <4; i++) all << _rms_in_sub_c_1[i]; for(int i = 0; i <3;
i++) all << _rms_in_sub_c_2[i]; for(int i = 0; i <2; i++) all << _sub_c[i];

branch(*this, all, FLOAT_VAR_NONE(), FLOAT_VAL_SPLIT_MIN());
}

virtual void
print(std::ostream& os) const {
os << "sub-component : " << _sub_c << "\nrms 1 : "<< _rms_in_sub_c_1<<
"\nrms2 : "<< _rms_in_sub_c_2 <<"\ncost : "<< _cost << std::endl;
}

virtual FloatVar cost(void) const{
return _cost;
}
Tests(bool share, Tests& s) : FloatMinimizeScript(share,s) { _sub_c.update
(*this, share, s._sub_c); _rms_in_sub_c_1.update(*this, share,
s._rms_in_sub_c_1); _rms_in_sub_c_2.update(*this, share, s._rms_in_sub_c_2);
_cost.update(*this, share, s._cost);
}

virtual Space*
copy(bool share) {
return new Tests(share,*this);
}
};
int main(int argc, char* argv[]) {
Options opt("Test");
opt.solutions(0);
FloatMinimizeScript::run<Tests,BAB,Options>(opt);
return 0;
}

When executing this code, the result is :
sub-component : {0, 1}
rms in sub-component 1 : {0, 0, 0, 1}
rms in sub-component 2 : {0, 0, 1}
cost : [18..18]

Exception: FloatVar::val: Attempt to access value of unassigned variable.

Problems:
1- The resulting solution is trivial but absolutely not optimal for the
cost: only the second sub-component has a positive coefficient (=1) with
only one raw material which is not the cheapest one;
2- In this example, all the constraints for the raw materials are: greater
than 0. But if I change the value of the constraints (e.g. greater than
0.1), I don't get any solution;
3- There is an exception error: FloatVar::val: Attempt to access value of
unassigned variable. This error disappears when I add the variable cost in
the branching, but the solution is still non optimal.

I think I have a problem with handling gecode because the problem is simple,
but I have no idea about the origin of the problem.
Best regards,
S.D.

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```