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<header>
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<h1 class="title">Module <code>miplearn.problems.knapsack</code></h1>
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</header>
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<section id="section-intro">
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<details class="source">
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<summary>
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<span>Expand source code</span>
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</summary>
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<pre><code class="python"># MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
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# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
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# Released under the modified BSD license. See COPYING.md for more details.
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import numpy as np
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import pyomo.environ as pe
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from scipy.stats import uniform, randint
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from scipy.stats.distributions import rv_frozen
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from miplearn.instance import Instance
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class ChallengeA:
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"""
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- 250 variables, 10 constraints, fixed weights
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- w ~ U(0, 1000), jitter ~ U(0.95, 1.05)
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- K = 500, u ~ U(0., 1.)
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- alpha = 0.25
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"""
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def __init__(
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self,
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seed=42,
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n_training_instances=500,
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n_test_instances=50,
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):
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np.random.seed(seed)
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self.gen = MultiKnapsackGenerator(
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n=randint(low=250, high=251),
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m=randint(low=10, high=11),
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w=uniform(loc=0.0, scale=1000.0),
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K=uniform(loc=500.0, scale=0.0),
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u=uniform(loc=0.0, scale=1.0),
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alpha=uniform(loc=0.25, scale=0.0),
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fix_w=True,
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w_jitter=uniform(loc=0.95, scale=0.1),
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)
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np.random.seed(seed + 1)
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self.training_instances = self.gen.generate(n_training_instances)
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np.random.seed(seed + 2)
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self.test_instances = self.gen.generate(n_test_instances)
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class MultiKnapsackInstance(Instance):
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"""Representation of the Multidimensional 0-1 Knapsack Problem.
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Given a set of n items and m knapsacks, the problem is to find a subset of items S maximizing
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sum(prices[i] for i in S). If selected, each item i occupies weights[i,j] units of space in
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each knapsack j. Furthermore, each knapsack j has limited storage space, given by capacities[j].
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This implementation assigns a different category for each decision variable, and therefore
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trains one ML model per variable. It is only suitable when training and test instances have
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same size and items don't shuffle around.
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"""
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def __init__(self, prices, capacities, weights):
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super().__init__()
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assert isinstance(prices, np.ndarray)
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assert isinstance(capacities, np.ndarray)
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assert isinstance(weights, np.ndarray)
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assert len(weights.shape) == 2
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self.m, self.n = weights.shape
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assert prices.shape == (self.n,)
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assert capacities.shape == (self.m,)
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self.prices = prices
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self.capacities = capacities
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self.weights = weights
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def to_model(self):
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model = pe.ConcreteModel()
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model.x = pe.Var(range(self.n), domain=pe.Binary)
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model.OBJ = pe.Objective(
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rule=lambda model: sum(model.x[j] * self.prices[j] for j in range(self.n)),
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sense=pe.maximize,
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)
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model.eq_capacity = pe.ConstraintList()
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for i in range(self.m):
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model.eq_capacity.add(
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sum(model.x[j] * self.weights[i, j] for j in range(self.n))
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<= self.capacities[i]
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)
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return model
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def get_instance_features(self):
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return np.hstack(
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[
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np.mean(self.prices),
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self.capacities,
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]
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)
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def get_variable_features(self, var, index):
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return np.hstack(
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[
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self.prices[index],
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self.weights[:, index],
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]
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)
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# def get_variable_category(self, var, index):
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# return index
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class MultiKnapsackGenerator:
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def __init__(
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self,
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n=randint(low=100, high=101),
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m=randint(low=30, high=31),
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w=randint(low=0, high=1000),
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K=randint(low=500, high=500),
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u=uniform(loc=0.0, scale=1.0),
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alpha=uniform(loc=0.25, scale=0.0),
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fix_w=False,
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w_jitter=uniform(loc=1.0, scale=0.0),
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round=True,
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):
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"""Initialize the problem generator.
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Instances have a random number of items (or variables) and a random number of knapsacks
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(or constraints), as specified by the provided probability distributions `n` and `m`,
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respectively. The weight of each item `i` on knapsack `j` is sampled independently from
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the provided distribution `w`. The capacity of knapsack `j` is set to:
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alpha_j * sum(w[i,j] for i in range(n)),
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where `alpha_j`, the tightness ratio, is sampled from the provided probability
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distribution `alpha`. To make the instances more challenging, the costs of the items
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are linearly correlated to their average weights. More specifically, the weight of each
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item `i` is set to:
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sum(w[i,j]/m for j in range(m)) + K * u_i,
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where `K`, the correlation coefficient, and `u_i`, the correlation multiplier, are sampled
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from the provided probability distributions. Note that `K` is only sample once for the
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entire instance.
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If fix_w=True is provided, then w[i,j] are kept the same in all generated instances. This
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also implies that n and m are kept fixed. Although the prices and capacities are derived
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from w[i,j], as long as u and K are not constants, the generated instances will still not
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be completely identical.
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If a probability distribution w_jitter is provided, then item weights will be set to
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w[i,j] * gamma[i,j] where gamma[i,j] is sampled from w_jitter. When combined with
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fix_w=True, this argument may be used to generate instances where the weight of each item
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is roughly the same, but not exactly identical, across all instances. The prices of the
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items and the capacities of the knapsacks will be calculated as above, but using these
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perturbed weights instead.
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By default, all generated prices, weights and capacities are rounded to the nearest integer
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number. If `round=False` is provided, this rounding will be disabled.
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Parameters
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----------
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n: rv_discrete
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Probability distribution for the number of items (or variables)
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m: rv_discrete
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Probability distribution for the number of knapsacks (or constraints)
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w: rv_continuous
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Probability distribution for the item weights
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K: rv_continuous
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Probability distribution for the profit correlation coefficient
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u: rv_continuous
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Probability distribution for the profit multiplier
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alpha: rv_continuous
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Probability distribution for the tightness ratio
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fix_w: boolean
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If true, weights are kept the same (minus the noise from w_jitter) in all instances
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w_jitter: rv_continuous
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Probability distribution for random noise added to the weights
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round: boolean
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If true, all prices, weights and capacities are rounded to the nearest integer
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"""
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assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
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assert isinstance(m, rv_frozen), "m should be a SciPy probability distribution"
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assert isinstance(w, rv_frozen), "w should be a SciPy probability distribution"
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assert isinstance(K, rv_frozen), "K should be a SciPy probability distribution"
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assert isinstance(u, rv_frozen), "u should be a SciPy probability distribution"
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assert isinstance(
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alpha, rv_frozen
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), "alpha should be a SciPy probability distribution"
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assert isinstance(fix_w, bool), "fix_w should be boolean"
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assert isinstance(
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w_jitter, rv_frozen
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), "w_jitter should be a SciPy probability distribution"
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self.n = n
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self.m = m
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self.w = w
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self.K = K
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self.u = u
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self.alpha = alpha
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self.w_jitter = w_jitter
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self.round = round
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if fix_w:
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self.fix_n = self.n.rvs()
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self.fix_m = self.m.rvs()
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self.fix_w = np.array([self.w.rvs(self.fix_n) for _ in range(self.fix_m)])
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self.fix_u = self.u.rvs(self.fix_n)
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self.fix_K = self.K.rvs()
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else:
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self.fix_n = None
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self.fix_m = None
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self.fix_w = None
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self.fix_u = None
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self.fix_K = None
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def generate(self, n_samples):
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def _sample():
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if self.fix_w is not None:
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n = self.fix_n
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m = self.fix_m
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w = self.fix_w
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u = self.fix_u
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K = self.fix_K
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else:
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n = self.n.rvs()
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m = self.m.rvs()
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w = np.array([self.w.rvs(n) for _ in range(m)])
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u = self.u.rvs(n)
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K = self.K.rvs()
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w = w * np.array([self.w_jitter.rvs(n) for _ in range(m)])
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alpha = self.alpha.rvs(m)
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p = np.array([w[:, j].sum() / m + K * u[j] for j in range(n)])
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b = np.array([w[i, :].sum() * alpha[i] for i in range(m)])
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if self.round:
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p = p.round()
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b = b.round()
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w = w.round()
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return MultiKnapsackInstance(p, b, w)
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return [_sample() for _ in range(n_samples)]
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class KnapsackInstance(Instance):
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"""
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Simpler (one-dimensional) Knapsack Problem, used for testing.
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"""
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def __init__(self, weights, prices, capacity):
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super().__init__()
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self.weights = weights
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self.prices = prices
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self.capacity = capacity
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|
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def to_model(self):
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model = pe.ConcreteModel()
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items = range(len(self.weights))
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model.x = pe.Var(items, domain=pe.Binary)
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model.OBJ = pe.Objective(
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expr=sum(model.x[v] * self.prices[v] for v in items), sense=pe.maximize
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)
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model.eq_capacity = pe.Constraint(
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expr=sum(model.x[v] * self.weights[v] for v in items) <= self.capacity
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)
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return model
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def get_instance_features(self):
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return np.array(
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[
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self.capacity,
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np.average(self.weights),
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]
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)
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|
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def get_variable_features(self, var, index):
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return np.array(
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[
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self.weights[index],
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self.prices[index],
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]
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)
|
|
|
|
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class GurobiKnapsackInstance(KnapsackInstance):
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"""
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Simpler (one-dimensional) knapsack instance, implemented directly in Gurobi
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instead of Pyomo, used for testing.
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"""
|
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def __init__(self, weights, prices, capacity):
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super().__init__(weights, prices, capacity)
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def to_model(self):
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import gurobipy as gp
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from gurobipy import GRB
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model = gp.Model("Knapsack")
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n = len(self.weights)
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x = model.addVars(n, vtype=GRB.BINARY, name="x")
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model.addConstr(
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gp.quicksum(x[i] * self.weights[i] for i in range(n)) <= self.capacity,
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"eq_capacity",
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)
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model.setObjective(
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gp.quicksum(x[i] * self.prices[i] for i in range(n)), GRB.MAXIMIZE
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)
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return model</code></pre>
|
|
</details>
|
|
</section>
|
|
<section>
|
|
</section>
|
|
<section>
|
|
</section>
|
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<section>
|
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</section>
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<section>
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<h2 class="section-title" id="header-classes">Classes</h2>
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<dl>
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<dt id="miplearn.problems.knapsack.ChallengeA"><code class="flex name class">
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<span>class <span class="ident">ChallengeA</span></span>
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<span>(</span><span>seed=42, n_training_instances=500, n_test_instances=50)</span>
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</code></dt>
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<dd>
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<section class="desc"><ul>
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<li>250 variables, 10 constraints, fixed weights</li>
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<li>w ~ U(0, 1000), jitter ~ U(0.95, 1.05)</li>
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<li>K = 500, u ~ U(0., 1.)</li>
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<li>alpha = 0.25</li>
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</ul></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">class ChallengeA:
|
|
"""
|
|
- 250 variables, 10 constraints, fixed weights
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- w ~ U(0, 1000), jitter ~ U(0.95, 1.05)
|
|
- K = 500, u ~ U(0., 1.)
|
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- alpha = 0.25
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"""
|
|
|
|
def __init__(
|
|
self,
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seed=42,
|
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n_training_instances=500,
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n_test_instances=50,
|
|
):
|
|
|
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np.random.seed(seed)
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self.gen = MultiKnapsackGenerator(
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n=randint(low=250, high=251),
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m=randint(low=10, high=11),
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w=uniform(loc=0.0, scale=1000.0),
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|
K=uniform(loc=500.0, scale=0.0),
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u=uniform(loc=0.0, scale=1.0),
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alpha=uniform(loc=0.25, scale=0.0),
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fix_w=True,
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w_jitter=uniform(loc=0.95, scale=0.1),
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)
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np.random.seed(seed + 1)
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self.training_instances = self.gen.generate(n_training_instances)
|
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|
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np.random.seed(seed + 2)
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self.test_instances = self.gen.generate(n_test_instances)</code></pre>
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</details>
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|
</dd>
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<dt id="miplearn.problems.knapsack.GurobiKnapsackInstance"><code class="flex name class">
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<span>class <span class="ident">GurobiKnapsackInstance</span></span>
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<span>(</span><span>weights, prices, capacity)</span>
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</code></dt>
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<dd>
|
|
<section class="desc"><p>Simpler (one-dimensional) knapsack instance, implemented directly in Gurobi
|
|
instead of Pyomo, used for testing.</p></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">class GurobiKnapsackInstance(KnapsackInstance):
|
|
"""
|
|
Simpler (one-dimensional) knapsack instance, implemented directly in Gurobi
|
|
instead of Pyomo, used for testing.
|
|
"""
|
|
|
|
def __init__(self, weights, prices, capacity):
|
|
super().__init__(weights, prices, capacity)
|
|
|
|
def to_model(self):
|
|
import gurobipy as gp
|
|
from gurobipy import GRB
|
|
|
|
model = gp.Model("Knapsack")
|
|
n = len(self.weights)
|
|
x = model.addVars(n, vtype=GRB.BINARY, name="x")
|
|
model.addConstr(
|
|
gp.quicksum(x[i] * self.weights[i] for i in range(n)) <= self.capacity,
|
|
"eq_capacity",
|
|
)
|
|
model.setObjective(
|
|
gp.quicksum(x[i] * self.prices[i] for i in range(n)), GRB.MAXIMIZE
|
|
)
|
|
return model</code></pre>
|
|
</details>
|
|
<h3>Ancestors</h3>
|
|
<ul class="hlist">
|
|
<li><a title="miplearn.problems.knapsack.KnapsackInstance" href="#miplearn.problems.knapsack.KnapsackInstance">KnapsackInstance</a></li>
|
|
<li><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></li>
|
|
<li>abc.ABC</li>
|
|
</ul>
|
|
<h3>Inherited members</h3>
|
|
<ul class="hlist">
|
|
<li><code><b><a title="miplearn.problems.knapsack.KnapsackInstance" href="#miplearn.problems.knapsack.KnapsackInstance">KnapsackInstance</a></b></code>:
|
|
<ul class="hlist">
|
|
<li><code><a title="miplearn.problems.knapsack.KnapsackInstance.build_lazy_constraint" href="../instance.html#miplearn.instance.Instance.build_lazy_constraint">build_lazy_constraint</a></code></li>
|
|
<li><code><a title="miplearn.problems.knapsack.KnapsackInstance.find_violated_lazy_constraints" href="../instance.html#miplearn.instance.Instance.find_violated_lazy_constraints">find_violated_lazy_constraints</a></code></li>
|
|
<li><code><a title="miplearn.problems.knapsack.KnapsackInstance.get_instance_features" href="../instance.html#miplearn.instance.Instance.get_instance_features">get_instance_features</a></code></li>
|
|
<li><code><a title="miplearn.problems.knapsack.KnapsackInstance.get_variable_category" href="../instance.html#miplearn.instance.Instance.get_variable_category">get_variable_category</a></code></li>
|
|
<li><code><a title="miplearn.problems.knapsack.KnapsackInstance.get_variable_features" href="../instance.html#miplearn.instance.Instance.get_variable_features">get_variable_features</a></code></li>
|
|
<li><code><a title="miplearn.problems.knapsack.KnapsackInstance.to_model" href="../instance.html#miplearn.instance.Instance.to_model">to_model</a></code></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</dd>
|
|
<dt id="miplearn.problems.knapsack.KnapsackInstance"><code class="flex name class">
|
|
<span>class <span class="ident">KnapsackInstance</span></span>
|
|
<span>(</span><span>weights, prices, capacity)</span>
|
|
</code></dt>
|
|
<dd>
|
|
<section class="desc"><p>Simpler (one-dimensional) Knapsack Problem, used for testing.</p></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">class KnapsackInstance(Instance):
|
|
"""
|
|
Simpler (one-dimensional) Knapsack Problem, used for testing.
|
|
"""
|
|
|
|
def __init__(self, weights, prices, capacity):
|
|
super().__init__()
|
|
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(
|
|
expr=sum(model.x[v] * self.prices[v] for v in items), sense=pe.maximize
|
|
)
|
|
model.eq_capacity = pe.Constraint(
|
|
expr=sum(model.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],
|
|
]
|
|
)</code></pre>
|
|
</details>
|
|
<h3>Ancestors</h3>
|
|
<ul class="hlist">
|
|
<li><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></li>
|
|
<li>abc.ABC</li>
|
|
</ul>
|
|
<h3>Subclasses</h3>
|
|
<ul class="hlist">
|
|
<li><a title="miplearn.problems.knapsack.GurobiKnapsackInstance" href="#miplearn.problems.knapsack.GurobiKnapsackInstance">GurobiKnapsackInstance</a></li>
|
|
</ul>
|
|
<h3>Inherited members</h3>
|
|
<ul class="hlist">
|
|
<li><code><b><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></b></code>:
|
|
<ul class="hlist">
|
|
<li><code><a title="miplearn.instance.Instance.build_lazy_constraint" href="../instance.html#miplearn.instance.Instance.build_lazy_constraint">build_lazy_constraint</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.find_violated_lazy_constraints" href="../instance.html#miplearn.instance.Instance.find_violated_lazy_constraints">find_violated_lazy_constraints</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_instance_features" href="../instance.html#miplearn.instance.Instance.get_instance_features">get_instance_features</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_variable_category" href="../instance.html#miplearn.instance.Instance.get_variable_category">get_variable_category</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_variable_features" href="../instance.html#miplearn.instance.Instance.get_variable_features">get_variable_features</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.to_model" href="../instance.html#miplearn.instance.Instance.to_model">to_model</a></code></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</dd>
|
|
<dt id="miplearn.problems.knapsack.MultiKnapsackGenerator"><code class="flex name class">
|
|
<span>class <span class="ident">MultiKnapsackGenerator</span></span>
|
|
<span>(</span><span>n=<scipy.stats._distn_infrastructure.rv_frozen object>, m=<scipy.stats._distn_infrastructure.rv_frozen object>, w=<scipy.stats._distn_infrastructure.rv_frozen object>, K=<scipy.stats._distn_infrastructure.rv_frozen object>, u=<scipy.stats._distn_infrastructure.rv_frozen object>, alpha=<scipy.stats._distn_infrastructure.rv_frozen object>, fix_w=False, w_jitter=<scipy.stats._distn_infrastructure.rv_frozen object>, round=True)</span>
|
|
</code></dt>
|
|
<dd>
|
|
<section class="desc"><p>Initialize the problem generator.</p>
|
|
<p>Instances have a random number of items (or variables) and a random number of knapsacks
|
|
(or constraints), as specified by the provided probability distributions <code>n</code> and <code>m</code>,
|
|
respectively. The weight of each item <code>i</code> on knapsack <code>j</code> is sampled independently from
|
|
the provided distribution <code>w</code>. The capacity of knapsack <code>j</code> is set to:</p>
|
|
<pre><code>alpha_j * sum(w[i,j] for i in range(n)),
|
|
</code></pre>
|
|
<p>where <code>alpha_j</code>, the tightness ratio, is sampled from the provided probability
|
|
distribution <code>alpha</code>. 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 <code>i</code> is set to:</p>
|
|
<pre><code>sum(w[i,j]/m for j in range(m)) + K * u_i,
|
|
</code></pre>
|
|
<p>where <code>K</code>, the correlation coefficient, and <code>u_i</code>, the correlation multiplier, are sampled
|
|
from the provided probability distributions. Note that <code>K</code> is only sample once for the
|
|
entire instance.</p>
|
|
<p>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.</p>
|
|
<p>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.</p>
|
|
<p>By default, all generated prices, weights and capacities are rounded to the nearest integer
|
|
number. If <code>round=False</code> is provided, this rounding will be disabled.</p>
|
|
<h2 id="parameters">Parameters</h2>
|
|
<dl>
|
|
<dt><strong><code>n</code></strong> : <code>rv_discrete</code></dt>
|
|
<dd>Probability distribution for the number of items (or variables)</dd>
|
|
<dt><strong><code>m</code></strong> : <code>rv_discrete</code></dt>
|
|
<dd>Probability distribution for the number of knapsacks (or constraints)</dd>
|
|
<dt><strong><code>w</code></strong> : <code>rv_continuous</code></dt>
|
|
<dd>Probability distribution for the item weights</dd>
|
|
<dt><strong><code>K</code></strong> : <code>rv_continuous</code></dt>
|
|
<dd>Probability distribution for the profit correlation coefficient</dd>
|
|
<dt><strong><code>u</code></strong> : <code>rv_continuous</code></dt>
|
|
<dd>Probability distribution for the profit multiplier</dd>
|
|
<dt><strong><code>alpha</code></strong> : <code>rv_continuous</code></dt>
|
|
<dd>Probability distribution for the tightness ratio</dd>
|
|
<dt><strong><code>fix_w</code></strong> : <code>boolean</code></dt>
|
|
<dd>If true, weights are kept the same (minus the noise from w_jitter) in all instances</dd>
|
|
<dt><strong><code>w_jitter</code></strong> : <code>rv_continuous</code></dt>
|
|
<dd>Probability distribution for random noise added to the weights</dd>
|
|
<dt><strong><code>round</code></strong> : <code>boolean</code></dt>
|
|
<dd>If true, all prices, weights and capacities are rounded to the nearest integer</dd>
|
|
</dl></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">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)]</code></pre>
|
|
</details>
|
|
<h3>Methods</h3>
|
|
<dl>
|
|
<dt id="miplearn.problems.knapsack.MultiKnapsackGenerator.generate"><code class="name flex">
|
|
<span>def <span class="ident">generate</span></span>(<span>self, n_samples)</span>
|
|
</code></dt>
|
|
<dd>
|
|
<section class="desc"></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">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)]</code></pre>
|
|
</details>
|
|
</dd>
|
|
</dl>
|
|
</dd>
|
|
<dt id="miplearn.problems.knapsack.MultiKnapsackInstance"><code class="flex name class">
|
|
<span>class <span class="ident">MultiKnapsackInstance</span></span>
|
|
<span>(</span><span>prices, capacities, weights)</span>
|
|
</code></dt>
|
|
<dd>
|
|
<section class="desc"><p>Representation of the Multidimensional 0-1 Knapsack Problem.</p>
|
|
<p>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].</p>
|
|
<p>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.</p></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">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):
|
|
super().__init__()
|
|
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],
|
|
]
|
|
)</code></pre>
|
|
</details>
|
|
<h3>Ancestors</h3>
|
|
<ul class="hlist">
|
|
<li><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></li>
|
|
<li>abc.ABC</li>
|
|
</ul>
|
|
<h3>Inherited members</h3>
|
|
<ul class="hlist">
|
|
<li><code><b><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></b></code>:
|
|
<ul class="hlist">
|
|
<li><code><a title="miplearn.instance.Instance.build_lazy_constraint" href="../instance.html#miplearn.instance.Instance.build_lazy_constraint">build_lazy_constraint</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.find_violated_lazy_constraints" href="../instance.html#miplearn.instance.Instance.find_violated_lazy_constraints">find_violated_lazy_constraints</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_instance_features" href="../instance.html#miplearn.instance.Instance.get_instance_features">get_instance_features</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_variable_category" href="../instance.html#miplearn.instance.Instance.get_variable_category">get_variable_category</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_variable_features" href="../instance.html#miplearn.instance.Instance.get_variable_features">get_variable_features</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.to_model" href="../instance.html#miplearn.instance.Instance.to_model">to_model</a></code></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</section>
|
|
</article>
|
|
<nav id="sidebar">
|
|
<h1>Index</h1>
|
|
<div class="toc">
|
|
<ul></ul>
|
|
</div>
|
|
<ul id="index">
|
|
<li><h3>Super-module</h3>
|
|
<ul>
|
|
<li><code><a title="miplearn.problems" href="index.html">miplearn.problems</a></code></li>
|
|
</ul>
|
|
</li>
|
|
<li><h3><a href="#header-classes">Classes</a></h3>
|
|
<ul>
|
|
<li>
|
|
<h4><code><a title="miplearn.problems.knapsack.ChallengeA" href="#miplearn.problems.knapsack.ChallengeA">ChallengeA</a></code></h4>
|
|
</li>
|
|
<li>
|
|
<h4><code><a title="miplearn.problems.knapsack.GurobiKnapsackInstance" href="#miplearn.problems.knapsack.GurobiKnapsackInstance">GurobiKnapsackInstance</a></code></h4>
|
|
</li>
|
|
<li>
|
|
<h4><code><a title="miplearn.problems.knapsack.KnapsackInstance" href="#miplearn.problems.knapsack.KnapsackInstance">KnapsackInstance</a></code></h4>
|
|
</li>
|
|
<li>
|
|
<h4><code><a title="miplearn.problems.knapsack.MultiKnapsackGenerator" href="#miplearn.problems.knapsack.MultiKnapsackGenerator">MultiKnapsackGenerator</a></code></h4>
|
|
<ul class="">
|
|
<li><code><a title="miplearn.problems.knapsack.MultiKnapsackGenerator.generate" href="#miplearn.problems.knapsack.MultiKnapsackGenerator.generate">generate</a></code></li>
|
|
</ul>
|
|
</li>
|
|
<li>
|
|
<h4><code><a title="miplearn.problems.knapsack.MultiKnapsackInstance" href="#miplearn.problems.knapsack.MultiKnapsackInstance">MultiKnapsackInstance</a></code></h4>
|
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</li>
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</ul>
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</li>
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