import sys
import itertools
import poek as pk
quicksum = pk.quicksum
model = pk.model()
n = int(sys.argv[1])
m = n
dx = 1.0 / n
T = 1.58
dt = T / n
h2 = dx**2
a = 0.001
y = pk.variable((n + 1, m + 1), lb=0.0, ub=1.0)
u = pk.variable(n + 1, lb=-1.0, ub=1.0)
model.use(y)
model.use(u)
def yt(j, dx):
return 0.5 * (1 - (j * dx) * (j * dx))
#obj
model.add(0.25 * dx * ((y[m, 0] - yt(0, dx))**2 + 2 * quicksum(
(y[m, j] - yt(j, dx))**2
for j in range(1, n)) + (y[m, n] - yt(n, dx))**2) + 0.25 * a * dt *
(2 * quicksum(u[i]**2 for i in range(1, m)) + u[m]**2))
import sys
import math
import poek as pk
N = 1000*int(sys.argv[1])
h = 1.0/N
alpha = 350
model = pk.model()
t = pk.variable(N+1, lb=-1, ub=1)
u = pk.variable(N+1, initial=0.01)
x = pk.variable(N+1, lb=-0.05, ub=0.05)
model.use(t)
model.use(u)
model.use(x)
for i in range(N+1):
t[i].initial = 0.05*math.cos((i+1)*h)
x[i].initial = 0.05*math.cos((i+1)*h)
ex = 0
for i in range(N):
ex += 0.5*h*(u[i+1]**2+u[i]**2) + 0.5*alpha*h*(pk.cos(t[i+1])+pk.cos(t[i]))
model.add( ex )
for i in range(N):
model.add( x[i+1] - x[i] - (0.5*h)*(pk.sin(t[i+1])+pk.sin(t[i])) == 0 )
for i in range(N):
import sys
import random
import itertools
import poek as pk
random.seed(1000)
N = int(sys.argv[1])*1000
W = N/10.0
model = pk.model()
w = {}
v = {}
for i in range(N):
w[i] = random.uniform(0.0,1.0)
v[i] = random.uniform(0.0,1.0)
x = pk.variable(N, lb=0.0, ub=1.0)
model.use(x)
model.add( pk.quicksum(v[i]*x[i] for i in range(N)) )
model.add( pk.quicksum(w[i]*x[i] for i in range(N)) <= W )
opt = pk.solver('gurobi')
opt.set_option('TimeLimit', 0)
opt.solve(model)
import sys
import itertools
import poek as pk
model = pk.model()
N = int(sys.argv[1])
x = pk.variable((N, N), lb=0.0, ub=1.0, binary=True)
model.use(x)
# obj
model.add(pk.affine_expression([x[i, j] for i in range(N) for j in range(N)]))
# one per row
for i in range(N):
model.add(pk.affine_expression([x[i, j] for j in range(N)]) == 1)
# one per column
for j in range(N):
model.add(pk.affine_expression([x[i, j] for i in range(N)]) == 1)
# \diagonals_col
for i in range(N - 1):
model.add(
x[0, i] + pk.affine_expression([x[j, i + j]
for j in range(1, N - i)]) <= 1)
# \diagonals_row
for i in range(1, N - 1):
model.add(
x[i, 0] + pk.affine_expression([x[i + j, j]
import sys
import itertools
import poek as pk
quicksum = pk.quicksum
model = pk.model()
F = int(sys.argv[1])
G = F
G_ = G + 1
d = pk.variable()
y = pk.variable((F, 2), lb=0.0, ub=1.0)
z = pk.variable((G_, G_, F), binary=True)
s = pk.variable((G_, G_, F), lb=0.0)
r = pk.variable((G_, G_, F, 2))
model.use(d)
model.use(y)
model.use(z)
model.use(s)
model.use(r)
#obj
model.add(d)
#assmt
for i, j in itertools.product(range(G_), range(G_)):
model.add(quicksum(z[i, j, f] for f in range(F)) == 1)
M = 2 * 1.414
import poek as pk
random.seed(1000)
model = pk.model()
N = int(sys.argv[1]) # Locations
M = N # Customers
P = int(sys.argv[2]) # Facilities
d = {}
for n in range(N):
for m in range(M):
d[n, m] = random.uniform(1.0, 2.0)
x = pk.variable((N, M), lb=0.0, ub=1.0, initial=0.0)
y = pk.variable(N, lb=0.0, ub=1.0, initial=0.0)
model.use(x)
model.use(y)
# obj
model.add(pk.quicksum(d[n, m] * x[n, m] for n in range(N) for m in range(M)))
# single_x
for m in range(M):
model.add(pk.quicksum(x[n, m] for n in range(N)) == 1)
# bound_y
for n, m in itertools.product(range(N), range(M)):
model.add(x[n, m] - y[n] <= 0)