#################### Simultaneous Escape Routing Problem 
########################## Date: 16 March 2015 ###################################

# MODEL 1 LOCAL ROUTING:
#Sets:

set Rows;
set Columns;
set Points within Rows cross Columns;
set Boundarypoints within Points;
set Connectingpoints within Points;
set SD within Points;
set Localflows within SD;
set LFandBP within Points;
set Destination {Localflows} within Points;
set Pointsneighbors {Connectingpoints} within Points;
set Boundarypointsneighbors {Boundarypoints} within Points;



#Decision Variable:

var X{SD,Points} binary;


#Objective function:

minimize connectingpoints: sum{(i,j) in SD}(sum{(l,m) in Points} X[i,j,l,m]);

#Constraint 1:This constraint will ensure selection of 
#source.

subject to source_select{(i,j) in Localflows}:
X[i,j,i,j]=1;

#Constraint 2:This constraint will ensure selection of 
#source neighbor.

subject to source_neighbor{(i,j) in Localflows}:
sum{(l,m) in Pointsneighbors[i,j]} X[i,j,l,m]=1;

#Constraint 3:This constraint will ensure continuation.

subject to Continuity{(i,j) in Localflows, (l,m) in Connectingpoints diff Localflows}: 
2 * X[i,j,l,m] <= sum{(a,b) in Pointsneighbors[l,m]} X[i,j,a,b];

#Constraint 4:This constraint will ensure that flow received at #dest through one point.

subject to UniPathDest{(i,j) in Localflows}:sum{(l,m) in Boundarypoints} X[i,j,l,m]=1;


#Constraints for 2nd point:

#Constraint 5:This constraint will ensure selection of 
#source.

subject to source_select_1{(i,j) in Localflows,(a,b) in Destination[i,j]}: X[a,b,a,b]=1;

#Constraint 6:This constraint will ensure selection of 
#source neighbor.

subject to source_neighbor_1{(i,j) in Localflows,(a,b) in Destination
[i,j]}:sum{(l,m) in Pointsneighbors[a,b]} X[a,b,l,m]=1;

#Constraint 7:This constraint will ensure continuation.

subject to Continuity_1{(c,d) in Localflows,(i,j) in Destination
[c,d], (l,m) in Connectingpoints diff Destination[c,d]}: 
2 * X[i,j,l,m] <= sum{(a,b) in Pointsneighbors[l,m]} X[i,j,a,b];


#Constraint 8:This constraint will ensure that flow 
#received at dest through one point.

subject to UniPathDest1{(i,j) in Localflows, (a,b) in Destination[i,j]}:sum{(l,m) in Boundarypoints} X[a,b,l,m]=1;

#constraint 9: dual selection prohibitation.

subject to Dual1{(a,b) in Connectingpoints}:sum{(i,j) in SD} X[i,j,a,b]<=1;

#Constraint 10: prohibits loop.

subject to loop{(a,b) in Localflows,(l,m) in Connectingpoints }:sum{(c,d) in Pointsneighbors[l,m]} (X[a,b,c,d])<=2;



####Model 2:
###Global Routing

#parameters:

param startx {Localflows}  default 0.0;
param starty {Localflows} default 0.0;

param endx {Localflows}  default 0.0;
param endy {Localflows}  default 0.0;


#Decision Variable:

var Y{Localflows,Boundarypoints} binary;

#Objective function:

maximize flow: sum{(i,j) in Localflows}(sum{(c,d) in Boundarypointsneighbors[startx[i,j],starty[i,j]]} Y[i,j,c,d]);

#constraints:

#Constraint 1: source selection.

subject to source_select_2{(a,b) in Localflows}:
Y[a,b,startx[a,b],starty[a,b]]=1;

#Constraint 2: source neighbor selection.

subject to source_neighbor_2{(a,b) in Localflows}: 
sum{(c,d) in Boundarypointsneighbors[startx[a,b],starty[a,b]]} (Y[a,b,c,d])<= 1;

#Constraint 3: Continuity.

subject to connectedge_2{(a,b) in Localflows, (l,m) in Boundarypoints diff {(startx[a,b],starty[a,b])} diff {(endx[a,b],endy[a,b])}}:
      2 * Y[a,b,l,m] <= sum{(c,d) in Boundarypointsneighbors[l,m]} Y[a,b,c,d];

#Constraint 4: Continuity2

subject to checking{(a,b) in Localflows, (l,m) in Boundarypoints }:sum{(c,d) in Boundarypointsneighbors[l,m]} (Y[a,b,c,d])<=2;


#Constraint 5: Destination selection.

subject to dest_select {(a,b) in Localflows}: Y[a,b,endx
[a,b],endy[a,b]]<=1;

#Constarint 6: destination neighbor selection.

subject to Edge_dest{(a,b) in Localflows}:sum{(c,d) in Boundarypointsneighbors[endx[a,b],endy[a,b]]} (Y[a,b,c,d])=1;

#constraint 7: dual selection prohibitation.

subject to Dual_2{(a,b) in Boundarypoints}:sum{(i,j) in Localflows} Y[i,j,a,b]<=1;