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section3.1-2.py
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section3.1-2.py
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"""
Section 3.1 The Number Partitioning Problem
Partition a set of numbers into two subsets such that the subset sums are as close to each other as possible.
Test list size 100 - too big to solve on the D-Wave 2000Q using minor-embedding,
so we have to use a decomposer to break the large problem into sub-problems.
"""
import copy
import dimod
import hybrid
import random
import sys
import time
from dwave.system.samplers import DWaveSampler
from dwave.system.composites import EmbeddingComposite
def generate_numbers(num_numbers):
random.seed(51229)
numbers = random.sample(range(1, 1000), num_numbers)
return numbers
def to_bqm(numbers):
c = sum(numbers)
c_square = c ** c
linear = {}
quadratic = {}
offset = 0.0
vartype = dimod.BINARY
for index, value in enumerate(numbers):
linear[index + 1] = value * (value - c)
for index1, value1 in enumerate(numbers[:-1]):
for index2 in range(index1 + 1, len(numbers)):
value = value1 * numbers[index2]
idx = (index1 + 1, index2 + 1)
quadratic[idx] = quadratic[tuple(reversed(idx))] = value
bqm = dimod.BinaryQuadraticModel(linear, quadratic, offset, vartype)
print(len(linear))
print(len(quadratic))
return bqm
def solve(sampler, bqm, num_reads=None):
params = {}
if num_reads:
params["num_reads"] = num_reads
return sampler.sample(bqm, **params)
def split_numbers_list(numbers, result):
list1 = []
list2 = []
for key, include_in_list in result.items():
index = key - 1
if include_in_list:
list1.append(numbers[index])
else:
list2.append(numbers[index])
return list1, list2
def print_result(sample_set):
for sample in sample_set.samples():
list1, list2 = split_numbers_list(numbers, sample)
print(
"list1: {}, sum: {}, list2: {}, sum: {}".format(
list1, sum(list1), list2, sum(list2)
)
)
dwave_sampler = EmbeddingComposite(DWaveSampler())
print("#" * 80)
numbers = generate_numbers(
100
) # generate a list of numbers to be split into equal sums
bqm = to_bqm(numbers)
# Redefine the workflow: a rolling decomposition window
decomposer = hybrid.EnergyImpactDecomposer(size=50, rolling_history=0.15)
sampler = hybrid.QPUSubproblemAutoEmbeddingSampler()
composer = hybrid.SplatComposer()
iteration = hybrid.RacingBranches(decomposer | sampler | composer) | hybrid.ArgMin()
workflow = hybrid.LoopUntilNoImprovement(iteration, convergence=3)
init_state = hybrid.State.from_problem(bqm)
start = time.time()
final_state = workflow.run(init_state).result()
end = time.time()
print("Using dwave-hybrid (elapsed time: {}s)".format(end - start))
print(final_state.samples)
print_result(final_state.samples)
print("")
# Using dwave-hybrid (elapsed time: 17.1963908672s)
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ... 100 energy num_oc.
# 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 ... 1 -460370757.0 1
# ['BINARY', 1 rows, 1 samples, 100 variables]
# list1: [447, 112, 485, 293, 452, 173, 106, 66, 320, 235, 259, 87, 204, 336, 165, 248, 104, 98, 68, 471, 255, 269, 466, 23, 82, 397, 254, 6, 196, 241, 423, 402, 80, 309, 152, 435, 478, 231, 130, 377, 477, 407, 261, 39, 418, 17, 111, 333, 464, 1], sum: 12463, list2: [871, 488, 831, 605, 902, 966, 579, 983, 750, 883, 958, 744, 591, 486, 507, 988, 959, 496, 648, 669, 541, 537, 504, 956, 944, 569, 864, 985, 521, 601, 916, 581, 715, 926, 889, 820, 787, 526, 666, 987, 533, 499, 665, 742, 913, 679, 868, 845, 783, 673], sum: 36939
# Change rolling_history=0.5, traversal='bfs' and num_reads=1000
decomposer = hybrid.EnergyImpactDecomposer(
size=50, rolling_history=0.5, traversal="bfs"
)
sampler = hybrid.QPUSubproblemAutoEmbeddingSampler(num_reads=1000)
composer = hybrid.SplatComposer()
iteration = hybrid.RacingBranches(decomposer | sampler | composer) | hybrid.ArgMin()
workflow = hybrid.LoopUntilNoImprovement(iteration, convergence=3)
init_state = hybrid.State.from_problem(bqm)
start = time.time()
final_state = workflow.run(init_state).result()
end = time.time()
print("Using dwave-hybrid (elapsed time: {}s)".format(end - start))
print(final_state.samples)
print_result(final_state.samples)
print("")
# Using dwave-hybrid (elapsed time: 30.7170920372s)
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ... 100 energy num_oc.
# 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ... 1 -605135232.0 1
# ['BINARY', 1 rows, 1 samples, 100 variables]
# list1: [871, 447, 112, 488, 831, 605, 485, 293, 452, 173, 902, 966, 106, 66, 320, 579, 235, 259, 983, 87, 750, 883, 958, 744, 204, 336, 165, 591, 248, 486, 507, 104, 988, 98, 959, 496, 68, 648, 471, 669, 541, 255, 269, 537, 466, 23, 82, 397, 254, 6, 1], sum: 22464, list2: [196, 504, 956, 944, 569, 864, 241, 985, 521, 601, 916, 581, 715, 926, 889, 820, 423, 402, 787, 80, 309, 526, 152, 666, 435, 478, 231, 130, 377, 987, 533, 477, 499, 665, 407, 742, 261, 39, 418, 913, 679, 17, 868, 845, 111, 333, 783, 673, 464], sum: 26938