Re: [Help-glpk] "Integer" linear programming with non-uniform quantization

[Xypron]

Hello Oscar,

if your problem is sufficiently small you can simply assign a binary to 
each value your variables can take. See example below.

If you want to write your own branch and bound heuristic on top of GLPK, 
have a look at glpk-4.45/glpios09.c

Best regards

Xypron

set X;
set Y;

var x;
var y;

var wx{i in X}, binary;
var wy{j in Y}, binary;

maximize obj : x + y;

s.t. c1 : x + .5 * y <=4;
s.t. c2 : .3 * x + y <= 3.8;

s.t. x1 : x = sum{i in X} i * wx[i];
s.t. x2 : 1 = sum{i in X} wx[i];
s.t. y1 : y = sum{j in Y} j * wy[j];
s.t. y2 : 1 = sum{j in Y} wy[j];

solve;

display x,y;

data;

set X := 1 1.6 2.3 3.5 5;
set Y := .8 1.3 1.7 2.1 2.7 4.1;

end;


Oscar Gustafsson wrote:
> This may be slightly off-topic as it partly is a general optimization 
> question. Sorry about that. However, GLPK is mentioned later on.
>
> I have a linear programming formulation to which I want to find 
> optimized variables that can take on only certain values (not always 
> integers). As far as I can tell, it should be possible to use 
> branch-and-bound for this problem as well. Can anyone confirm this and 
> is there a term for this?
>
> As I want to solve the problem, I clearly need to define my own 
> branch-and-bound algorithm, both in terms of bounds and branching 
> strategies.
> Would GLPK be a suitable alternative for this or are there packages 
> where the bounding and branching is easier to extract? I get the 
> impression that SYMPHONY is more or less built for this (playing 
> around with different strategies). SCIP?
>
> With best regards
>
> Oscar Gustafsson
>
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