# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization # Copyright (C) 2020-2021, UChicago Argonne, LLC. All rights reserved. # Released under the modified BSD license. See COPYING.md for more details. from dataclasses import dataclass from typing import List, Dict, Optional import numpy as np import pyomo.environ as pe from overrides import overrides from scipy.stats import uniform, randint, rv_discrete from scipy.stats.distributions import rv_frozen from miplearn.instance.base import Instance @dataclass class MultiKnapsackData: prices: np.ndarray capacities: np.ndarray weights: np.ndarray 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: np.ndarray, capacities: np.ndarray, weights: np.ndarray, ) -> None: 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 @overrides def to_model(self) -> pe.ConcreteModel: model = pe.ConcreteModel() model.x = pe.Var(range(self.n), domain=pe.Binary) model.OBJ = pe.Objective( expr=sum(-model.x[j] * self.prices[j] for j in range(self.n)), sense=pe.minimize, ) 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 # noinspection PyPep8Naming class MultiKnapsackGenerator: def __init__( self, n: rv_frozen = randint(low=100, high=101), m: rv_frozen = randint(low=30, high=31), w: rv_frozen = randint(low=0, high=1000), K: rv_frozen = randint(low=500, high=501), u: rv_frozen = uniform(loc=0.0, scale=1.0), alpha: rv_frozen = uniform(loc=0.25, scale=0.0), fix_w: bool = False, w_jitter: rv_frozen = uniform(loc=1.0, scale=0.0), p_jitter: rv_frozen = uniform(loc=1.0, scale=0.0), round: bool = 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.u = u self.K = K self.alpha = alpha self.w_jitter = w_jitter self.p_jitter = p_jitter self.round = round self.fix_n: Optional[int] = None self.fix_m: Optional[int] = None self.fix_w: Optional[np.ndarray] = None self.fix_u: Optional[np.ndarray] = None self.fix_K: Optional[float] = None 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() def generate(self, n_samples: int) -> List[MultiKnapsackData]: def _sample() -> MultiKnapsackData: if self.fix_w is not None: assert self.fix_m is not None assert self.fix_n is not None assert self.fix_u is not None assert self.fix_K 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)] ) * self.p_jitter.rvs(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 MultiKnapsackData(p, b, w) return [_sample() for _ in range(n_samples)] def build_multiknapsack_model(data: MultiKnapsackData) -> pe.ConcreteModel: model = pe.ConcreteModel() m, n = data.weights.shape model.x = pe.Var(range(n), domain=pe.Binary) model.OBJ = pe.Objective( expr=sum(-model.x[j] * data.prices[j] for j in range(n)), sense=pe.minimize, ) model.eq_capacity = pe.ConstraintList() for i in range(m): model.eq_capacity.add( sum(model.x[j] * data.weights[i, j] for j in range(n)) <= data.capacities[i] ) return model