def obtainWassersteinProblem( roadnet, 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;
"""
# for convenience
#ROADS = [ key for u,v,key in roadnet.edges_iter( keys=True ) ]
class node : pass
node_s = node() ; node_t = node()
digraph = nx.DiGraph()
digraph.add_node( node_s )
digraph.add_node( node_t )
""" insert supply and demand of roads """
for u,v, road, data in roadnet.edges_iter( keys=True, data=True ) :
roadlen = data.get( length, 1. )
assert roadlen >= 0.
oneway = data.get( 'oneway', False )
surplus = data.get( weight1, 0. ) - data.get( weight2, 0. )
deficit = -surplus
# supply layer
if surplus > 0. :
digraph.add_edge( node_s, road, capacity=surplus )
w = roadlen / surplus
if oneway : ends = [ v ]
else : ends = [ u, v ]
for node in ends :
digraph.add_edge( road, node, decision_weight=w )
# demand layers
if deficit > 0. :
digraph.add_edge( road, node_t, capacity=deficit )
w = roadlen / deficit
if oneway : ends = [ u ]
else : ends = [ u, v ]
for node in ends :
digraph.add_edge( node, road, decision_weight=w )
""" insert supply and demand of nodes """
for u, data in roadnet.nodes_iter( data=True ) :
surplus = data.get( weight1, 0. ) - data.get( weight2, 0. )
deficit = -surplus
# supply layer
if surplus > 0. :
digraph.add_edge( node_s, u, capacity=surplus )
if deficit > 0. :
digraph.add_edge( u, node_t, capacity=deficit )
""" setup the network flow structure """
conns = roadmap_basic.connectivity_graph( roadnet, length_in=length )
for u, v, data in conns.edges_iter( data=True ) :
w = data.get( 'length', 1 )
digraph.add_edge( u, v, weight=w )
#return digraph, node_s, node_t # this *just* produced a flowgraph; no problem
flowgraph = flownets.obtainFlowNetwork( digraph, node_s, node_t )
costgraph = flownets.obtainWeightedCosts( flowgraph, digraph ) # cute trick
#return flowgraph, costgraph
for u,v, data in digraph.edges_iter( data=True ) :
dec_weight = data.get( 'decision_weight', None )
if dec_weight is None : continue
#
fdata = flowgraph.get_edge_data( u, v, 0 ) # key=0, because we have tightly controlled this construction
flow = fdata.get( 'flow' )
cost = .5 * dec_weight * cvxpy.square( flow )
#print dec_weight, flow, cost
cdata = costgraph.get_edge_data( u, v, 0 )
#print cdata
cdata['cost'] = cost
return flowgraph, costgraph
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
