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frank_wolfe_heterogeneous.py
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frank_wolfe_heterogeneous.py
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import numpy as np
from frank_wolfe_2 import total_free_flow_cost, search_direction, \
line_search, solver_3
from process_data import construct_igraph, construct_od
from utils import multiply_cognitive_cost, heterogeneous_demand
def search_direction_multi(f, graphs, gs, ods, L, grad):
# extension of search_direction routine in frank_wolfe_2.py
# for the heterogeneous game
links = graphs[0].shape[0]
types = len(graphs)
for j, (graph, g, od) in enumerate(zip(graphs, gs, ods)):
l, gr = search_direction(np.sum(np.reshape(f, (types, links)).T, 1),
graph, g, od)
L[(j * links): ((j + 1) * links)] = l
grad[(j * links): ((j + 1) * links)] = gr
return L, grad
def merit(f, graphs, gs, ods, L, grad):
# this computes the merit function associated to the VI problem
# max_y <F(x), x-y>
L, grad = search_direction_multi(f, graphs, gs, ods, L, grad)
return grad.dot(f - L)
def fw_heterogeneous_1(graphs, demands, max_iter=100, eps=1e-8, q=None,
display=0, past=None, stop=1e-8):
'''
Frank-Wolfe algorithm on the heterogeneous game
given a list of graphs in the format
g = [[link_id from to a0 a1 a2 a3 a4]]
and demand in the format
d = [[o d flow]]
'''
# construct graph and demand objects suiteable for AoN_igraph
gs = [construct_igraph(graph) for graph in graphs]
ods = [construct_od(demand) for demand in demands]
# construct empty vector to be filled in with values
links = graphs[0].shape[0]
types = len(graphs)
# initial flow assignment is null
f = np.zeros(links * types, dtype="float64")
L = np.zeros(links * types, dtype="float64")
grad = np.zeros(links * types, dtype="float64")
error = 'N/A'
# compute re-normalization constant
K = sum([total_free_flow_cost(g, od) for g, od in zip(gs, ods)])
if K < eps:
K = sum([np.sum(demand[:, 2]) for demand in demands])
elif display >= 1:
print 'average free-flow travel time', \
K / sum([np.sum(demand[:, 2]) for demand in demands])
# compute iterations
for i in range(max_iter):
if display >= 1:
if i <= 1:
print 'iteration: {}'.format(i + 1)
else:
print 'iteration: {}, error: {}'.format(i + 1, error)
# construct weighted graph with latest flow assignment
L, grad = search_direction_multi(f, graphs, gs, ods, L, grad)
if i >= 1:
error = grad.dot(f - L) / K
if error < stop:
return np.reshape(f, (types, links)).T
f = f + 2. * (L - f) / (i + 2.)
return np.reshape(f, (types, links)).T
def fw_heterogeneous_2(graphs, demands, past=10, max_iter=100, eps=1e-8, q=50,
display=0, stop=1e-8):
'''
Frank-Wolfe algorithm on the heterogeneous game
given a list of graphs in the format
g = [[link_id from to a0 a1 a2 a3 a4]]
and demand in the format
d = [[o d flow]]
'''
assert past <= q, "'q' must be bigger or equal to 'past'"
# construct graph and demand objects suiteable for AoN_igraph
gs = [construct_igraph(graph) for graph in graphs]
ods = [construct_od(demand) for demand in demands]
# construct empty vector to be filled in with values
links = graphs[0].shape[0]
types = len(graphs)
# initial flow assignment is null
f = np.zeros(links * types, dtype="float64")
fs = np.zeros((links * types, past), dtype="float64")
L = np.zeros(links * types, dtype="float64")
grad = np.zeros(links * types, dtype="float64")
L2 = np.zeros(links * types, dtype="float64")
grad2 = np.zeros(links * types, dtype="float64")
error = 'N/A'
# compute re-normalization constant
K = sum([total_free_flow_cost(g, od) for g, od in zip(gs, ods)])
if K < eps:
K = sum([np.sum(demand[:, 2]) for demand in demands])
elif display >= 1:
print 'average free-flow travel time', \
K / sum([np.sum(demand[:, 2]) for demand in demands])
# compute iterations
for i in range(max_iter):
if display >= 1:
print 'iteration: {}, error: {}'.format(i + 1, error)
# construct weighted graph with latest flow assignment
# print 'f', f
# print 'reshape', np.reshape(f,(links,types))
total_f = np.sum(np.reshape(f, (types, links)).T, 1)
# print 'total flow', total_f
for j, (graph, g, od) in enumerate(zip(graphs, gs, ods)):
l, gr = search_direction(total_f, graph, g, od)
L[(j * links): ((j + 1) * links)] = l
grad[(j * links): ((j + 1) * links)] = gr
# print 'L', L
# print 'grad', grad
fs[:, i % past] = L
w = L - f
if i >= 1:
error = -grad.dot(w) / K
# if error < stop and error > 0.0:
if error < stop:
if display >= 1:
print 'stop with error: {}'.format(error)
return np.reshape(f, (types, links)).T
if i > q:
# step 3 of Fukushima
v = np.sum(fs, axis=1) / min(past, i + 1) - f
norm_v = np.linalg.norm(v, 1)
if norm_v < eps:
if display >= 1:
print 'stop with norm_v: {}'.format(norm_v)
return np.reshape(f, (types, links)).T
norm_w = np.linalg.norm(w, 1)
if norm_w < eps:
if display >= 1:
print 'stop with norm_w: {}'.format(norm_w)
return np.reshape(f, (types, links)).T
# step 4 of Fukushima
gamma_1 = grad.dot(v) / norm_v
gamma_2 = grad.dot(w) / norm_w
if gamma_2 > -eps:
if display >= 1:
print 'stop with gamma_2: {}'.format(gamma_2)
return np.reshape(f, (types, links)).T
d = v if gamma_1 < gamma_2 else w
# step 5 of Fukushima
s = line_search(lambda a: merit(
f + a * d, graphs, gs, ods, L2, grad2))
# print 'step', s
if s < eps:
if display >= 1:
print 'stop with step_size: {}'.format(s)
return np.reshape(f, (types, links)).T
f = f + s * d
else:
f = f + 2. * w / (i + 2.)
return np.reshape(f, (types, links)).T
def parametric_study_2(alphas, g, d, node, geometry, thres, cog_cost, output,
stop=1e-2):
g_nr, small_capacity = multiply_cognitive_cost(
g, geometry, thres, cog_cost)
if (type(alphas) is float) or (type(alphas) is int):
alphas = [alphas]
for alpha in alphas:
# special case where in fact homogeneous game
if alpha == 0.0:
print 'non-routed = 1.0, routed = 0.0'
f_nr = solver_3(g_nr, d, max_iter=1000, display=1, stop=stop)
fs = np.zeros((f_nr.shape[0], 2))
fs[:, 0] = f_nr
elif alpha == 1.0:
print 'non-routed = 0.0, routed = 1.0'
f_r = solver_3(g, d, max_iter=1000, display=1, stop=stop)
fs = np.zeros((f_r.shape[0], 2))
fs[:, 1] = f_r
# run solver
else:
print 'non-routed = {}, routed = {}'.format(1 - alpha, alpha)
d_nr, d_r = heterogeneous_demand(d, alpha)
fs = fw_heterogeneous_1([g_nr, g], [d_nr, d_r], max_iter=1000,
display=1, stop=stop)
np.savetxt(output.format(int(alpha * 100)), fs,
delimiter=',', header='f_nr,f_r')
def parametric_study_3(alphas, beta, g, d, node, geometry, thres, cog_cost,
output, stop=1e-2):
g_nr, small_capacity = multiply_cognitive_cost(
g, geometry, thres, cog_cost)
if (type(alphas) is float) or (type(alphas) is int):
alphas = [alphas]
for alpha in alphas:
# special case where in fact homogeneous game
if alpha == 0.0:
print 'non-routed = 1.0, routed = 0.0'
f_nr = solver_3(g_nr, d, max_iter=1000, display=1, stop=stop)
fs = np.zeros((f_nr.shape[0], 2))
fs[:, 0] = f_nr
elif alpha == 1.0:
print 'non-routed = 0.0, routed = 1.0'
f_r = solver_3(g, d, max_iter=1000, display=1, stop=stop)
fs = np.zeros((f_r.shape[0], 2))
fs[:, 1] = f_r
# run solver
else:
print 'non-routed = {}, routed = {}'.format(1 - alpha, alpha)
d_nr, d_r = heterogeneous_demand(d, alpha)
fs = fw_heterogeneous_1([g_nr, g], [d_nr, d_r], max_iter=1000,
display=1, stop=stop)
np.savetxt(output.format(int(alpha * 100), int(beta * 100)), fs,
delimiter=',', header='f_nr,f_r')