def run_random_trial(self):
G = nx.MultiDiGraph()
nodes = range(1, 10)
edges = generate_edges(nodes, 50)
G.add_edges_from(edges)
source = random.choice(G.nodes())
while True:
target = random.choice(G.nodes())
if target != source:
break
amount = random.randint(1, 10)
G.node[source]['demand'] = -amount
G.node[target]['demand'] = amount
cost, flow_dict, exception = None, None, None
try:
cost, flow_dict = min_cost_flow(G)
except nx.NetworkXException as e:
exception = e
H = unmulti(G)
try:
cost2, flow_dict2 = nx.network_simplex(H)
except nx.NetworkXException as e:
self.assertEquals(type(e) != type(exception))
self.assertEquals(cost, None)
else:
self.assertEquals(cost, cost2)
self.assertEquals(exception, None)
def test_simple_multi(self):
G = nx.MultiDiGraph()
nodes = [
(1, {
'demand': -2
}),
(2, {
'demand': 2
}),
]
edges = [
(1, 2, {
'capacity': 2,
'weight': 1
}),
(1, 2, {
'capacity': 1,
'weight': 0
}),
]
G.add_nodes_from(nodes)
G.add_edges_from(edges)
flow_cost, flow_dict = min_cost_flow(G)
soln = {1: {2: {0: 1, 1: 1}}, 2: {}}
self.assertEquals(flow_dict, soln)
self.assertEquals(flow_cost, 1)
def run_random_trial(self):
G = nx.MultiDiGraph()
nodes = range(1, 10)
edges = generate_edges(nodes, 50)
G.add_edges_from(edges)
source = random.choice(G.nodes())
while True:
target = random.choice(G.nodes())
if target != source:
break
amount = random.randint(1, 10)
G.node[source]['demand'] = -amount
G.node[target]['demand'] = amount
cost, flow_dict, exception = None, None, None
try:
cost, flow_dict = min_cost_flow(G)
except nx.NetworkXException as e:
exception = e
H = unmulti(G)
try:
cost2, flow_dict2 = nx.network_simplex(H)
except nx.NetworkXException as e:
self.assertEquals(type(e) != type(exception))
self.assertEquals(cost, None)
else:
self.assertEquals(cost, cost2)
self.assertEquals(exception, None)
def test_simple_digraph(self):
G = nx.DiGraph()
G.add_node('a', demand=-5)
G.add_node('d', demand=5)
G.add_edge('a', 'b', weight=3, capacity=4)
G.add_edge('a', 'c', weight=6, capacity=10)
G.add_edge('b', 'd', weight=1, capacity=9)
G.add_edge('c', 'd', weight=2, capacity=5)
cost, flow_dict = min_cost_flow(G)
soln = {
'a': {
'b': {
0: 4
},
'c': {
0: 1
}
},
'b': {
'd': {
0: 4
}
},
'c': {
'd': {
0: 1
}
},
'd': {}
}
self.assertEquals(cost, 24)
self.assertEquals(flow_dict, soln)
def test_networkx_simplex_killer(self):
G = nx.DiGraph()
nodes = [
(1, {}),
(2, {
'demand': -4
}),
(3, {
'demand': 4
}),
]
edges = [
(1, 2, {
'capacity': 3,
'weight': 600000
}),
(2, 1, {
'capacity': 2,
'weight': 0
}),
(2, 3, {
'capacity': 5,
'weight': 714285
}),
(3, 2, {
'capacity': 2,
'weight': 0
}),
]
G.add_nodes_from(nodes)
G.add_edges_from(edges)
flow_cost, flow_dict = min_cost_flow(G)
soln = {1: {2: {0: 0}}, 2: {1: {0: 0}, 3: {0: 4}}, 3: {2: {0: 0}}}
self.assertEquals(flow_dict, soln)
self.assertEquals(flow_cost, 714285 * 4)
def test_simple_multi(self):
G = nx.MultiDiGraph()
nodes = [(1, {'demand': -2}),
(2, {'demand': 2}),
]
edges = [(1, 2, {'capacity': 2, 'weight': 1}),
(1, 2, {'capacity': 1, 'weight': 0}),
]
G.add_nodes_from(nodes)
G.add_edges_from(edges)
flow_cost, flow_dict = min_cost_flow(G)
soln = {1: {2: {0: 1, 1: 1}},
2: {}}
self.assertEquals(flow_dict, soln)
self.assertEquals(flow_cost, 1)
def test_simple_digraph(self):
G = nx.DiGraph()
G.add_node('a', demand=-5)
G.add_node('d', demand=5)
G.add_edge('a', 'b', weight=3, capacity=4)
G.add_edge('a', 'c', weight=6, capacity=10)
G.add_edge('b', 'd', weight=1, capacity=9)
G.add_edge('c', 'd', weight=2, capacity=5)
cost, flow_dict = min_cost_flow(G)
soln = {'a': {'b': {0: 4}, 'c': {0: 1}},
'b': {'d': {0: 4}},
'c': {'d': {0: 1}},
'd': {}}
self.assertEquals(cost, 24)
self.assertEquals(flow_dict, soln)
def test_one_edge(self):
G = nx.DiGraph()
nodes = [(1, {'demand': -1}),
(2, {'demand': 1}),
]
weight = 3
edges = [(1, 2, {'capacity': 2, 'weight': weight}),
]
G.add_nodes_from(nodes)
G.add_edges_from(edges)
cost, flow_dict = min_cost_flow(G)
self.assertEquals(cost, 3)
self.assertEquals(flow_dict, {1: {2: {0: 1}}, 2: {}})
def test_networkx_simplex_killer(self):
G = nx.DiGraph()
nodes = [(1, {}),
(2, {'demand': -4}),
(3, {'demand': 4}),
]
edges = [(1, 2, {'capacity': 3, 'weight': 600000}),
(2, 1, {'capacity': 2, 'weight': 0}),
(2, 3, {'capacity': 5, 'weight': 714285}),
(3, 2, {'capacity': 2, 'weight': 0}),
]
G.add_nodes_from(nodes)
G.add_edges_from(edges)
flow_cost, flow_dict = min_cost_flow(G)
soln = {1: {2: {0: 0}},
2: {1: {0: 0}, 3: {0: 4}},
3: {2: {0: 0}}}
self.assertEquals(flow_dict, soln)
self.assertEquals(flow_cost, 714285 * 4)
def min_cost_flow(self, amount):
"""
Determine minimum cost route for given amount between payer and
recipient.
Raises NoRoutesError if there is no route from payer to recipient.
Raises InsufficientCreditError if the network cannot support the
specified flow amount.
"""
self._set_endpoint_demand(amount)
if self.recipient.alias not in self.graph.nodes():
raise NoRoutesError()
try:
_, flow_dict = min_cost_flow(self.graph)
except nx.NetworkXUnfeasible:
raise InsufficientCreditError()
else:
amounts = creditline_amounts(flow_dict, self.graph)
return amounts
def min_cost_flow(self, amount):
"""
Determine minimum cost route for given amount between payer and
recipient.
Raises NoRoutesError if there is no route from payer to recipient.
Raises InsufficientCreditError if the network cannot support the
specified flow amount.
"""
self._set_endpoint_demand(amount)
if self.recipient.alias not in self.graph.nodes():
raise NoRoutesError()
try:
_, flow_dict = min_cost_flow(self.graph)
except nx.NetworkXUnfeasible:
raise InsufficientCreditError()
else:
amounts = creditline_amounts(flow_dict, self.graph)
return amounts
def test_transshipment(self):
G = nx.DiGraph()
G.add_node('a', demand = 1)
G.add_node('b', demand = -2)
G.add_node('c', demand = -2)
G.add_node('d', demand = 3)
G.add_node('e', demand = -4)
G.add_node('f', demand = -4)
G.add_node('g', demand = 3)
G.add_node('h', demand = 2)
G.add_node('r', demand = 3)
G.add_edge('a', 'c', weight = 3)
G.add_edge('r', 'a', weight = 2)
G.add_edge('b', 'a', weight = 9)
G.add_edge('r', 'c', weight = 0)
G.add_edge('b', 'r', weight = -6)
G.add_edge('c', 'd', weight = 5)
G.add_edge('e', 'r', weight = 4)
G.add_edge('e', 'f', weight = 3)
G.add_edge('h', 'b', weight = 4)
G.add_edge('f', 'd', weight = 7)
G.add_edge('f', 'h', weight = 12)
G.add_edge('g', 'd', weight = 12)
G.add_edge('f', 'g', weight = -1)
G.add_edge('h', 'g', weight = -10)
flowCost, H = min_cost_flow(G)
soln = {'a': {'c': {0: 0}},
'b': {'a': {0: 0}, 'r': {0: 2}},
'c': {'d': {0: 3}},
'd': {},
'e': {'r': {0: 3}, 'f': {0: 1}},
'f': {'d': {0: 0}, 'g': {0: 3}, 'h': {0: 2}},
'g': {'d': {0: 0}},
'h': {'b': {0: 0}, 'g': {0: 0}},
'r': {'a': {0: 1}, 'c': {0: 1}}}
self.assertEquals(flowCost, 41)
self.assertEquals(H, soln)
def test_digraph1(self):
# From Bradley, S. P., Hax, A. C. and Magnanti, T. L. Applied
# Mathematical Programming. Addison-Wesley, 1977.
G = nx.DiGraph()
G.add_node(1, demand = -20)
G.add_node(4, demand = 5)
G.add_node(5, demand = 15)
G.add_edges_from([(1, 2, {'capacity': 15, 'weight': 4}),
(1, 3, {'capacity': 8, 'weight': 4}),
(2, 3, {'weight': 2}),
(2, 4, {'capacity': 4, 'weight': 2}),
(2, 5, {'capacity': 10, 'weight': 6}),
(3, 4, {'capacity': 15, 'weight': 1}),
(3, 5, {'capacity': 5, 'weight': 3}),
(4, 5, {'weight': 2}),
(5, 3, {'capacity': 4, 'weight': 1})])
flowCost, H = min_cost_flow(G)
soln = {1: {2: {0:12}, 3: {0:8}},
2: {3: {0:8}, 4: {0:4}, 5: {0:0}},
3: {4: {0:11}, 5: {0:5}},
4: {5: {0:10}},
5: {3: {0:0}}}
self.assertEquals(flowCost, 150)
self.assertEquals(H, soln)
def test_one_edge(self):
G = nx.DiGraph()
nodes = [
(1, {
'demand': -1
}),
(2, {
'demand': 1
}),
]
weight = 3
edges = [
(1, 2, {
'capacity': 2,
'weight': weight
}),
]
G.add_nodes_from(nodes)
G.add_edges_from(edges)
cost, flow_dict = min_cost_flow(G)
self.assertEquals(cost, 3)
self.assertEquals(flow_dict, {1: {2: {0: 1}}, 2: {}})
def test_digraph1(self):
# From Bradley, S. P., Hax, A. C. and Magnanti, T. L. Applied
# Mathematical Programming. Addison-Wesley, 1977.
G = nx.DiGraph()
G.add_node(1, demand=-20)
G.add_node(4, demand=5)
G.add_node(5, demand=15)
G.add_edges_from([(1, 2, {
'capacity': 15,
'weight': 4
}), (1, 3, {
'capacity': 8,
'weight': 4
}), (2, 3, {
'weight': 2
}), (2, 4, {
'capacity': 4,
'weight': 2
}), (2, 5, {
'capacity': 10,
'weight': 6
}), (3, 4, {
'capacity': 15,
'weight': 1
}), (3, 5, {
'capacity': 5,
'weight': 3
}), (4, 5, {
'weight': 2
}), (5, 3, {
'capacity': 4,
'weight': 1
})])
flowCost, H = min_cost_flow(G)
soln = {
1: {
2: {
0: 12
},
3: {
0: 8
}
},
2: {
3: {
0: 8
},
4: {
0: 4
},
5: {
0: 0
}
},
3: {
4: {
0: 11
},
5: {
0: 5
}
},
4: {
5: {
0: 10
}
},
5: {
3: {
0: 0
}
}
}
self.assertEquals(flowCost, 150)
self.assertEquals(H, soln)
def test_transshipment(self):
G = nx.DiGraph()
G.add_node('a', demand=1)
G.add_node('b', demand=-2)
G.add_node('c', demand=-2)
G.add_node('d', demand=3)
G.add_node('e', demand=-4)
G.add_node('f', demand=-4)
G.add_node('g', demand=3)
G.add_node('h', demand=2)
G.add_node('r', demand=3)
G.add_edge('a', 'c', weight=3)
G.add_edge('r', 'a', weight=2)
G.add_edge('b', 'a', weight=9)
G.add_edge('r', 'c', weight=0)
G.add_edge('b', 'r', weight=-6)
G.add_edge('c', 'd', weight=5)
G.add_edge('e', 'r', weight=4)
G.add_edge('e', 'f', weight=3)
G.add_edge('h', 'b', weight=4)
G.add_edge('f', 'd', weight=7)
G.add_edge('f', 'h', weight=12)
G.add_edge('g', 'd', weight=12)
G.add_edge('f', 'g', weight=-1)
G.add_edge('h', 'g', weight=-10)
flowCost, H = min_cost_flow(G)
soln = {
'a': {
'c': {
0: 0
}
},
'b': {
'a': {
0: 0
},
'r': {
0: 2
}
},
'c': {
'd': {
0: 3
}
},
'd': {},
'e': {
'r': {
0: 3
},
'f': {
0: 1
}
},
'f': {
'd': {
0: 0
},
'g': {
0: 3
},
'h': {
0: 2
}
},
'g': {
'd': {
0: 0
}
},
'h': {
'b': {
0: 0
},
'g': {
0: 0
}
},
'r': {
'a': {
0: 1
},
'c': {
0: 1
}
}
}
self.assertEquals(flowCost, 41)
self.assertEquals(H, soln)