def mip_prob():
# {LP, MIP}
x = cp.Int(1)
prob = cp.Problem(cp.Minimize(x),[x >= 0])
return CVXProblem(problemID="mip_prob",
problem=prob,
opt_val=0.0)
def eqAssign(Y, C, minC=1, accurateAssign=False):
n, nF = Y.shape
nC = C.shape[0]
assert C.shape[1] == nF
YCdist = np.zeros((n, nC))
for i in range(n):
for j in range(nC):
YCdist[i, j] = np.linalg.norm(Y[i] - C[j], ord=2)
if accurateAssign:
X = cvx.Int(n, nC)
else:
X = cvx.Variable(n, nC)
obj = cvx.sum_entries(cvx.mul_elemwise(YCdist, X))
cons = [
cvx.sum_entries(X, axis=1) == 1,
cvx.sum_entries(X, axis=0) >= minC, 0 <= X, X <= 1
]
prob = cvx.Problem(cvx.Maximize(obj), cons)
# Solve
if accurateAssign:
prob.solve(solver=cvx.ECOS_BB) #, mi_max_iters=100
Xopt = X.value
assign = np.zeros(n)
for i in range(n):
for j in range(nC):
if Xopt[i, j] > 0.9:
assign[i] = j
break
else:
prob.solve(solver=cvx.ECOS) # , mi_max_iters=100
Xopt = X.value
#assign = np.argmax(Xopt, axis=1).ravel()
assign = np.zeros(n, dtype=int)
for i in range(n):
maxX = 0
maxJ = 0
for j in range(nC):
if Xopt[i, j] > maxX:
maxX = Xopt[i, j]
maxJ = j
assign[i] = np.round(maxJ)
return assign, Xopt, prob.status
def cvxpySolver(A, B):
# declare the integer-valued optimization variable
x = cvxpy.Int(variablesNum + 1)
# set up the L2-norm minimization problem
obj = cvxpy.Minimize(cvxpy.norm(list(map(list, zip(*A))) * x - B, 1))
#obj = cvxpy.Minimize(cvxpy.norm(A * x - B, 2))
prob = cvxpy.Problem(obj)
# solve the problem using an appropriate solver
sol = prob.solve(solver = 'ECOS_BB')
# the optimal value of x is
C = x.value
C = np.matrix.tolist(C)
C = list(map(list, zip(*C)))[0]
print("Int: C = ", C)
for i in range(0, len(C)):
C[i] = round(C[i])
print("Round Int: C = ", C)
return C
def _minimize_q(self, n, half_n, orig_loss, cost):
"""
Minimize over q while keeping epsilon and w constant.
:param n: the number of instances
:param half_n: half of n
:param orig_loss: the original loss calculations
:param cost: cost: the cost vector, has length of size of instances
"""
# Setup variables and constants
epsilon = self._old_epsilon
w = self._old_w
q = cvx.Int(n)
# Calculate constants - see comment above
cnst = self.gamma * w.dot(w)
epsilon_diff_eta = epsilon - orig_loss
# Setup CVX problem
func = cnst
for i in range(n):
func += q[i] * epsilon_diff_eta[i]
constraints = [0 <= q, q <= 1]
cost_for_q = 0.0
for i in range(half_n):
constraints.append(q[i] + q[i + half_n] == 1)
cost_for_q += cost[i + half_n] * q[i + half_n]
constraints += [cost_for_q <= self.total_cost]
prob = cvx.Problem(cvx.Minimize(func), constraints)
prob.solve(solver=cvx.ECOS_BB, verbose=self.verbose, parallel=True)
q_value = np.array(q.value).flatten()
self._old_q = []
for i in range(n):
self._old_q.append(round(q_value[i]))
self._old_q = np.copy(np.array(self._old_q, dtype=int))
def mip_prob():
# {LP, MIP}
x = cp.Int(1)
return cp.Problem(cp.Minimize(x))
[1631203151, 2039156791, -1073442812, 1],
[-1736958565, 2037741599, 635288874, 1],
[-210093103, 354655146, -718127209, 1]]
B = [-955806000, -407953638, -3774700162, -564748247]
A = [[-68308474.0, -68308472.0, -341366010.0, 1],
[-47581579.0, -47581577.0, -1504785200.0, 1],
[-18930757.0, -18930755.0, -2143493400.0, 1],
[-19290484.0, -19290482.0, -2057089700.0, 1]]
B = [-68308471.0, -47581576.0, -18930754.0, -19290481.0]
print("A = ", A)
print("rank A = ", np.linalg.matrix_rank(A))
print("B = ", B)
# declare the integer-valued optimization variable
x = cvxpy.Int(n)
# set up the L2-norm minimization problem
obj = cvxpy.Minimize(cvxpy.norm(list(map(list, zip(*A))) * x - B, 1))
prob = cvxpy.Problem(obj)
# solve the problem using an appropriate solver
# sol = prob.solve(solver = 'ECOS_BB')
sol = prob.solve()
# the optimal value of x is
C = x.value
C = np.matrix.tolist(C)
C = list(map(list, zip(*C)))[0]
print("Int: C = ", C)
def addIntVar(self, name):
# name is unused for cvxpy
return cvxpy.Int()
import cvxpy as cp import numpy as np # goal is to solve the problem in example_survey_responses.txt with an optimizer # define a new fxn for every constraint, then add them all up for the obj function? (each sub function returns # 1 if met and -1000 if not met) #ages a1 = cp.Int() a2 = cp.Int() a3 = cp.Int() a4 = cp.Int() a5 = cp.Int() a6 = cp.Int() a7 = cp.Int() a8 = cp.Int() a9 = cp.Int() a10 = cp.Int() #household indicators hh1_1 = cp.Int() hh1_2 = cp.Int() hh1_3 = cp.Int() hh1_4 = cp.Int() hh1_5 = cp.Int() hh1_6 = cp.Int() hh1_7 = cp.Int() hh1_8 = cp.Int() hh1_9 = cp.Int() hh1_10 = cp.Int() hh2_1 = cp.Int()
## generate A and y
#m, n = 10, 10
#A = np.random.randn(m,n)
#B = np.random.randn(m)
## declare the integer-valued optimization variable
#x = cvxpy.Int(n)
A = [[614071408, 1569877410, -1844044328, 1],
[1631203151, 2039156791, -1073442812, 1],
[-1736958565, 2037741599, 635288874, 1],
[-210093103, 354655146, -718127209, 1]]
B = [-955806000, -407953638, -3774700162, -564748247]
#x = cvxpy.Int(4)
x = cvxpy.Int(4)
x2 = cvxpy.Variable(4)
# set up the L2-norm minimization problem
obj = cvxpy.Minimize(cvxpy.norm(A * x - B, 2))
prob = cvxpy.Problem(obj)
obj2 = cvxpy.Minimize(cvxpy.norm(A * x2 - B, 2))
prob2 = cvxpy.Problem(obj2)
print("prob is DCP:", prob.is_dcp())
print("prob2 is DCP:", prob2.is_dcp())
# solve the problem using an appropriate solver
sol = prob.solve(solver='ECOS_BB')
sol2 = prob2.solve(solver='ECOS_BB')
] # the amount of required reserve (over demand) in each of the three hours assets = [0, 1, 2] # There are three assets hours = [0, 1, 2] # There are three hours no_of_assets = len(assets) no_of_hours = len(hours) # VARIABLES # 1) p_jk: the output power of unit j during period k # 2) y_jk: a binary variable that is equal to 1, if unit j is started up at the beginnig of period k and 0, otherwise # 3) z_jk: a binary variable that is equal to 1, if unit j is shut down at the beginning of period k, and 0, otherwise # 4) v_jk: a binary variable that is equal to 1, if unit j is online during period k and 0, otherwise p_jk = cvx.Variable(no_of_assets, no_of_hours) y_jk = cvx.Int(no_of_assets, no_of_hours) z_jk = cvx.Int(no_of_assets, no_of_hours) v_jk = cvx.Int(no_of_assets, no_of_hours) # OBJECTIVE # For each hour, for each unit, minimise: p_jk*B_j + y_jk*C_j + z_jk*E_j + v_jk*A_j # where, # p_jk: the output power of unit j during period k # B_j: the variable cost of unit j # y_jk: a binary variable that is equal to 1, if unit j is started up at the beginnig of period k and 0, otherwise # C_j: the startup cost of unit j # z_jk: a binary variable that is equal to 1, if unit j is shut down at the beginning of period k, and 0, otherwise # E_j: the shutdown cost of unit j # v_jk: a binary variable that is equal to 1, if unit j is online during period k and 0, otherwise # A_j: the fixed cost of unit j
#
# A sample code to solve a knapsack_problem with cvxpy
#
# Author: Atsushi Sakai (@Atsushi_twi)
#
import cvxpy
import numpy as np
size = np.array([21, 11, 15, 9, 34, 25, 41, 52])
weight = np.array([22, 12, 16, 10, 35, 26, 42, 53])
capacity = 100
x = cvxpy.Int(size.shape[0])
objective = cvxpy.Maximize(weight * x)
constraints = [capacity >= size * x]
constraints += [x >= 0]
prob = cvxpy.Problem(objective, constraints)
prob.solve(solver=cvxpy.ECOS_BB)
result = [round(ix[0, 0]) for ix in x.value]
print("status:", prob.status)
print("optimal value", prob.value)
print("size :", size * x.value)
print("result x:", result)
