exercise4.gms

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Laboratorio 2 - MOS
Ejercicio 4

Realizado por:
Juan Andrés Romero C - 202013449
Juan Sebastián Alegría - 202011282
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Sets i      'Graph nodes'           /i1*i7/
     coords 'Coordinate dimensions' /coordX, coordY/
     alias(j,i);

Table positions(i,coords)

    coordX  coordY
i1      20      6
i2      22      1
i3       9      2
i4       3     25
i5      21     10
i6      29      2
i7      14     12;

Parameters distance(i,j) 'Distances between nodes'
           graph(i,j)    'Resulting graph of connections between the node set';

loop((i,j),
    distance(i,j) = sqrt(sqr(positions(i,'coordX')-positions(j,'coordX')) + sqr(positions(i,'coordY')-positions(j,'coordY')));
    if ((distance(i,j) <= 20 and distance(i,j) > 0),
        graph(i,j) = distance(i,j);
    else
        graph(i,j) = 999;
    );
);

Scalar sourceNode      /4/;
Scalar destinationNode /6/;

Variables x(i,j) 'Indicates if the link i-j is selected or not'
          z      'Objective function';

Binary Variable x;

Equations
targetFunc                    'target function'
sourceNodeRestriction(i)      'source node'
destinationNodeRestriction(j) 'destination node'
intermediateNodeRestriction   'intermediate node';

targetFunc..                                                                           z =e= sum((i,j), graph(i,j)*x(i,j));
sourceNodeRestriction(i)$(ord(i) = sourceNode)..                                       sum((j), x(i,j)) =e= 1;
destinationNodeRestriction(j)$(ord(j) = destinationNode)..                             sum((i), x(i,j)) =e= 1;
intermediateNodeRestriction(i)$(ord(i) <> sourceNode and ord(i) <> destinationNode)..  sum((j), x(i,j)) - sum((j), x(j,i)) =e= 0;

Model Exercise4 /all/ ;
option mip=cplex
Solve Exercise4 using mip minimizing z;

Display graph;
Display x.l;
Display z.l;