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Alinson S. Xavier
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miplearn/problems/__init__.py
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# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.

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miplearn/problems/knapsack.py
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# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.
import miplearn
from miplearn import Instance
import numpy as np
import pyomo.environ as pe
from scipy.stats import uniform, randint, bernoulli
from scipy.stats.distributions import rv_frozen
class ChallengeA:
"""
- 250 variables, 10 constraints, fixed weights
- w ~ U(0, 1000), jitter ~ U(0.95, 1.05)
- K = 500, u ~ U(0., 1.)
- alpha = 0.25
"""
def __init__(self,
seed=42,
n_training_instances=500,
n_test_instances=50):
np.random.seed(seed)
self.gen = MultiKnapsackGenerator(n=randint(low=250, high=251),
m=randint(low=10, high=11),
w=uniform(loc=0.0, scale=1000.0),
K=uniform(loc=500.0, scale=0.0),
u=uniform(loc=0.0, scale=1.0),
alpha=uniform(loc=0.25, scale=0.0),
fix_w=True,
w_jitter=uniform(loc=0.95, scale=0.1),
)
np.random.seed(seed + 1)
self.training_instances = self.gen.generate(n_training_instances)
np.random.seed(seed + 2)
self.test_instances = self.gen.generate(n_test_instances)
class MultiKnapsackInstance(Instance):
"""Representation of the Multidimensional 0-1 Knapsack Problem.
Given a set of n items and m knapsacks, the problem is to find a subset of items S maximizing
sum(prices[i] for i in S). If selected, each item i occupies weights[i,j] units of space in
each knapsack j. Furthermore, each knapsack j has limited storage space, given by capacities[j].
This implementation assigns a different category for each decision variable, and therefore
trains one ML model per variable. It is only suitable when training and test instances have
same size and items don't shuffle around.
"""
def __init__(self,
prices,
capacities,
weights):
assert isinstance(prices, np.ndarray)
assert isinstance(capacities, np.ndarray)
assert isinstance(weights, np.ndarray)
assert len(weights.shape) == 2
self.m, self.n = weights.shape
assert prices.shape == (self.n,)
assert capacities.shape == (self.m,)
self.prices = prices
self.capacities = capacities
self.weights = weights
def to_model(self):
model = pe.ConcreteModel()
model.x = pe.Var(range(self.n), domain=pe.Binary)
model.OBJ = pe.Objective(rule=lambda model: sum(model.x[j] * self.prices[j]
for j in range(self.n)),
sense=pe.maximize)
model.eq_capacity = pe.ConstraintList()
for i in range(self.m):
model.eq_capacity.add(sum(model.x[j] * self.weights[i,j]
for j in range(self.n)) <= self.capacities[i])
return model
def get_instance_features(self):
return np.hstack([
np.mean(self.prices),
self.capacities,
])
def get_variable_features(self, var, index):
return np.hstack([
self.prices[index],
self.weights[:, index],
])
# def get_variable_category(self, var, index):
# return index
class MultiKnapsackGenerator:
def __init__(self,
n=randint(low=100, high=101),
m=randint(low=30, high=31),
w=randint(low=0, high=1000),
K=randint(low=500, high=500),
u=uniform(loc=0.0, scale=1.0),
alpha=uniform(loc=0.25, scale=0.0),
fix_w=False,
w_jitter=uniform(loc=1.0, scale=0.0),
round=True,
):
"""Initialize the problem generator.
Instances have a random number of items (or variables) and a random number of knapsacks
(or constraints), as specified by the provided probability distributions `n` and `m`,
respectively. The weight of each item `i` on knapsack `j` is sampled independently from
the provided distribution `w`. The capacity of knapsack `j` is set to:
alpha_j * sum(w[i,j] for i in range(n)),
where `alpha_j`, the tightness ratio, is sampled from the provided probability
distribution `alpha`. To make the instances more challenging, the costs of the items
are linearly correlated to their average weights. More specifically, the weight of each
item `i` is set to:
sum(w[i,j]/m for j in range(m)) + K * u_i,
where `K`, the correlation coefficient, and `u_i`, the correlation multiplier, are sampled
from the provided probability distributions. Note that `K` is only sample once for the
entire instance.
If fix_w=True is provided, then w[i,j] are kept the same in all generated instances. This
also implies that n and m are kept fixed. Although the prices and capacities are derived
from w[i,j], as long as u and K are not constants, the generated instances will still not
be completely identical.
If a probability distribution w_jitter is provided, then item weights will be set to
w[i,j] * gamma[i,j] where gamma[i,j] is sampled from w_jitter. When combined with
fix_w=True, this argument may be used to generate instances where the weight of each item
is roughly the same, but not exactly identical, across all instances. The prices of the
items and the capacities of the knapsacks will be calculated as above, but using these
perturbed weights instead.
By default, all generated prices, weights and capacities are rounded to the nearest integer
number. If `round=False` is provided, this rounding will be disabled.
Parameters
----------
n: rv_discrete
Probability distribution for the number of items (or variables)
m: rv_discrete
Probability distribution for the number of knapsacks (or constraints)
w: rv_continuous
Probability distribution for the item weights
K: rv_continuous
Probability distribution for the profit correlation coefficient
u: rv_continuous
Probability distribution for the profit multiplier
alpha: rv_continuous
Probability distribution for the tightness ratio
fix_w: boolean
If true, weights are kept the same (minus the noise from w_jitter) in all instances
w_jitter: rv_continuous
Probability distribution for random noise added to the weights
round: boolean
If true, all prices, weights and capacities are rounded to the nearest integer
"""
assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
assert isinstance(m, rv_frozen), "m should be a SciPy probability distribution"
assert isinstance(w, rv_frozen), "w should be a SciPy probability distribution"
assert isinstance(K, rv_frozen), "K should be a SciPy probability distribution"
assert isinstance(u, rv_frozen), "u should be a SciPy probability distribution"
assert isinstance(alpha, rv_frozen), "alpha should be a SciPy probability distribution"
assert isinstance(fix_w, bool), "fix_w should be boolean"
assert isinstance(w_jitter, rv_frozen), \
"w_jitter should be a SciPy probability distribution"
self.n = n
self.m = m
self.w = w
self.K = K
self.u = u
self.alpha = alpha
self.w_jitter = w_jitter
self.round = round
if fix_w:
self.fix_n = self.n.rvs()
self.fix_m = self.m.rvs()
self.fix_w = np.array([self.w.rvs(self.fix_n) for _ in range(self.fix_m)])
self.fix_u = self.u.rvs(self.fix_n)
self.fix_K = self.K.rvs()
else:
self.fix_n = None
self.fix_m = None
self.fix_w = None
self.fix_u = None
self.fix_K = None
def generate(self, n_samples):
def _sample():
if self.fix_w is not None:
n = self.fix_n
m = self.fix_m
w = self.fix_w
u = self.fix_u
K = self.fix_K
else:
n = self.n.rvs()
m = self.m.rvs()
w = np.array([self.w.rvs(n) for _ in range(m)])
u = self.u.rvs(n)
K = self.K.rvs()
w = w * np.array([self.w_jitter.rvs(n) for _ in range(m)])
alpha = self.alpha.rvs(m)
p = np.array([w[:,j].sum() / m + K * u[j] for j in range(n)])
b = np.array([w[i,:].sum() * alpha[i] for i in range(m)])
if self.round:
p = p.round()
b = b.round()
w = w.round()
return MultiKnapsackInstance(p, b, w)
return [_sample() for _ in range(n_samples)]
class KnapsackInstance(Instance):
"""
Simpler (one-dimensional) Knapsack Problem, used for testing.
"""
def __init__(self, weights, prices, capacity):
self.weights = weights
self.prices = prices
self.capacity = capacity
def to_model(self):
model = pe.ConcreteModel()
items = range(len(self.weights))
model.x = pe.Var(items, domain=pe.Binary)
model.OBJ = pe.Objective(rule=lambda m: sum(m.x[v] * self.prices[v] for v in items),
sense=pe.maximize)
model.eq_capacity = pe.Constraint(rule=lambda m: sum(m.x[v] * self.weights[v]
for v in items) <= self.capacity)
return model
def get_instance_features(self):
return np.array([
self.capacity,
np.average(self.weights),
])
def get_variable_features(self, var, index):
return np.array([
self.weights[index],
self.prices[index],
])

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miplearn/problems/stab.py
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# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.
import numpy as np
import pyomo.environ as pe
import networkx as nx
from miplearn import Instance
import random
from scipy.stats import uniform, randint, bernoulli
from scipy.stats.distributions import rv_frozen
class ChallengeA:
def __init__(self,
seed=42,
n_training_instances=500,
n_test_instances=50,
):
np.random.seed(seed)
self.generator = MaxWeightStableSetGenerator(w=uniform(loc=100., scale=50.),
n=randint(low=200, high=201),
p=uniform(loc=0.05, scale=0.0),
fix_graph=True)
np.random.seed(seed + 1)
self.training_instances = self.generator.generate(n_training_instances)
np.random.seed(seed + 2)
self.test_instances = self.generator.generate(n_test_instances)
class MaxWeightStableSetGenerator:
"""Random instance generator for the Maximum-Weight Stable Set Problem.
The generator has two modes of operation. When `fix_graph=True` is provided, one random
Erdős-Rényi graph $G_{n,p}$ is generated in the constructor, where $n$ and $p$ are sampled
from user-provided probability distributions `n` and `p`. To generate each instance, the
generator independently samples each $w_v$ from the user-provided probability distribution `w`.
When `fix_graph=False`, a new random graph is generated for each instance; the remaining
parameters are sampled in the same way.
"""
def __init__(self,
w=uniform(loc=10.0, scale=1.0),
n=randint(low=250, high=251),
p=uniform(loc=0.05, scale=0.0),
fix_graph=True):
"""Initialize the problem generator.
Parameters
----------
w: rv_continuous
Probability distribution for vertex weights.
n: rv_discrete
Probability distribution for parameter $n$ in Erdős-Rényi model.
p: rv_continuous
Probability distribution for parameter $p$ in Erdős-Rényi model.
"""
assert isinstance(w, rv_frozen), "w should be a SciPy probability distribution"
assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
assert isinstance(p, rv_frozen), "p should be a SciPy probability distribution"
self.w = w
self.n = n
self.p = p
self.fix_graph = fix_graph
self.graph = None
if fix_graph:
self.graph = self._generate_graph()
def generate(self, n_samples):
def _sample():
if self.graph is not None:
graph = self.graph
else:
graph = self._generate_graph()
weights = self.w.rvs(graph.number_of_nodes())
return MaxWeightStableSetInstance(graph, weights)
return [_sample() for _ in range(n_samples)]
def _generate_graph(self):
return nx.generators.random_graphs.binomial_graph(self.n.rvs(), self.p.rvs())
class MaxWeightStableSetInstance(Instance):
"""An instance of the Maximum-Weight Stable Set Problem.
Given a graph G=(V,E) and a weight w_v for each vertex v, the problem asks for a stable
set S of G maximizing sum(w_v for v in S). A stable set (also called independent set) is
a subset of vertices, no two of which are adjacent.
This is one of Karp's 21 NP-complete problems.
"""
def __init__(self, graph, weights):
self.graph = graph
self.weights = weights
self.model = None
def to_model(self):
nodes = list(self.graph.nodes)
edges = list(self.graph.edges)
self.model = model = pe.ConcreteModel()
model.x = pe.Var(nodes, domain=pe.Binary)
model.OBJ = pe.Objective(rule=lambda m : sum(m.x[v] * self.weights[v] for v in nodes),
sense=pe.maximize)
model.edge_eqs = pe.ConstraintList()
for edge in edges:
model.edge_eqs.add(model.x[edge[0]] + model.x[edge[1]] <= 1)
return model
def get_instance_features(self):
return np.array(self.weights)
def get_variable_features(self, var, index):
return np.ones(0)
def get_variable_category(self, var, index):
return index

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miplearn/problems/tests/__init__.py
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# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.

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miplearn/problems/tests/test_knapsack.py
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# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.
from miplearn import LearningSolver
from miplearn.problems.knapsack import MultiKnapsackGenerator, MultiKnapsackInstance
from scipy.stats import uniform, randint
import numpy as np
def test_knapsack_generator():
gen = MultiKnapsackGenerator(n=randint(low=100, high=101),
m=randint(low=30, high=31),
w=randint(low=0, high=1000),
K=randint(low=500, high=501),
u=uniform(loc=1.0, scale=1.0),
alpha=uniform(loc=0.50, scale=0.0),
)
instances = gen.generate(100)
w_sum = sum(instance.weights for instance in instances) / len(instances)
p_sum = sum(instance.prices for instance in instances) / len(instances)
b_sum = sum(instance.capacities for instance in instances) / len(instances)
assert round(np.mean(w_sum), -1) == 500.
assert round(np.mean(p_sum), -1) == 1250.
assert round(np.mean(b_sum), -3) == 25000.

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miplearn/problems/tests/test_stab.py
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# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.
from miplearn import LearningSolver
from miplearn.problems.stab import MaxWeightStableSetInstance
from miplearn.problems.stab import MaxWeightStableSetGenerator
import networkx as nx
import numpy as np
from scipy.stats import uniform, randint
def test_stab():
graph = nx.cycle_graph(5)
weights = [1., 1., 1., 1., 1.]
instance = MaxWeightStableSetInstance(graph, weights)
solver = LearningSolver()
solver.solve(instance)
assert instance.model.OBJ() == 2.
def test_stab_generator_fixed_graph():
from miplearn.problems.stab import MaxWeightStableSetGenerator
gen = MaxWeightStableSetGenerator(w=uniform(loc=50., scale=10.),
n=randint(low=10, high=11),
p=uniform(loc=0.05, scale=0.),
fix_graph=True)
instances = gen.generate(1_000)
weights = np.array([instance.weights for instance in instances])
weights_avg_actual = np.round(np.average(weights, axis=0))
weights_avg_expected = [55.0] * 10
assert list(weights_avg_actual) == weights_avg_expected
def test_stab_generator_random_graph():
from miplearn.problems.stab import MaxWeightStableSetGenerator
gen = MaxWeightStableSetGenerator(w=uniform(loc=50., scale=10.),
n=randint(low=30, high=41),
p=uniform(loc=0.5, scale=0.),
fix_graph=False)
instances = gen.generate(1_000)
n_nodes = [instance.graph.number_of_nodes() for instance in instances]
n_edges = [instance.graph.number_of_edges() for instance in instances]
assert np.round(np.mean(n_nodes)) == 35.
assert np.round(np.mean(n_edges), -1) == 300.

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miplearn/problems/tests/test_tsp.py
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# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.
from miplearn import LearningSolver
from miplearn.problems.tsp import TravelingSalesmanGenerator, TravelingSalesmanInstance
import numpy as np
from numpy.linalg import norm
from scipy.spatial.distance import pdist, squareform
from scipy.stats import uniform, randint
def test_generator():
instances = TravelingSalesmanGenerator(x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=100, high=101),
gamma=uniform(loc=0.95, scale=0.1),
fix_cities=True).generate(100)
assert len(instances) == 100
assert instances[0].n_cities == 100
assert norm(instances[0].distances - instances[0].distances.T) < 1e-6
d = [instance.distances[0,1] for instance in instances]
assert np.std(d) > 0
def test_instance():
n_cities = 4
distances = np.array([
[0., 1., 2., 1.],
[1., 0., 1., 2.],
[2., 1., 0., 1.],
[1., 2., 1., 0.],
])
instance = TravelingSalesmanInstance(n_cities, distances)
for solver_name in ['gurobi', 'cplex']:
solver = LearningSolver(solver=solver_name)
solver.solve(instance)
x = instance.solution["x"]
assert x[0,1] == 1.0
assert x[0,2] == 0.0
assert x[0,3] == 1.0
assert x[1,2] == 1.0
assert x[1,3] == 0.0
assert x[2,3] == 1.0
assert instance.lower_bound == 4.0
assert instance.upper_bound == 4.0
def test_subtour():
n_cities = 6
cities = np.array([
[0., 0.],
[1., 0.],
[2., 0.],
[3., 0.],
[0., 1.],
[3., 1.],
])
distances = squareform(pdist(cities))
instance = TravelingSalesmanInstance(n_cities, distances)
for solver_name in ['gurobi', 'cplex']:
solver = LearningSolver(solver=solver_name)
solver.solve(instance)
x = instance.solution["x"]
assert x[0,1] == 1.0
assert x[0,4] == 1.0
assert x[1,2] == 1.0
assert x[2,3] == 1.0
assert x[3,5] == 1.0
assert x[4,5] == 1.0

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miplearn/problems/tsp.py
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# MIPLearn, an extensible framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2019-2020 Argonne National Laboratory. All rights reserved.
# Written by Alinson S. Xavier <axavier@anl.gov>
import numpy as np
import pyomo.environ as pe
from miplearn import Instance
from scipy.stats import uniform, randint
from scipy.spatial.distance import pdist, squareform
from scipy.stats.distributions import rv_frozen
import networkx as nx
import random
class ChallengeA:
def __init__(self,
seed=42,
n_training_instances=500,
n_test_instances=50,
):
np.random.seed(seed)
self.generator = TravelingSalesmanGenerator(x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=350, high=351),
gamma=uniform(loc=0.95, scale=0.1),
fix_cities=True,
round=True,
)
np.random.seed(seed + 1)
self.training_instances = self.generator.generate(n_training_instances)
np.random.seed(seed + 2)
self.test_instances = self.generator.generate(n_test_instances)
class TravelingSalesmanGenerator:
"""Random generator for the Traveling Salesman Problem."""
def __init__(self,
x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=100, high=101),
gamma=uniform(loc=1.0, scale=0.0),
fix_cities=True,
round=True,
):
"""Initializes the problem generator.
Initially, the generator creates n cities (x_1,y_1),...,(x_n,y_n) where n, x_i and y_i are
sampled independently from the provided probability distributions `n`, `x` and `y`. For each
(unordered) pair of cities (i,j), the distance d[i,j] between them is set to:
d[i,j] = gamma[i,j] \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}
where gamma is sampled from the provided probability distribution `gamma`.
If fix_cities=True, the list of cities is kept the same for all generated instances. The
gamma values, and therefore also the distances, are still different.
By default, all distances d[i,j] are rounded to the nearest integer. If `round=False`
is provided, this rounding will be disabled.
Arguments
---------
x: rv_continuous
Probability distribution for the x-coordinate of each city.
y: rv_continuous
Probability distribution for the y-coordinate of each city.
n: rv_discrete
Probability distribution for the number of cities.
fix_cities: bool
If False, cities will be resampled for every generated instance. Otherwise, list of
cities will be computed once, during the constructor.
round: bool
If True, distances are rounded to the nearest integer.
"""
assert isinstance(x, rv_frozen), "x should be a SciPy probability distribution"
assert isinstance(y, rv_frozen), "y should be a SciPy probability distribution"
assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
assert isinstance(gamma, rv_frozen), "gamma should be a SciPy probability distribution"
self.x = x
self.y = y
self.n = n
self.gamma = gamma
self.round = round
if fix_cities:
self.fixed_n, self.fixed_cities = self._generate_cities()
else:
self.fixed_n = None
self.fixed_cities = None
def generate(self, n_samples):
def _sample():
if self.fixed_cities is not None:
n, cities = self.fixed_n, self.fixed_cities
else:
n, cities = self._generate_cities()
distances = squareform(pdist(cities)) * self.gamma.rvs(size=(n, n))
distances = np.tril(distances) + np.triu(distances.T, 1)
if self.round:
distances = distances.round()
return TravelingSalesmanInstance(n, distances)
return [_sample() for _ in range(n_samples)]
def _generate_cities(self):
n = self.n.rvs()
cities = np.array([(self.x.rvs(), self.y.rvs()) for _ in range(n)])
return n, cities
class TravelingSalesmanInstance(Instance):
"""An instance ot the Traveling Salesman Problem.
Given a list of cities and the distance between each pair of cities, the problem asks for the
shortest route starting at the first city, visiting each other city exactly once, then
returning to the first city. This problem is a generalization of the Hamiltonian path problem,
one of Karp's 21 NP-complete problems.
"""
def __init__(self, n_cities, distances):
assert isinstance(distances, np.ndarray)
assert distances.shape == (n_cities, n_cities)
self.n_cities = n_cities
self.distances = distances
def to_model(self):
model = pe.ConcreteModel()
model.edges = edges = [(i,j)
for i in range(self.n_cities)
for j in range(i+1, self.n_cities)]
model.x = pe.Var(edges, domain=pe.Binary)
model.obj = pe.Objective(expr=sum(model.x[i,j] * self.distances[i,j]
for (i,j) in edges),
sense=pe.minimize)
model.eq_degree = pe.ConstraintList()
model.eq_subtour = pe.ConstraintList()
for i in range(self.n_cities):
model.eq_degree.add(sum(model.x[min(i,j), max(i,j)]
for j in range(self.n_cities) if i != j) == 2)
return model
def get_instance_features(self):
return np.array([1])
def get_variable_features(self, var_name, index):
return np.array([1])
def get_variable_category(self, var_name, index):
return index
def find_violations(self, model):
selected_edges = [e for e in model.edges if model.x[e].value > 0.5]
graph = nx.Graph()
graph.add_edges_from(selected_edges)
components = [frozenset(c) for c in list(nx.connected_components(graph))]
violations = []
for c in components:
if len(c) < self.n_cities:
violations += [c]
return violations
def build_lazy_constraint(self, model, component):
cut_edges = [e for e in model.edges
if (e[0] in component and e[1] not in component) or
(e[0] not in component and e[1] in component)]
return model.eq_subtour.add(sum(model.x[e] for e in cut_edges) >= 2)