def NormalBackupModelExample(plot_options, num_nodes,p,invstd,mip_gap, time_limit):
#######################################
# Generating graphs
#######################################
#Generates a complete indirect graph
H = nx.complete_graph(num_nodes)
# transforms the indirect graph in directed one
G = H.to_directed()
#Generates a list with all links (edges) in the graph
links = G.edges()
#Generates a list with all nodes (vertex) in the graph
nodes = G.nodes()
capacity={}
mean={}
std={}
Aux=1
for s,d in links:
#generating capacity for each s,d link
capacity[s,d] = Aux
#Generate mean for each s,d link based on Bernouilli distribution
mean[s,d] = Aux*p
#Generate std for each s,d link based on Bernouilli distribution
std[s,d]=math.sqrt(Aux*p*(1-(Aux*p)))
if capacity[s,d] > 0:
G.add_weighted_edges_from([(s,d,capacity[s,d])])
else:
G.add_weighted_edges_from([(s,d,capacity[s,d])])
if plot_options == 1:
pos = plotGraph(G, option=0, position=None)
################################
#
# optimization
#
################################
links = tuplelist(links)
BackupNet = Backup(nodes,links,capacity,mean,std,invstd)
solution = BackupNet.optimize(mip_gap,time_limit)
#penalizes the links chosen to be backup links
for i,j in links:
if solution[i,j] < 0.1:
G.remove_edge(i, j)
if plot_options == 1:
option=1
plotGraph(G, option, pos)
def PathBackupModelExample(plot_options,num_nodes,p,invstd,mip_gap,time_limit,cutoff):
""
#######################################
# Generating graphs
#######################################
#Generates a complete indirect graph
H = nx.complete_graph(num_nodes)
# transforms the indirect graph in directed one
G = H.to_directed()
#Generates a list with all links (edges) in the graph
links = G.edges()
#Generates a list with all nodes (vertex) in the graph
nodes = G.nodes()
capacity={}
Aux = 1
for s,d in links:
#generating capacity for each s,d link
capacity[s,d] = Aux
if capacity[s,d] > 0:
G.add_weighted_edges_from([(s,d,capacity[s,d])])
else:
G.add_weighted_edges_from([(s,d,capacity[s,d])])
if plot_options == 1:
##############################################
# Plot Initial Graph
##############################################
pos = plotGraph(G, option=None, position=None)
#######################################
# Optimization Model
#######################################
#Find all possible paths in the graph for all source -> destination pairs
paths = getAllPaths(G,cutoff)
#Find all possible paths for each source (s) -> destination (d) pair
Psd = {}
for s,d in links:
Psd[s,d] = nx.all_simple_paths(G, s, d,cutoff)
#Find all s->d paths that uses the i->j link
Pij={}
for i,j in links:
for s,d in links:
Pij[i,j,s,d] = getLinkPaths(G,i,j,s,d,cutoff)
capacity={}
mean={}
std={}
AuxCount = 0
Aux=1
for s,d in links:
#generating capacity for each s,d link
capacity[s,d] = Aux
#Generate mean for each s,d link based on Binomial distribution
mean[s,d] = Aux*p
#Generate std for each s,d link based on Binomial distribution
std[s,d]=math.sqrt(Aux*p*(1-(Aux*p)))
AuxCount = AuxCount+1
#optimization
links = tuplelist(links)
# Creating a backup network model
BackupNet = PathBackup(nodes,links,paths,Psd,Pij,capacity,mean,std,invstd)
# Find a optimal solution
solution = BackupNet.optimize(mip_gap,time_limit)
#Remove links not chosen as backup link
for i,j in links:
if solution[i,j] < 0.1:
G.remove_edge(i, j)
##############################################
# Plot Solution
##############################################
if plot_options == 1:
option=1
plotGraph(G, option, pos)
