How to get the minimization value of the objective function, not negative maximum value.

[bin sun]

Dear Johan,

I have five available positions and I choose two of them. distB and I are dependent on the positions. I want to get the maximum value and minimum value of B=distB*I'. I can get the maximum value( using f=-sum(distB*I');) but when I try to get the minimum value I get the negative max( using f=sum(distB*I');). Could you tell me how to get the minimum value? (not negative maximum value)

The code is attached:

d=[1*5 matrix]

c=[5*5 maxtrix]

dshort=0.15;

distB=2e-7./[-dshort,dist1-dshort,2*dist1-dshort,3*dist1-dshort,4*dist1-dshort;-(dist1+dshort),-dshort,dshort,dshort+dist1,dshort+2*dist1;

        -(2*dist1+dshort),-(dist1+dshort),-dshort,dshort,dshort+dist1; -(3*dist1+dshort),-(2*dist1+dshort),-(dist1+dshort),-(0*dist1+dshort),dshort];

I=intvar(1,5); 

pos=binvar(1,5); 

intvar Ibase;   

f=-sum(distB*I');

desired = [ zeros(1,3) Ibase  Ibase];

F=[implies(pos,I== 0)]; 

F=F+[sum(pos)==3]; 

F=F+[(c*(I.^2)')./d' <= 1]; 

F=F+[sort(I)==desired];      

F=F+[0<=I<=600];    

F=F+[1<=Ibase<=600]; 

sol=optimize(F,f);

I=value(I)   

pos=value(pos)

Ibase=value(Ibase)

B=value(distB*I')

[Johan Löfberg]

Not clear what you mean with "get"

If you want to minimize f, you use the objective objective = f, and the minimum value will be value(f)

If you want to maximize f, you use the objective objective = -f, and the maximum value will be value(f)

[bin sun]

Yeah. I use f=-sum(distB*I'); to get the maximum value is 

B =1.0e-03 *

    0.2459

    0.3826

    0.9564

   -0.0000

But when I use f=sum(distB*I'); to get the minimum value I get 

B =

   1.0e-03 *

   -0.0000

   -0.9564

   -0.3826

   -0.2459
This is not what I want. I hope to get sumB equal to zero or a very small positive value.

Thank you very much,

Best,

Bin

[Johan Löfberg]

Impossible to say anything out of context. For anyone just looking at those numbers, it's pretty close to zero...

Maximization leading to stuff*1e-3 and minimization leading to -stuff*1e-3 tells me the problem is badly scaled.

[bin sun]

So if I want to restrict the objective function is positive. How can I do that? 

Another similiar problem I have if use f=-sum(I); to get the maximum, I get: 456. But if use f=sum(I); to get minimum, I get -456. This is not what I need. I hope to get some very small positive value.

[Johan Löfberg]

If you want something to be positive, you just add the constraint something>=0, like always.

[bin sun]

Maximum value can be calculate correctly using the code attached. I hope to get the minimum value and I get the code like this and I add the code F=F+[distB*I'], then B=[0;0;0;0]. Can you tell me how to change this code? I choose three positions from 5 available positions. Unchoose part have I=0, choose part follow the restrict:F=F+[(c*(I.^2)')./d' <= 1]; And My objective function is f=sum(distB*I');

d=[401933.568419812,401933.568419812,401933.568419812,401933.568419812,401933.568419812];

c=[1,0.385740902327350,0.252086400923626,0.180051756213799,0.134338625773115;0.385740902327350,1,0.385740902327350,0.252086400923626,0.180051756213799;0.252086400923626,0.385740902327350,1,0.385740902327350,0.252086400923626;0.180051756213799,0.252086400923626,0.385740902327350,1,0.385740902327350;0.134338625773115,0.180051756213799,0.252086400923626,0.385740902327350,1];

I=intvar(1,5); 

pos=binvar(1,5); 

intvar Ibase; 

dshort=0.15;

distB=2e-7./[-dshort,dist1-dshort,2*dist1-dshort,3*dist1-dshort,4*dist1-dshort;-(dist1+dshort),-dshort,dshort,dshort+dist1,dshort+2*dist1;

        -(2*dist1+dshort),-(dist1+dshort),-dshort,dshort,dshort+dist1; -(3*dist1+dshort),-(2*dist1+dshort),-(dist1+dshort),-(0*dist1+dshort),dshort];

f=sum(distB*I');

desired = [ zeros(1,2) Ibase  Ibase Ibase];

F=[implies(pos,I== 0)]; 

F=F+[sum(pos)==2]; 

[Johan Löfberg]

Undefined function or variable 'dist1'.

 

[bin sun]

L=1; %buried depth

dist1=0.3;  %distance between each other

dist2=0.5;   %distance of two row

n=15;   %how many cables

[Johan Löfberg]

To begin with, with the unnecessary multiplcation with 2e-7, your objective coefficients is in the order of 1e-5. Completely unnecessary introduction of bad data.

What is the problem then? When I minimize I get

>> value(I)

ans =

  476.0000  476.0000  476.0000         0         0

and when I maximize I get

>> value(I)

ans =

         0         0  476.0000  476.0000  476.0000

with objectives 7011 and -7011 respectively (after removing the unnecessary scaling with 2e-7)...

[bin sun]

The value I calculated have direction. So -7011 and 7011 just different direction but same result. What I want is to get the result have big I but zero sum(B)(f=sum(distB*I');). For example, if I=476, change the positions can get sumB=0 

[Johan Löfberg]

You get what you ask for. Now you asked for a small sum, hence you get a small sum. If you want to a small absolute value, you have to minimize that objective

[bin sun]

So I should write objective function like: f=sum(abs(distB*I'));?

[Johan Löfberg]

We don't now what you actually want. Either that or perhaps abs(sum((distB*I'))), or sum((distB*I').^2), ....We don't know how you define "small"