def test_decode2(self):
x = Matrix("x", n_row=2, n_col=2)
exp = Constraint(-(x[1, 1] - x[0, 1])**2, label="const")
model = exp.compile()
self.assertRaises(
ValueError,
lambda: model.decode_solution([1, 0], var_type="binary"))
def test_decode2(self):
x = Array.create("x", (2, 2), vartype="BINARY")
exp = Constraint(-(x[1, 1] - x[0, 1])**2, label="const")
model = exp.compile()
self.assertRaises(
ValueError,
lambda: model.decode_solution([1, 0], vartype="BINARY"))
def Create_Qubo(N, _lambda, P, A, returns, sigma):
x = Array.create("vector", 2 * N, "BINARY")
term1 = 0
H = 0
for i in range(N):
for j in range(N):
H += (
_lambda
* (sigma[i][j])
* (x[2 * i] + x[2 * i + 1] - 1)
* (x[2 * j] + x[2 * j + 1] - 1)
)
term1 += Constraint(H, label="Sigma")
term2 = 0
H = 0
for i in range(N):
H -= (1 - _lambda) * returns[i] * (x[2 * i] + x[2 * i + 1] - 1)
term2 = Constraint(H, label="Returns")
H = 0
for i in range(N):
H += x[2 * i] + x[2 * i + 1] - 1
H -= A
H = H ** 2
H *= P
select_n = Constraint(H, label="select_n_projects")
model = H.compile()
return model.to_qubo()
def test_equality_of_express_with_const(self):
a, b = Qbit("a"), Spin("b")
exp = a + b - 1 + Constraint(a * b, label="const")
expected_exp = AddList(
[a, Num(-1.0), b,
Constraint(Mul(a, b), label="const")])
self.assertTrue(exp == expected_exp)
def build_solver(self,member_num,expectation_member_capacity):
X = Array.create('X', (self.department_num,self.term_num, member_num), 'BINARY')
# Term_Member Once Constraint
C_TM_Once = 0.0
for t in range(self.term_num):
for m in range(member_num):
C_TM_Once += Constraint(
(Sum(start_index=0,end_index=self.department_num,func=lambda d:X[d,t,m]) - 1)**2
, label=f"TM_Once_{t},{m}")
# Department_Member Once Constraint
C_DM_Once = 0.0
for d in range(self.department_num):
for m in range(member_num):
C_DM_Once += Constraint(
(Sum(start_index=0,end_index=self.term_num,func=lambda t:X[d,t,m]) - 1)**2
, label=f"DM_Once_{t},{m}")
# Member Capacity Constraint
C_MC = 0.0
for d in range(self.department_num):
for t in range(self.term_num):
C_MC += Constraint(
(Sum(start_index=0,end_index=member_num,func=lambda m:X[d,t,m]) - expectation_member_capacity[d,t])**2
, label=f"MC_{d},{t}")
P_TM_Once = Placeholder("PTMO")
P_DM_Once = Placeholder("PDMO")
P_MC = Placeholder("PMC")
H = P_TM_Once*C_TM_Once + P_DM_Once*C_DM_Once + P_MC*C_MC
model = H.compile()
return model
def get_qubo(num_nodes, num_colors, edges):
x = Array.create('x', (num_nodes, num_colors), "BINARY")
adjacent_const = 0.0
for (i, j) in edges:
for k in range(num_colors):
adjacent_const += Constraint(x[i, k] * x[j, k],
label="adjacent({},{})".format(i, j))
onecolor_const = 0.0
for i in range(num_nodes):
onecolor_const += Constraint(
(Sum(0, num_colors, lambda j: x[i, j]) - 1)**2,
label="onecolor{}".format(i))
# combine the two components
alpha = Placeholder("alpha")
H = alpha * onecolor_const + adjacent_const
model = H.compile()
alpha = 1.0
# search for an alpha for which each node has only one color
print("Broken constraints")
while True:
qubo, offset = model.to_qubo(feed_dict={"alpha": alpha})
solution = solve_qubo(qubo)
decoded_solution, broken_constraints, energy = model.decode_solution(
solution, vartype="BINARY", feed_dict={"alpha": alpha})
print(len(broken_constraints))
if not broken_constraints:
break
for (key, value) in broken_constraints.items():
if 'o' == key[0]: # onecolor
alpha += 0.1
break
if 'a' == key[0]: # adjacent
break
return qubo, decoded_solution
def test_equality_of_const(self):
c1 = Constraint(Qbit("a"), label="c1")
c2 = Constraint(Qbit("b"), label="c1")
c3 = Constraint(Qbit("a"), label="c3")
c4 = Constraint(Qbit("a"), label="c1")
self.assertTrue(c1 == c4)
self.assertFalse(c1 != c4)
self.assertTrue(hash(c1) == hash(c4))
self.assertTrue(c1 != c2)
self.assertTrue(c1 != c3)
self.assertTrue(c1 != Qbit("a"))
def test_constraint(self):
sampler = dimod.ExactSolver()
x = Array.create('x', shape=(3), vartype="BINARY")
H = Constraint(x[0] * x[1] * x[2], label="C1")
model = H.compile()
bqm = model.to_bqm()
responses = sampler.sample(bqm)
solutions = model.decode_sampleset(responses)
for sol in solutions:
if sol.energy == 1.0:
self.assertEqual(sol.subh['C1'], 1.0)
def test_compile_const(self):
a, b, w = Qbit("a"), Qbit("b"), Placeholder("w")
exp = Constraint(Constraint(w * (a + b - 1), label="const1") +
Constraint((a + b - 1)**2, label="const2"),
label="const_all")
expected_qubo = {('a', 'a'): 2.0, ('a', 'b'): 2.0, ('b', 'b'): 2.0}
expected_offset = -2.0
expected_structure = {'a': ('a', ), 'b': ('b', )}
self.compile_check(exp,
expected_qubo,
expected_offset,
expected_structure,
feed_dict={"w": 3.0})
def make_energy(num_city, distance):
# set binary variables
x = Array.create('x', shape=(num_city, num_city), vartype='BINARY')
# # fix variables for preprocess
# x = np.array(x)
# x[0][0] = 1
# for i in range(1, num_city):
# x[0][i] = 0
# for t in range(1, num_city):
# x[t][0] = 0
# set hyperparameters
lambda_a = []
lambda_b = []
for i in range(num_city):
lambda_a.append(Placeholder('h_a_{}'.format(i)))
lambda_b.append(Placeholder('h_b_{}'.format(i)))
lambda_c = Placeholder('h_c')
# set one-hot encoding for time
h_a = []
for t in range(num_city):
tmp = sum([x[t][i] for i in range(num_city)]) - 1
h_a.append(tmp)
# set one-hot encoding for city
h_b = []
for i in range(num_city):
tmp = sum([x[t][i] for t in range(num_city)]) - 1
h_b.append(tmp)
# set function for augmented lagrangian function
h_c = sum([h_a[i]**2 for i in range(num_city)])
h_c += sum([h_b[i]**2 for i in range(num_city)])
# convert to constraint
for i in range(num_city):
h_a[i] = Constraint(h_a[i], label='h_a_{}'.format(i))
h_b[i] = Constraint(h_b[i], label='h_b_{}'.format(i))
h_c = Constraint(h_c, label='h_c')
# set objective function
obj = 0
for t in range(num_city):
for i in range(num_city):
for j in range(num_city):
obj += distance[i][j] * x[t][i] * x[(t + 1) % num_city][j]
# compute total energy
hamiltonian = obj + lambda_c / 2 * h_c
hamiltonian += sum([lambda_a[i] * h_a[i] for i in range(num_city)])
hamiltonian += sum([lambda_b[i] * h_b[i] for i in range(num_city)])
# compile
model = hamiltonian.compile()
return model
def test_placeholder_in_constraint(self):
a = Binary("a")
exp = Constraint(2 * Placeholder("c") + a, "const1")
m = exp.compile()
sol, broken, energy = m.decode_solution({"a": 1},
vartype="BINARY",
feed_dict={"c": 1})
self.assertEqual(energy, 3.0)
self.assertEqual(broken,
{'const1': {
'result': {
'a': 1
},
'penalty': 3.0
}})
self.assertEqual(sol, {'a': 1})
def optimize_leap(self):
from pyqubo import Array,Constraint,Placeholder,UnaryEncInteger,Sum #LogEncInteger
from dwave.system import LeapHybridSampler
x = Array.create("x",shape=(self.num),vartype="BINARY")
#y = LogEncInteger("y",lower=0,upper=5)
y = UnaryEncInteger("y",lower=0,upper=5)
#価値が最大になるように（符号を反転させる）
H1 = -Sum(0,self.num,lambda i :x[i]*self.p[i].get_value() )
#H1 = -sum([x[i]*self.p[i].get_value() for i in range(self.num)])
#重さが目的の重量になるように
H2 = Constraint((self.limit_weight -sum([x[i]*p_i.get_weight() for i,p_i in enumerate(self.p)]) - y*10)**2,"Const Weight")
H = H1 + H2*Placeholder("balancer")
model = H.compile()
balance_dict = {"balancer":1.0}
bqm = model.to_dimod_bqm(feed_dict=balance_dict)
sampler = LeapHybridSampler()
responses = sampler.sample(bqm,time_limit=3)
solutions = model.decode_dimod_response(responses,feed_dict=balance_dict)
if len(solutions[0][1]) == 0:
print(f" y= { sum(2**i*y_i for i,y_i in enumerate(solutions[0][0]['y']))}")
print("## LeapHybridSolver Optimized Result")
self.print([int(solutions[0][0]['x'][i]) for i in range(self.num)])
else:
print("## LeapHybridSolver Optimizing Failed")
def define_model(self):
'''
pyqubo.Modelインスタンス作成。モデル作成結果はself.modelに格納
H1(距離 目的関数)、H2,H3（都市、順序のワンホット制約)
parameters
-----
なし
returns
-----
なし
'''
city_num = self.size
#変数定義
x = Array.create('x', shape=(city_num, city_num), vartype="BINARY")
#距離のペナルティ
H1 = 0
#i番目に都市j、i+1番目に都市kを訪れる
for i, j in product(range(city_num), range(city_num)):
for k in range(city_num):
H1 += self.dist(j, k) * x[i][j] * x[(i + 1) % city_num][k]
#ある時刻には訪れる都市は1つだけ
H2 = 0
for i in range(city_num):
H2 += Constraint((Sum(0, city_num, lambda j: x[i][j]) - 1)**2,
label=f"Constraint one hot for time{i}")
#ある都市に訪れるのは1度だけ
H3 = 0
for i in range(city_num):
H3 += Constraint((Sum(0, city_num, lambda j: x[j][i]) - 1)**2,
label=f"Constraint one hot for city {i}")
H = Placeholder("H1") * H1 + H2 + H3
#モデル作成
self.model = H.compile()
def test_compile_constraint(self):
a, b, c = Binary("a"), Binary("b"), Binary("c")
exp = Constraint(a * b * c, label="constraint")
# expected_qubo = {('a', '0*1'): -10.0, ('b', '0*1'): -10.0, ('0*1', '0*1'): 15.0, ('a', 'a'): 0.0, ('a', 'b'): 5.0, ('c', '0*1'): 1.0, ('b', 'b'): 0.0, ('c', 'c'): 0.0}
expected_qubo = {
('a', 'a * b'): -10.0,
('b', 'a * b'): -10.0,
('a * b', 'a * b'): 15.0,
('a', 'b'): 5.0,
('c', 'a * b'): 1.0
}
expected_offset = 0
self.compile_check(exp, expected_qubo, expected_offset, feed_dict={})
def tsp(n_city):
t0 = time.time()
x = Array.create('c', (n_city, n_city), 'BINARY')
# Constraint not to visit more than two cities at the same time.
time_const = 0.0
for i in range(n_city):
# If you wrap the hamiltonian by Const(...), this part is recognized as constraint
time_const += Constraint(
(sum(x[i, j] for j in range(n_city)) - 1)**2,
label="time{}".format(i))
# Constraint not to visit the same city more than twice.
city_const = 0.0
for j in range(n_city):
city_const += Constraint(
(sum(x[i, j] for i in range(n_city)) - 1)**2,
label="city{}".format(j))
# distance of route
distance = 0.0
for i in range(n_city):
for j in range(n_city):
for k in range(n_city):
# we set the constant distance
d_ij = 10
distance += d_ij * x[k, i] * x[(k + 1) % n_city, j]
# Construct hamiltonian
A = Placeholder("A")
H = distance + A * (time_const + city_const)
# Compile model
t1 = time.time()
model = H.compile()
qubo, offset = model.to_qubo(index_label=True, feed_dict={"A": 2.0})
t2 = time.time()
return t1 - t0, t2 - t1
def dijkstra_solver(G, node1, node2, lagrange):
H = 0
pq_vars = {}
# Constraints
# Find the complete set of edges, and create PyQUBO variables
for edge in G.edges():
edge_label = sorted(edge)[0] + sorted(edge)[1]
pq_vars[edge_label] = Binary(edge_label)
for node in G:
neighbors = G.edges(node)
incident_edges = [
pq_vars[sorted(edge)[0] + sorted(edge)[1]] for edge in neighbors
]
if node == node1 or node == node2:
# Starting or ending node - 1 in N condition
H += lagrange * Constraint(
(sum(incident_edges) - 1)**2, label=' special ' + node)
else:
# Other node - may be 0 or 2 in N
# In QUBO, the 0 case does not contribute, assuming the sum is
# 0 (valid solution)
sum_z = sum(incident_edges)
for n in range(2, len(incident_edges) + 1):
for c in combinations(incident_edges, n):
m_prod = np.prod(c)
sum_z += qubo_c(n) * m_prod
H += lagrange * Constraint(sum_z, ' usual ' + node)
# Objective terms
for edge in G.edges():
edge_label = sorted(edge)[0] + sorted(edge)[1]
H += pq_vars[edge_label] * G[sorted(edge)[0]][sorted(edge)
[1]]['weight']
model = H.compile()
return model
def optimize_advantage(self,count=False,Best=0,balancer=1.0):
from pyqubo import Array,Constraint,Placeholder,UnaryEncInteger,Sum #LogEncInteger
from dwave.system import EmbeddingComposite,DWaveSampler
x = Array.create("x",shape=(self.num),vartype="BINARY")
#y = LogEncInteger("y",lower=0,upper=5)
y = UnaryEncInteger("y",lower=0,upper=5)
#価値が最大になるように（符号を反転させる）
#H1 = -sum([x[i]*self.p[i].get_value() for i in range(self.num)])
H1 = -Sum(0,self.num,lambda i :x[i]*self.p[i].get_value() )
#重さが目的の重量になるように
#H2 = Constraint((self.limit_weight -sum([x[i]*p_i.get_weight() for i,p_i in enumerate(self.p)]) - y*10)**2,"Const Weight")
H2 = Constraint((self.limit_weight -Sum(0,self.num,lambda i: x[i]*self.p[i].get_weight()) - y*10)**2,"Const Weight")
#H2 = Constraint((self.limit_weight -Sum(0,self.num,lambda i: x[i]*self.p[i].get_weight()))**2,"Const Weight")
H = H1 + H2*Placeholder("balancer")
model = H.compile()
balance_dict = {"balancer":balancer}
bqm = model.to_dimod_bqm(feed_dict=balance_dict)
sampler = EmbeddingComposite(DWaveSampler(solver="Advantage_system1.1"))
#sampler = EmbeddingComposite(DWaveSampler(solver="DW_2000Q_6"))
responses = sampler.sample(bqm,num_reads=1000)
solutions = model.decode_dimod_response(responses,feed_dict=balance_dict)
#Optuna用 バランス調査
if count == True:
counter = 0
for idx,sol in enumerate(solutions):
const_str = sol[1]
val = sum(int(sol[0]['x'][i])*self.p[i].get_value() for i in range(self.num))
weight = sum(int(sol[0]['x'][i])*self.p[i].get_weight() for i in range(self.num))
#重量が制限以下、かつ価値が最適解の9割以上をカウント
if len(const_str) == 0 and val > Best*0.9 and weight <= self.limit_weight:
counter += responses.record[idx][2]
del H1,H2,H,model,bqm,responses,solutions
gc.collect()
return counter
if len(solutions[0][1]) == 0:
print(f" y= { sum(2**i*y_i for i,y_i in enumerate(solutions[0][0]['y']))}")
print("## Advantage Solver Optimized Result")
self.print([int(solutions[0][0]['x'][i]) for i in range(self.num)])
else:
print("## Advantage Solver Optimizing Failed")
def parse_to_pyqubo_model(
self,
objectives: List[ObjectiveTerm] = [],
constraints: List[ConstraintTerm] = [],
) -> pyqubo.Model:
parsed_objectives = [
Placeholder(o["label"]) * self.parse_mathjson(o["tex"])
for o in objectives
]
parsed_constraints = [
Placeholder(c["label"]) *
Constraint(self.parse_mathjson(c["tex"]), label=c["label"])
for c in constraints
]
H = cast(Express, sum(parsed_objectives) + sum(parsed_constraints))
pyqubo_model = H.compile()
return pyqubo_model
def __init__(self, label, value_range, strength):
lower, upper = value_range
assert upper > lower, "upper value should be larger than lower value"
assert isinstance(lower, int)
assert isinstance(upper, int)
assert isinstance(strength, int) or isinstance(strength, float) or\
isinstance(strength, Placeholder)
self._num_variables = (upper - lower + 1)
self.array = Array.create(label, shape=self._num_variables, vartype='BINARY')
self.constraint = Constraint((sum(self.array)-1)**2, label=label+"_const", condition=lambda x: x==0)
express = SubH(lower + sum(i*x for i, x in enumerate(self.array)), label=label)
penalty = self.constraint * strength
super().__init__(
label=label,
value_range=value_range,
express=express,
penalty=penalty)
max_coeff = abs(np.max(list(qubo.values())))
min_coeff = abs(np.min(list(qubo.values())))
norm = max_coeff if max_coeff - min_coeff > 0 else min_coeff
return exp / norm
# Cost function
exp_origin = sum(distances[origin][others[i]]*1*q[i][0] +
distances[others[i]][origin]*q[i][N-2]*1 for i in range(N-1))
exp_others = sum(distances[others[i]][others[j]]*q[i][t]*q[j][t+1]
for i in range(N-1) for j in range(N-1) for t in range(N-2))
H_cost = normalize(exp_origin + exp_others)
# Constraint
H_city = Constraint(normalize(sum((sum(q[i][t] for t in range(N-1))-1)**2 for i in range(N-1))), 'city')
H_time = Constraint(normalize(sum((sum(q[i][t] for i in range(N-1))-1)**2 for t in range(N-1))), 'time')
# Express objective function and compile it to model
H = H_cost + Placeholder('lam') * (H_city + H_time)
model = H.compile()
# --- Solve QUBO ---
# Get the QUBO matrix from the model
feed_dict = {'lam':5.0} # the value of constraint
qubo, offset = model.to_qubo(feed_dict=feed_dict)
# Run QUBO on Leap's Hybrid Solver (hybrid_v1)
sampler = LeapHybridSampler(token='')
def test_decode(self):
x = Matrix("x", n_row=2, n_col=2)
exp = Constraint((x[1, 1] - x[0, 1])**2, label="const")
model = exp.compile()
# check __repr__ of CompiledQubo
expected_repr = "CompiledQubo({('x[0][1]', 'x[0][1]'): 1.0,\n" \
" ('x[0][1]', 'x[1][1]'): -2.0,\n" \
" ('x[1][1]', 'x[1][1]'): 1.0}, offset=0.0)"
self.assertEqual(repr(model.compiled_qubo), expected_repr)
# check __repr__ of Model
expected_repr = "Model(CompiledQubo({('x[0][1]', 'x[0][1]'): 1.0,\n"\
" ('x[0][1]', 'x[1][1]'): -2.0,\n"\
" ('x[1][1]', 'x[1][1]'): 1.0}, offset=0.0), "\
"structure={'x[0][0]': ('x', 0, 0),\n"\
" 'x[0][1]': ('x', 0, 1),\n"\
" 'x[1][0]': ('x', 1, 0),\n"\
" 'x[1][1]': ('x', 1, 1)})"
self.assertEqual(repr(model), expected_repr)
# when the constraint is not broken
# type of solution is dict[label, bit]
decoded_sol, broken, energy = model.decode_solution(
{
'x[0][1]': 1.0,
'x[1][1]': 1.0
}, var_type="binary")
self.assertTrue(decoded_sol == {'x': {0: {1: 1}, 1: {1: 1}}})
self.assertTrue(len(broken) == 0)
self.assertTrue(energy == 0)
# type of solution is list[bit]
decoded_sol, broken, energy = model.decode_solution([1, 1],
var_type="binary")
self.assertTrue(decoded_sol == {'x': {0: {1: 1}, 1: {1: 1}}})
self.assertTrue(len(broken) == 0)
self.assertTrue(energy == 0)
# type of solution is dict[index_label(int), bit]
decoded_sol, broken, energy = model.decode_solution({
0: 1.0,
1: 1.0
},
var_type="binary")
self.assertTrue(decoded_sol == {'x': {0: {1: 1}, 1: {1: 1}}})
self.assertTrue(len(broken) == 0)
self.assertTrue(energy == 0)
# when the constraint is broken
# type of solution is dict[label, bit]
decoded_sol, broken, energy = model.decode_solution(
{
'x[0][1]': 0.0,
'x[1][1]': 1.0
}, var_type="binary")
self.assertTrue(decoded_sol == {'x': {0: {1: 0}, 1: {1: 1}}})
self.assertTrue(len(broken) == 1)
self.assertTrue(energy == 1)
# type of solution is dict[label, spin]
decoded_sol, broken, energy = model.decode_solution(
{
'x[0][1]': 1.0,
'x[1][1]': -1.0
}, var_type="spin")
self.assertTrue(decoded_sol == {'x': {0: {1: 1}, 1: {1: -1}}})
self.assertTrue(len(broken) == 1)
self.assertTrue(energy == 1)
# invalid solution
self.assertRaises(
ValueError,
lambda: model.decode_solution([1, 1, 1], var_type="binary"))
self.assertRaises(
ValueError, lambda: model.decode_solution(
{
'x[0][2]': 1.0,
'x[1][1]': 0.0
}, var_type="binary"))
self.assertRaises(
TypeError, lambda: model.decode_solution(
(1, 1), var_type="binary"))
# invalid var_type
self.assertRaises(AssertionError,
lambda: model.decode_solution([1, 1], var_type="sp"))
margin = 2
#ペナルティ
alpha = 1
#荷物の入れる／入れない
x = Array.create('x', n, 'BINARY')
#スラック変数
s = Array.create('s', margin, 'BINARY')
#価値
total_value = sum(x_i * v_1 for x_i, v_1 in zip(x, values))
#重さ
total_weight = sum(x_i * w_1 for x_i, w_1 in zip(x, weights))
#ハミルトニアン
H = -1 * total_value + alpha * Constraint(
(total_weight - weight_limit + sum(s_i for s_i in s))**2,
label='weight_limit')
#quboモデル
model = H.compile()
qubo, offset = model.to_qubo()
# OpenJijで解く
#--------------------------------------
sampler = oj.SASampler()
response = sampler.sample_qubo(qubo, num_reads=1000)
plt.hist(-(response.energies + offset))
## エネルギーが一番低い状態を取り出します。
dict_solution = response.first.sample
## デコードします。
decoded_solution, broken, energy = model.decode_solution(dict_solution,
vartype="BINARY")
import dimod
from pyqubo import Constraint, Array
exactsolver = dimod.ExactSolver()
# Set up variables
x = Array.create('x', shape=5, vartype='BINARY')
# Set up the QUBO. Start with the equation insisting that there are 3
# numbers turned on, and then the equation insisting that they sum up to 8.
H = Constraint((sum(x) - 3)**2, label='3_hot')
H += Constraint(
(x[0] + (2 * x[1]) + (3 * x[2]) + (4 * x[3]) + (5 * x[4]) - 8)**2,
label='8_sum')
# Compile the model, and turn it into a QUBO object
model = H.compile()
Q = model.to_qubo()
bqm = dimod.BinaryQuadraticModel.from_qubo(Q[0], offset=Q[1])
# solve the problem
results = exactsolver.sample(bqm)
# print the results
for sample, energy in results.data(['sample', 'energy']):
_, broken, _ = model.decode_solution(sample, vartype='BINARY')
if not broken:
print(sample, energy)
routes[7] = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]
routes[8] = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]
routes[9] = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]
# Extra parameter
K = 3
# Initialize variable vector
size_of_variable_array = N + K * M
var = Array.create('vector', size_of_variable_array, 'BINARY')
# Defining constraints in the Model
minimize_costs = 0
minimize_costs += Constraint(Sum(0, N, lambda i: var[i] *
(c_t[i] - c_b[i]) + c_b[i]),
label="minimize_transport_costs")
capacity_constraint = 0
for j in range(M):
capacity_constraint += Constraint(
(Sum(0, N, lambda i: (1 - var[i]) * routes[i][j]) +
Sum(0, K, lambda i: var[N + j * K + i] * (2**(i))) - v[j])**2,
label="capacity_constraints")
teller = 0
while teller < 1:
teller = teller + 1
# parameter values
4: (0, 1)
}
# Plot cities
plot_city(cities)
plt.savefig(path + '/venv/results/test/test_simulator_empty.png')
plt.close()
n_city = len(cities)
# x is array of binary variables c[i][j] = 1 when city j is visited at time i and 0 otherwise
x = Array.create('c', (n_city, n_city), 'BINARY')
# Constraint not to visit more than two cities at the same time.
time_const = 0.0
for i in range(n_city):
time_const += Constraint((Sum(0, n_city, lambda j: x[i, j]) - 1)**2, label="time{}".format(i))
# Constraint not to visit the same city more than twice.
city_const = 0.0
for j in range(n_city):
city_const += Constraint((Sum(0, n_city, lambda i: x[i, j]) - 1)**2, label="city{}".format(j))
# distance of route
distance = 0.0
for i in range(n_city):
for j in range(n_city):
for k in range(n_city):
d_ij = dist(i, j, cities)
distance += d_ij * x[k, i] * x[(k+1)%n_city, j]
#定義上書き！
x = Array.create('x', shape=(n, m), vartype="BINARY")
#不等号表現用の補助スピン
y = []
for i in range(n):
#y.append(OneHotEncInteger(f"y{i}",lower=0,upper=JOB_SIZE*2,strength=Placeholder("IntChain")))
y.append(LogEncInteger(f"y{i}", lower=0, upper=JOB_SIZE * 2))
#目的関数定義相当
H1 = Sum(0, m, lambda j: Sum(0, n, lambda i: x[i][j] * c[i, j]))
#エージェントの利用可能資源量を超えない
H2 = Sum(
0, n, lambda i: Constraint(
Sum(0, m, lambda j: x[
(i, j)] * a[i, j] + y[i] - b[i])**2, f"Agent Resource {i}"))
#H2 = Sum(0,n,lambda i: Sum(0,m,lambda j: x[(i,j)]*a[i,j] - b[i])**2)
#全ての仕事をエージェントに割り振る
H3 = Sum(0, m,
lambda j: Constraint(Sum(0, n, lambda i: x[i][j] - 1)**2, f"Job{j}"))
H = Placeholder("balancer1") * H1 + Placeholder(
"balancer2") * H2 + Placeholder("balancer3") * H3
model = H.compile()
#パラメータ探索
study = optuna.create_study(storage='sqlite:///example.db',
study_name=f"m{m}n{n}_DW2000Q",
def _get_cost(edges: list, epsilon: float = 0.01):
"""Get the cost associated to the input graph.
:param edges: edges defining the input graph
:param epsilon: small number used for the penalties
:return: the corresponding cost
"""
vertices = get_vertices(edges)
cost = 0
for edge in edges:
cost += -Binary(str(tuple(edge)))**2
penalty_constants = _get_penalty_constants(edges, epsilon)
constraint_one_out = 0
constraint_one_in = 0
constraint_min_three = 0
for v in vertices:
# max one out
edges_out_v = get_edges_out_for_vertex(edges, v)
edges_out_v_pairs = [tuple(c) for c in combinations(edges_out_v, 2)]
cross_products_out = sum([
Binary(str((e[0]))) * Binary(str((e[1])))
for e in edges_out_v_pairs
])
if cross_products_out:
constraint_one_out += penalty_constants[v][0] * Constraint(
cross_products_out, label=f'one out for vertex: {v}')
# max one in
edges_in_v = get_edges_in_for_vertex(edges, v)
edges_in_v_pairs = [tuple(c) for c in combinations(edges_in_v, 2)]
cross_products_in = sum([
Binary(str((e[0]))) * Binary(str((e[1]))) for e in edges_in_v_pairs
])
if cross_products_in:
constraint_one_in += penalty_constants[v][1] * Constraint(
cross_products_in, label=f'one in for vertex: {v}')
edges_v = get_edges_for_vertex(edges, v)
edges_v_pairs = [tuple(c) for c in combinations(edges_v, 2)]
# cycle length at least three
cross_products_length_2_cycles = sum([
Binary(str((e[0]))) * Binary(str((e[1]))) for e in edges_v_pairs
if e[0][0] == e[1][1] and e[0][1] == e[1][0]
])
if cross_products_length_2_cycles:
# the factor 0.5 is to avoid double counting as each pair will be
# present twice as we are looping through the vertices
constraint_min_three += 0.5 * penalty_constants[v][2] * Constraint(
cross_products_length_2_cycles,
label=f'min three cycle length for vertex: {v}')
cost += constraint_one_out
cost += constraint_one_in
cost += constraint_min_three
return cost
K += 1
x = Array.create('arr', N + K, 'BINARY')
# Constraints in our model
#x' Sigmax
min_sigx = 0
H = 0
#temp hamiltonian for the Constraint
for i in range(N):
for j in range(N):
H += x[i] * x[j] * sigma[i][j]
min_sigx += Constraint(H, label="min_portfolio")
H = 0
#temp hamiltonian for the Constraint
for i in range(N):
H += x[i]
H -= n
H = H**2
select_n = Constraint(H, label="select_n_projects")
H = 0
#temp hamiltonian for the Constraint
for i in range(N):
H += returns[i] * x[i]
chainstrength = 70
numruns = 100
# Problem size
N_CARS = 2
N_ROUTES = 3
# Form the pyqubo binary variables representing (Car, Route)
q = Array.create('q', shape=(N_CARS, N_ROUTES), vartype='BINARY')
gamma = Placeholder('gamma')
# Constraints, one for each Car
H = 0
for i in range(N_CARS):
H += gamma * Constraint((sum(q[i, j] for j in range(N_ROUTES)) - 1) ** 2, label=str(i))
# Cost functions
# Be sure to count them once for each segment
# s0 and s3
H += 2 * ((q[0, 0] + q[0, 1] + q[1, 0] + q[1, 1]) ** 2)
# s2 and s7 and s10
H += 3 * ((q[0, 2] + q[1, 2]) ** 2)
# s6 and s9
H += 2 * ((q[0, 0] + q[1, 0]) ** 2)
# s8
H += (q[0, 1] + q[1, 1]) ** 2
# s11
H += (q[0, 1] + q[0, 2] + q[1, 1] + q[1, 2]) ** 2
# Compile the model, and turn it into a QUBO object
vertices = list(range(N))
edges = [
(0, 1),
(0, 4),
(0, 5),
(1, 2),
(1, 3),
(3, 4),
(4, 5),
]
# binary variable
x = Array.create("x", shape=N, vartype="BINARY")
# energy function (QUBO)
H_cover = Constraint(sum((1 - x[u]) * (1 - x[v]) for (u, v) in edges), "cover")
H_vertices = sum(x)
H = H_vertices + Placeholder("cover") * H_cover
model = H.compile()
feed_dict = {"cover": 1.0}
qubo, offset = model.to_qubo(feed_dict=feed_dict)
# search answer using SA
raw_solution = solve_qubo(qubo)
# decode answer
decoded_solution, broken, energy = model.decode_solution(raw_solution,
vartype="BINARY",
feed_dict=feed_dict)
