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190 lines
7.4 KiB
190 lines
7.4 KiB
# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
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# Copyright (C) 2020-2022, 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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from dataclasses import dataclass
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from typing import List, Optional, Union
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import gurobipy as gp
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import numpy as np
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from gurobipy import GRB
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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.io import read_pkl_gz
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from miplearn.solvers.gurobi import GurobiModel
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@dataclass
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class MultiKnapsackData:
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"""Data for the multi-dimensional knapsack problem
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Args
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----
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prices
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Item prices.
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capacities
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Knapsack capacities.
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weights
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Matrix of item weights.
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"""
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prices: np.ndarray
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capacities: np.ndarray
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weights: np.ndarray
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# noinspection PyPep8Naming
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class MultiKnapsackGenerator:
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"""Random instance generator for the multi-dimensional knapsack problem.
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Instances have a random number of items (or variables) and a random number of
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knapsacks (or constraints), as specified by the provided probability
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distributions `n` and `m`, respectively. The weight of each item `i` on knapsack
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`j` is sampled independently from the provided distribution `w`. The capacity of
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knapsack `j` is set to ``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`.
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To make the instances more challenging, the costs of the items are linearly
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correlated to their average weights. More specifically, the weight of each item
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`i` is set to ``sum(w[i,j]/m for j in range(m)) + K * u_i``, where `K`,
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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
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for the entire instance.
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If `fix_w=True`, then `weights[i,j]` are kept the same in all generated
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instances. This also implies that n and m are kept fixed. Although the prices and
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capacities are derived from `weights[i,j]`, as long as `u` and `K` are not
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constants, the generated instances will still not be completely identical.
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If a probability distribution `w_jitter` is provided, then item weights will be
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set to ``w[i,j] * gamma[i,j]`` where `gamma[i,j]` is sampled from `w_jitter`.
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When combined with `fix_w=True`, this argument may be used to generate instances
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where the weight of each item is roughly the same, but not exactly identical,
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across all instances. The prices of the items and the capacities of the knapsacks
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will be calculated as above, but using these perturbed weights instead.
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By default, all generated prices, weights and capacities are rounded to the
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nearest integer number. If `round=False` is provided, this rounding will be
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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
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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
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integer.
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"""
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def __init__(
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self,
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n: rv_frozen = randint(low=100, high=101),
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m: rv_frozen = randint(low=30, high=31),
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w: rv_frozen = randint(low=0, high=1000),
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K: rv_frozen = randint(low=500, high=501),
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u: rv_frozen = uniform(loc=0.0, scale=1.0),
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alpha: rv_frozen = uniform(loc=0.25, scale=0.0),
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fix_w: bool = False,
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w_jitter: rv_frozen = uniform(loc=1.0, scale=0.0),
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p_jitter: rv_frozen = uniform(loc=1.0, scale=0.0),
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round: bool = True,
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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.u = u
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self.K = K
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self.alpha = alpha
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self.w_jitter = w_jitter
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self.p_jitter = p_jitter
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self.round = round
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self.fix_n: Optional[int] = None
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self.fix_m: Optional[int] = None
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self.fix_w: Optional[np.ndarray] = None
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self.fix_u: Optional[np.ndarray] = None
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self.fix_K: Optional[float] = None
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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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def generate(self, n_samples: int) -> List[MultiKnapsackData]:
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def _sample() -> MultiKnapsackData:
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if self.fix_w is not None:
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assert self.fix_m is not None
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assert self.fix_n is not None
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assert self.fix_u is not None
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assert self.fix_K 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(
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[w[:, j].sum() / m + K * u[j] for j in range(n)]
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) * self.p_jitter.rvs(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 MultiKnapsackData(p, b, w)
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return [_sample() for _ in range(n_samples)]
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def build_multiknapsack_model(data: Union[str, MultiKnapsackData]) -> GurobiModel:
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"""Converts multi-knapsack problem data into a concrete Gurobipy model."""
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if isinstance(data, str):
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data = read_pkl_gz(data)
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assert isinstance(data, MultiKnapsackData)
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model = gp.Model()
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m, n = data.weights.shape
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x = model.addMVar(n, vtype=GRB.BINARY, name="x")
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model.addConstr(data.weights @ x <= data.capacities)
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model.setObjective(-data.prices @ x)
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model.update()
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return GurobiModel(model)
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