scheduling=MixedIntegerLinearProgram(maximization=false )
 
)

from sage.numerical.mip import Sum
 
variables
 
Sum

#####variables 


f = scheduling.new_variable (dim=4, binary=true)
 
f binary=true)
#f is the source to destination in time t
 
t 

l = scheduling.new_variable (dim=4, binary=true)
    #L id 0 if link op not selected for demand k in time t 
 
 A  = scheduling.new_variable(dim=6,binary=true)
    # A is binary s to d in link op in time t for demand k
z_op=scheduling.new_variable(dim=2,binary=true)
    #Z is 1 if is link op is on 
y = scheduling.new_variable(dim=1,binary=true)
 
parameters
 
scheduling.new_variable(dim=1,binary=true)



#####parameters  
Num_demand_slice= 1 
    #number of the time slice
 
slice



power_link_op= matrix ([[1,1,1,1,1],[1,1,1,1,1],[1,1,1,1,1],[1,1,1,1,1],[1,1,1,1,1]]) 
    # power of the link op that is considered as cost 
 
 demand_traffic_kt = matrix ([1]);
    # 0/1 matrix if demand has traffic in t is 1 
 
 rate_k= [2];
    #rate of the trafic of the demand k 
 
 link_capacity_op= matrix ([[0,0,30,30,30],[0,0,30,30,30],[30,30,0,0,0],[30,30,0,0,0],[30,30,0,0,0]])
    # zero if not exist this link in graph, others capacity of that 5 or 6 (not binary matrix)
power_sw_o= [[0,0,2,2,2]]
    #power of the sw o if is zero means that it is server 
V=5 
K=1 
B=Num_demand_slice * K
 
constraint
 
K



#####constraint
# v is the num of the node
 
node
# K is the num of the node
 
node 


for o in range (0,V):
    for p in range (0,V):
        if (link_capacity_op[o][p]==0):
            for t in range (0,Num_demand_slice):
                for k in range (0,K):
                    scheduling.add_constraint(l[o][p][k][t]==0)
 
scheduling.add_constraint(l[o][p][k][t]==0)



for t in range (0,Num_demand_slice ):
    for k in range (0,K):
        if demand_traffic_kt[k][t]==0 :
            for s in range (0,V ):
                for d in range (0,V ):
                    scheduling.add_constraint(f[s][d][k][t]==0)
 
scheduling.add_constraint(f[s][d][k][t]==0)




for t in range (0,Num_demand_slice ):
    for k in range (0,K):
        if demand_traffic_kt[k][t]==0 :
            for o in range (0,V ):
                for p in range (0,V ):
                    scheduling.add_constraint(l[o][p][k][t]==0)
 
scheduling.add_constraint(l[o][p][k][t]==0)




for t in range(0,Num_demand_slice):
    for d in range(0,V ):
        for k in range(0,K ):
            for o in range(0,V ):
                for p in range(0,V ):
                    for s in range(0,Num_demand_slice ):
                        scheduling.add_constraint(f[s][d][k][t] + l[o][p][k][t]- 1 <= A[s][d][k][o][p][t])
 
A[s][d][k][o][p][t])





for t in range(0,Num_demand_slice ):
    for d in range(0,V ):
        for k in range(0,K ):
            for o in range(0,V ):
                for p in range(0,V ):
                    for s in range(1,Num_demand_slice+1 ):
                        scheduling.add_constraint(f[s][d][k][t] + l[o][p][k][t] >= 2* A[s][d][k][o][p][t])
 
A[s][d][k][o][p][t])




for t in range(0,Num_demand_slice ):
    for k in range(0,K):
        for s in range (0,V ):
            for d in range (0,V ):
                for o in range (0,V ):
                   if s==o :
                      scheduling.add_constraint(rate_k[k]demand_traffic_kt[k][t](Sum(A[s][d][k][o][p][t] scheduling.add_constraint(rate_k[k]*demand_traffic_kt[k][t]*(Sum(A[s][d][k][o][p][t] for p in range(0,V))\
                        - Sum(A[s][d][k][p][o][t] for p in range (0,V))) == rate_k[k] * demand_traffic_kt[k][t]) 
 
 for t in range(0,Num_demand_slice ):
    for k in range(0,K):
        for s in range (0,V ):
            for d in range (0,V ):
                for o in range (0,V ):
                   if d==o :
                       scheduling.add_constraint(rate_k[k]* demand_traffic_kt[k][t](Sum(A[s][d][k][o][p][t] demand_traffic_kt[k][t]*(Sum(A[s][d][k][o][p][t] for p in range(0,V))\
                        - Sum(A[s][d][k][p][o][t] for p in range (0,V))) == - rate_k[k]demand_traffic_kt[k][t])
 
rate_k[k]*demand_traffic_kt[k][t])



for t in range(0,Num_demand_slice ):
    for k in range(0,K):
        for s in range (0,V ):
            for d in range (0,V ):
                for o in range (0,V ):
                   if (s!=o and d!=o):
                      scheduling.add_constraint(rate_k[k]* demand_traffic_kt[k][t]*(Sum(A[s][d][k][o][p][t] for p in range(0,V))\
                        - Sum(A[s][d][k][p][o][t] for p in range (0,V))) == 0)
 
for t in range(0,Num_demand_slice):
 
0)







#for t in range(0,Num_demand_slice):
 #   for o in range(0,V):
  #      for k in range (0,K):
   #         scheduling.add_constraint( 2Sum(rate_k[k] 2*Sum(rate_k[k]* demand_traffic_kt[k][t] * l[o][p][k][t]  for p in range (0,V)) \
    #        - Sum(Sum(rate_k[k] * demand_traffic_kt[k][t]* A[o][d][k][o][p][t] for p in range (0,V)) for d in range (0,V))\
     #       - Sum(Sum(rate_k[k] * demand_traffic_kt[k][t] * A[d][o][k][o][p][t]for p in range (0,V))for d in range (0,V))\
      #      - 2* Sum(rate_k[k]* demand_traffic_kt[k][t] * l[p][o][k][t] for p in range(0,V))\
       #     + Sum(Sum(rate_k[k]* demand_traffic_kt[k][t]* A[s][o][k][p][o][t] for p in range (0,V)) for s in range (0,V)) \
        #    + Sum (Sum (rate_k[k]* demand_traffic_kt[k][t] * A[o][d][k][p][o][t] for p in range(0,V)) for d in range (0,V)) ==\
        #    - rate_k[k] * demand_traffic_kt[k][t] * Sum(f[s][o][k][t]  for s in range (0,V)) \
         #   - rate_k[k] * demand_traffic_kt[k][t] * Sum(f[o][d][k][t]  for d in range (0,V)))
#
 
#

for t in range(0,Num_demand_slice):
    for k in range (0,K):
        scheduling.add_constraint (Sum(f[s][s][k][t] for s in range(0,V))== 0)
 
0)



for t in range(0,Num_demand_slice):
    for k in range (0,K):
        scheduling.add_constraint(Sum (Sum(f[s][d][k][t] for s in range (0,V)) for d in range(0,V)) == demand_traffic_kt[k][t])
 
demand_traffic_kt[k][t])




for t in range(0,Num_demand_slice): 
 
    for o in range (0,V):
        for p in range (0,V):
            scheduling.add_constraint(Sum( (rate_k[k] * l[o][p][k][t]) for k in range (0,K)) <= link_capacity_op[o][p])     
 
 for t in range(0,Num_demand_slice): 
 
    for k in range (0,K):
        for o in range (0,V):
            for p in range (0,V):
                scheduling.add_constraint(z_op[o][p] >= l[o][p][k][t]) 
 
 for t in range(0,Num_demand_slice): 
 
    for k in range (0,K):
        for o in range (0,V):
            for p in range (0,V):
                for i in range (0,B):
                    scheduling.add_constraint(z_op[o][p]- l[o][p][k][t]<= +Infinity * y[i])
 
y[i])






for t in range(0,Num_demand_slice): 
 
    for k in range (0,K):
        for o in range (0,V):
            for p in range (0,V):
                for i in range (0,B):
                    scheduling.add_constraint(z_op[o][p]- l[o][p][k][t]>= -Infinity * y[i])
 
y[i])


for t in range(0,Num_demand_slice): 
 
    scheduling.add_constraint(Sum(Sum(Sum( f[s][d][k][t] for s in range (0,V)) for d in range (0,V)) for k in range (0,K))\
    == sum(demand_traffic_kt[k][t] for k in range(0,K)))
 
range(0,K)))


scheduling.add_constraint(Sum(y[i] for i in range (0,B)) <= B-1)
 
optimization function
 
B-1)


#####optimization function

scheduling.set_objective(sum(sum(z_op[o][p] * (  power_sw_o[o] + power_link_op[o][p]) for o in range(0,V)) for p in range(0,V)))
 
scheduling.set_objective(Sum(Sum(Sum(Sum(l[o][p][k][t] range(0,V)))



#scheduling.set_objective(Sum(Sum(Sum(Sum(l[o][p][k][t] * power_link_op[o][p] for o in range(0,V)) for p in range(0,V)) \
 
for \ 
#for k in range (0,K)) for t in range (0,Num_demand_slice)))
 
scheduling.solve()
 (0,Num_demand_slice)))


scheduling.solve()