def measurenx_to_approxnx( roadnet, epsilon, length='length', weight1='weight1', weight2='weight2' ) :
"""
input: a road network, with weights on its elements
output:
returns a graph summarizing the network optimization problem instance;
roadnets are multi-digraph, where edge 'keys' are assumed to be unique,
i.e., road names; and should be different from node labels too;
"""
digraph = nx.DiGraph()
#digraph.add_node('s')
#digraph.add_node('t')
SUPPLY = []
DEMAND = []
""" insert supply and demand of roads """
for u,v, road, data in roadnet.edges_iter( keys=True, data=True ) :
roadlen = float( data.get( length, 1 ) ) # float() just in case
assert roadlen >= 0.
"""
split the road into equal-length segments;
create a node for each segment;
record boundary points, and mass contained
"""
N = int( np.ceil( roadlen / epsilon ) )
eps = roadlen / N
surplus = float( data.get( weight1, 0. ) ) - data.get( weight2, 0. )
deficit = -surplus
bd = np.linspace( 0, roadlen, N+1 )
bd = [ roadmaps.RoadAddress( road, x ) for x in bd ]
for i, boundary in enumerate( zip( bd[:-1], bd[1:] ) ) :
if surplus > 0. :
node = (road,i,'supply')
digraph.add_node( node, boundary=boundary )
digraph.add_edge( 's', node, flow=cvxpy.variable(), minflow=0., maxflow=surplus/N )
SUPPLY.append( node )
if deficit > 0. :
node = (road,i,'demand')
digraph.add_node( node, boundary=boundary )
digraph.add_edge( node, 't', flow=cvxpy.variable(), minflow=0., maxflow=deficit/N )
DEMAND.append( node )
""" ...and nodes """
for u, data in roadnet.nodes_iter( data=True ) :
surplus = data.get( weight1, 0. ) - data.get( weight2, 0. )
deficit = -surplus
if surplus > 0. :
boundary = [ roadmaps.roadify( roadnet, u, weight=length ) ]
node = (u,'supply')
digraph.add_node( node, boundary=boundary )
digraph.add_edge( 's', node, flow=cvxpy.variable(), minflow=0., maxflow=surplus )
SUPPLY.append( node )
if deficit > 0. :
boundary = [ roadmaps.roadify( roadnet, v, weight=length ) ]
node = (u,'demand')
digraph.add_node( node, boundary=boundary )
digraph.add_edge( node, 't', flow=cvxpy.variable(), minflow=0., maxflow=deficit )
DEMAND.append( node )
""" generate bipartite graph b/w SUPPLY and DEMAND """
for u, v in itertools.product( SUPPLY, DEMAND ) :
bd_u = digraph.node[u]['boundary']
bd_v = digraph.node[v]['boundary']
options = [ pair for pair in itertools.product( bd_u, bd_v ) ]
options = [ roadmaps.distance( roadnet, p, q, weight=length ) for p,q in options ]
#options = [ np.inf ]
w = min( options )
W = max( options )
flowvar = cvxpy.variable()
digraph.add_edge( u, v, flow=flowvar, minflow=0., w=w, W=W, cost_lo = w * flowvar, cost_hi = W * flowvar )
nxopt.attach_flownx_constraints( digraph )
return digraph # a flow network
def measurenx_to_approxnx(roadnet, epsilon, length="length", weight1="weight1", weight2="weight2"):
"""
input: a road network, with weights on its elements
output:
returns a graph summarizing the network optimization problem instance;
roadnets are multi-digraph, where edge 'keys' are assumed to be unique,
i.e., road names; and should be different from node labels too;
"""
digraph = nx.DiGraph()
digraph.add_node("s")
digraph.add_node("t")
""" insert supply and demand of roads """
for u, v, road, data in roadnet.edges_iter(keys=True, data=True):
roadlen = float(data.get(length, 1)) # float() just in case
assert roadlen >= 0.0
oneway = data.get("oneway", False)
surplus = float(data.get(weight1, 0.0)) - data.get(weight2, 0.0)
deficit = -surplus
"""
split the road into equal-length segments;
create a node for each segment;
"""
N = int(np.ceil(roadlen / epsilon))
eps = roadlen / N
if surplus > 0.0:
NODES = [(road, k, "supply") for k in range(N)]
for node in NODES:
digraph.add_edge(
"s", node, flow=cvxpy.variable(), minflow=0.0, maxflow=surplus / N, w_lo=-eps, w_hi=0.0
)
SEQ = [u] + NODES + [v]
for lnode, rnode in zip(SEQ[:-1], SEQ[1:]):
digraph.add_edge(lnode, rnode, flow=cvxpy.variable(), minflow=0.0, w_lo=eps, w_hi=eps)
if not oneway:
digraph.add_edge(rnode, lnode, flow=cvxpy.variable(), minflow=0.0, w_lo=eps, w_hi=eps)
if deficit > 0.0:
NODES = [(road, k, "demand") for k in range(N)]
for node in NODES:
digraph.add_edge(
node, "t", flow=cvxpy.variable(), minflow=0.0, maxflow=deficit / N, w_lo=-eps, w_hi=0.0
)
SEQ = [u] + NODES + [v]
for lnode, rnode in zip(SEQ[:-1], SEQ[1:]):
digraph.add_edge(lnode, rnode, flow=cvxpy.variable(), minflow=0.0, w_lo=eps, w_hi=eps)
if not oneway:
digraph.add_edge(rnode, lnode, flow=cvxpy.variable(), minflow=0.0, w_lo=eps, w_hi=eps)
""" insert supply and demand of nodes """
for u, data in roadnet.nodes_iter(data=True):
surplus = data.get(weight1, 0.0) - data.get(weight2, 0.0)
deficit = -surplus
# supply layer
if surplus > 0.0:
digraph.add_edge("s", u, flow=cvxpy.variable(), minflow=0.0, maxflow=surplus)
if deficit > 0.0:
digraph.add_edge(u, "t", flow=cvxpy.variable(), minflow=0.0, maxflow=deficit)
""" setup the network flow structure """
conns = roadmaps.connectivity_graph(roadnet)
for u, v, data in conns.edges_iter(data=True):
weight = data.get(length, 1)
flowvar = cvxpy.variable()
digraph.add_edge(u, v, flow=cvxpy.variable(), minflow=0.0, w_lo=weight, w_hi=weight)
""" turn the weights into costs """
for _, __, data in digraph.edges_iter(data=True):
flowvar = data["flow"]
if "w_lo" in data:
data["cost_lo"] = data["w_lo"] * flowvar
if "w_hi" in data:
data["cost_hi"] = data["w_hi"] * flowvar
nxopt.attach_flownx_constraints(digraph)
return digraph # a flownx
