[Help-glpk] Constraints and conditions

[nicolas66]

Hi,

For a project I'm working on, I need to solve the following problem. Suppose
we have a squared-grid (size=n) with n^2 cells with a 4-connexity
neighborhood. Each cell must contains exactly one building. We have several
building colors (blue, red and green) with an increasing amount of points.
The game rules are the following:

* No constraints on blue buildings.
* Red buildings must have at least one blue building in its neighborhood.
* Green buildings must have at least one red building and at least one blue
building in its neighborhood.

The goal is to maximize the number of points by having the biggest buildings
(green > red > blue). I have started to write the LP but I have some
difficulties to express the constraint on red buildings because it directly
depends on the values of the variables. So, I would like to transform the
following constraint

param n, integer, > 0, default 4;
var x{1..n, 1..n}, integer, >=0, <=2; /*blue=0, red=1 and green=2 */

s.t. r{i in 1..n, j in 1..n:x[i,j]=1}: sum{a in i-1..i+1, b in j-1..j+1:a>=1
and a<=n and b>=1 and b<=n and i!=a and b!=j and x[a,b]=0} x[i,j] >= 1;

into a valid one. I think there's a way to express it by using binary
variables but I don't see how. Does anybody can help me ? Thanks in advance
for your help.


Nicolas.
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