You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
253 lines
10 KiB
253 lines
10 KiB
# 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],
|
|
]) |