def solve(self, n=1, verbose=False):
"""Solve n optimization problems, and return argmin array."""
for i in range(n):
c = rand_matrix(3,1)
x = cvx.Variable(name='x')
y = cvx.Variable(name='y')
z = cvx.Variable(name='z')
# dummy variable to code semidefinite constraint
T = cvx.SDPVar(5,name='T')
spec = self.A * x + self.B * y + self.C * z + self.D
obj = cvx.Minimize(c[0,0]*x + c[1,0]*y + c[2,0]*z)
# check psd component
if self.psd_spec:
psd_status = cvx.get_status(
cvx.Problem(obj, [T == spec]).solve(verbose=verbose)
)
if psd_status == cvx.SOLVED:
self.mins.append([x.value, y.value, z.value])
elif psd_status == cvx.INFEASIBLE:
self.psd_spec = False
# check NSD component
if self.nsd_spec:
nsd_status = cvx.get_status(
cvx.Problem(obj, [T == -spec]).solve(verbose=verbose)
)
if nsd_status == cvx.SOLVED:
self.mins.append([x.value, y.value, z.value])
if psd_status == cvx.SOLVED:
self.fully_bounded_directions += 1
elif nsd_status == cvx.UNBOUNDED \
and psd_status == cvx.UNBOUNDED:
self.fully_unbounded_directions += 1
elif nsd_status == cvx.INFEASIBLE:
self.nsd_spec = False
self.trials += n
def solve_setcover(flights, strings):
N = 5
F = len(flights)
S = len(strings)
tc = 700
def get_ground_arcs():
ground_arcs = []
for s in strings:
for i in xrange(len(s)-1):
ground_arcs.append([s[0][0], s[i][3], s[i][-1], s[i+1][-2]])
return ground_arcs
ground_arcs = get_ground_arcs()
G = len(ground_arcs)
# 1. prepare a_{is}
a = np.zeros((F,S))
for f in xrange(F):
for s in xrange(S):
tmp_list = (np.array(strings[s])[:,1]).tolist()
#print tmp_list
#pdb.set_trace()
if (f+1) in tmp_list:
a[f,s] = 1
# 2. S_im, S_ip
Sim = [[] for i in xrange(F)]
Sip = [[] for i in xrange(F)]
for i in xrange(F):
for r in strings:
if r[0][1] == i:
Sip[i].append(r[0][0])
if r[-1][1] == i:
Sim[i].append(r[0][0])
#pdb.set_trace()
def get_num_ac_on_ground_at_time(wt):
num_ac = 0
seen_list = set()
for g in ground_arcs:
if not g[0] in seen_list:
if (g[-2] <= wt) and (g[-1] >= wt):# and g[1] == which_airport:
num_ac += 1
seen_list.update([g[0]])
return num_ac
# 3. y_{idm}, y_{idp}, y_{iam}, y_{iap}
yidm,yidp,yiam, yiap = np.zeros((F,)), np.zeros((F,)), \
np.zeros((F,)),np.zeros((F,))
for i in xrange(F):
yidm[i] = get_num_ac_on_ground_at_time(flights[i][-2]-1)
yidp[i] = get_num_ac_on_ground_at_time(flights[i][-2]+1)
yiam[i] = get_num_ac_on_ground_at_time(flights[i][-1]-1)
yiap[i] = get_num_ac_on_ground_at_time(flights[i][-1]+1)
# r_s
r = np.zeros((S,))
for ro in strings:
for roi in ro:
if (roi[-2] <= tc) and (roi[-1] >= tc):
r[roi[0]-1] = 1
# p_g
p = np.zeros((G,))
for i in xrange(G):
g = ground_arcs[i]
if (g[-2] <= tc) and (g[-1] >= tc):
p[i] = 1
# finally, set up the problem!
x = cp.Variable(S)
y = cp.Variable(G)
# objective
f = 0*x[0]
for s in xrange(S):
f = f + x[s]
# c1
c1 = []
for i in xrange(F):
c1.append(sum([a[i,s]*x[s] for s in xrange(S)])-1 == 0)
# c2
c2 = []
for i in xrange(F):
if len(Sip[i]) > 0:
c2.append(sum([x[s-1] for s in Sip[i]]) - yidm[i] + yidp[i] == 0)
# c3
c3 = []
for i in xrange(F):
if len(Sim[i]) > 0:
c3.append(sum([-x[s-1] for s in Sim[i]]) - yiam[i] + yiap[i] == 0)
# c4
c4 = [sum([r[s]*x[s] for s in xrange(S)]) + sum([p[g]*y[g] for g in xrange(G)]) <= N]
c5 = [0 <= y, x <= 1, 0 <= x]
c6 = [x[0] + x[4] + x[10] + x[11] + x[21] <= 4]
cons = c1+c2+c3+c4+c5+c6
#pdb.set_trace()
prob = cp.Problem(cp.Minimize(f), cons)
#res = prob.solve(solver=cp.CVXOPT)
res = prob.solve()
print res
print cp.get_status(res)
print x.value
print y.value
#print c1[0].dual_value
#print [(s, x[s].value) for s in xrange(S)]
pdb.set_trace()
def contains(cvx_set, value):
p = cp.Problem(cp.Minimize(0), [cvx_set == value])
return cp.get_status(p.solve()) == cp.SOLVED
def contains(cvx_set, value):
p = cp.Problem(cp.Minimize(0), [cvx_set == value])
return cp.get_status(p.solve()) == cp.SOLVED
