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@ -17,44 +17,45 @@ class ChallengeA:
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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__(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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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(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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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,
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prices,
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capacities,
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weights):
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def __init__(self, prices, capacities, weights):
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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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@ -65,83 +66,92 @@ class MultiKnapsackInstance(Instance):
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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(rule=lambda model: sum(model.x[j] * self.prices[j]
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for j in range(self.n)),
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sense=pe.maximize)
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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(sum(model.x[j] * self.weights[i,j]
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for j in range(self.n)) <= self.capacities[i])
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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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np.mean(self.prices),
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self.capacities,
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])
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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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self.prices[index],
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self.weights[:, index],
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])
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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__(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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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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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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@ -168,11 +178,14 @@ class MultiKnapsackGenerator:
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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(alpha, rv_frozen), "alpha 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(w_jitter, rv_frozen), \
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"w_jitter should be a SciPy probability distribution"
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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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@ -181,7 +194,7 @@ class MultiKnapsackGenerator:
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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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@ -194,7 +207,7 @@ class MultiKnapsackGenerator:
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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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@ -211,20 +224,22 @@ class MultiKnapsackGenerator:
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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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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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self.weights = weights
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self.prices = prices
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@ -234,23 +249,29 @@ class KnapsackInstance(Instance):
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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(expr=sum(model.x[v] * self.prices[v] for v in items),
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sense=pe.maximize)
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model.eq_capacity = pe.Constraint(expr=sum(model.x[v] * self.weights[v]
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for v in items) <= self.capacity)
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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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self.capacity,
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np.average(self.weights),
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])
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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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def get_variable_features(self, var, index):
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return np.array([
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self.weights[index],
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self.prices[index],
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])
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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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@ -258,6 +279,7 @@ class GurobiKnapsackInstance(KnapsackInstance):
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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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@ -268,9 +290,11 @@ class GurobiKnapsackInstance(KnapsackInstance):
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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(gp.quicksum(x[i] * self.weights[i]
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for i in range(n)) <= self.capacity,
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"eq_capacity")
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model.setObjective(gp.quicksum(x[i] * self.prices[i]
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for i in range(n)), GRB.MAXIMIZE)
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|
|
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
|
|
|
|
|
|
