228 lines
10 KiB
Python
228 lines
10 KiB
Python
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import numpy
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import numpy as np
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class GeneticAlgorithm:
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"""Genetic algorithm.
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Implementation of the real-valued Genetic algorithm. The mutations are
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normally distributed perturbations, the selection mechanism is a tournament
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selection, and the crossover oepration is the standard linear combination
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taken at a randomly generated cutting point.
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The total number of evaluations are popsize x ngen
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:param function: Function that can be used to evaluate the entire
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population. It needs to take an input of size pop_size x dim and
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return a numpy.array of size pop_size x 1
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:type function: Object
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:param dim: Number of dimensions
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:type dim: int
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:param lb: Lower variable bounds, of length dim
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:type lb: numpy.array
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:param ub: Lower variable bounds, of length dim
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:type ub: numpy.array
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:param int_var: List of indices with the integer valued variables
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(e.g., [0, 1, 5])
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:type int_var: list
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:param pop_size: Population size
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:type pop_size: int
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:param num_gen: Number of generations
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:type num_gen: int
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:param start: Method for generating the initial population
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:type start: string
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:ivar nvariables: Number of variables (dimensions)
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:ivar nindividuals: population size
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:ivar lower_boundary: lower bounds for the optimization problem
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:ivar upper_boundary: upper bounds for the optimization problem
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:ivar integer_variables: List of variables that are integer valued
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:ivar start: Method for generating the initial population
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:ivar sigma: Perturbation radius. Each pertubation is N(0, sigma)
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:ivar p_mutation: Mutation probability (1/dim)
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:ivar tournament_size: Size of the tournament (5)
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:ivar p_cross: Cross-over probability (0.9)
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:ivar ngenerations: Number of generations
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:ivar function: Object that can be used to evaluate the objective function
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"""
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def __init__(self, function, dim, lb, ub, int_var=None, pop_size=20, num_gen=300, start="Random"):
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self.nvariables = dim # column
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self.nindividuals = pop_size + (pop_size % 2) # Make sure this is even row
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self.lower_boundary = np.array(lb)
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self.upper_boundary = np.array(ub)
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self.integer_variables = []
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if int_var is not None:
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self.integer_variables = np.array(int_var)
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self.start = start
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self.sigma = 0.2
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self.p_mutation = 1.0 / dim
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self.tournament_size = 5
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self.p_cross = 0.9
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self.ngenerations = num_gen
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self.function = function
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def optimize(self):
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"""Method used to run the Genetic algorithm
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:return: Returns the best individual and its function value
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:rtype: numpy.array, float
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"""
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# Initialize population
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if isinstance(self.start, np.ndarray):
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if self.start.shape[0] != self.nindividuals or self.start.shape[1] != self.nvariables:
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raise ValueError("Initial population has incorrect size")
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if any(np.min(self.start, axis=0) < self.lower_boundary) or any(
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np.max(self.start, axis=0) > self.upper_boundary
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):
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raise ValueError("Initial population is outside the domain", self.lower_boundary, self.upper_boundary,
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self.start)
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population = self.start
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elif self.start == "SLHD":
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from pySOT.experimental_design import SymmetricLatinHypercube
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exp_des = SymmetricLatinHypercube(self.nvariables, self.nindividuals)
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population = self.lower_boundary + exp_des.generate_points() * (self.upper_boundary - self.lower_boundary)
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elif self.start == "LHD":
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from pySOT.experimental_design import LatinHypercube
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exp_des = LatinHypercube(self.nvariables, self.nindividuals)
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population = self.lower_boundary + exp_des.generate_points() * (self.upper_boundary - self.lower_boundary)
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elif self.start == "Random":
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population = self.lower_boundary + np.random.rand(self.nindividuals, self.nvariables) * (
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self.upper_boundary - self.lower_boundary
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)
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else:
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raise ValueError("Unknown argument for initial population")
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new_population = []
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# Round positions
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if len(self.integer_variables) > 0: # 对特定列进行操作
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new_population = np.copy(population)
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population[:, self.integer_variables] = np.round(population[:, self.integer_variables])
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for i in self.integer_variables:
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ind = np.where(population[:, i] < self.lower_boundary[i])
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population[ind, i] += 1
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ind = np.where(population[:, i] > self.upper_boundary[i])
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population[ind, i] -= 1
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# Evaluate all individuals
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# function_values = self.function(population) we cannot compute in this way to ensure x is one-dim in policy
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n_row, n_dim = population.shape
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function_values = []
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for r in range(n_row):
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function_values.append(self.function(population[r, :]))
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function_values = np.array(function_values)
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if len(function_values.shape) == 2:
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function_values = np.squeeze(np.asarray(function_values))
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# Save the best individual
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ind = np.argmin(function_values)
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best_individual = np.copy(population[ind, :]) # 找到最优个体
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best_value = function_values[ind]
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if len(self.integer_variables) > 0:
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population = new_population
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# Main loop
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for _ in range(self.ngenerations):
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print('------------------------------')
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print("当前为第{}代".format(_))
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print("最优个体为:{}".format(best_individual))
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print("最优值为:{}".format(best_value))
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print("------------------------------")
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# Do tournament selection to select the parents
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competitors = np.random.randint(0, self.nindividuals, (self.nindividuals, self.tournament_size))
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ind = np.argmin(function_values[competitors], axis=1)
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winner_indices = np.zeros(self.nindividuals, dtype=int)
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for i in range(self.tournament_size): # This loop is short
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winner_indices[np.where(ind == i)] = competitors[np.where(ind == i), i]
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parent1 = population[winner_indices[0: self.nindividuals // 2], :]
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parent2 = population[winner_indices[self.nindividuals // 2: self.nindividuals], :]
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# Averaging Crossover
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cross = np.where(np.random.rand(self.nindividuals // 2) < self.p_cross)[0]
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nn = len(cross) # Number of crossovers
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alpha = np.random.rand(nn, 1)
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# Create the new chromosomes
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parent1_new = np.multiply(alpha, parent1[cross, :]) + np.multiply(1 - alpha, parent2[cross, :])
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parent2_new = np.multiply(alpha, parent2[cross, :]) + np.multiply(1 - alpha, parent1[cross, :])
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parent1[cross, :] = parent1_new
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parent2[cross, :] = parent2_new
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population = np.concatenate((parent1, parent2))
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# Apply mutation
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scale_factors = self.sigma * (self.upper_boundary - self.lower_boundary) # Scale
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perturbation = np.random.randn(self.nindividuals, self.nvariables) # Generate perturbations
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perturbation = np.multiply(perturbation, scale_factors) # Scale accordingly
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perturbation = np.multiply(
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perturbation, (np.random.rand(self.nindividuals, self.nvariables) < self.p_mutation)
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)
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perturbation = round_vars(perturbation, self.integer_variables, self.lower_boundary, self.upper_boundary)
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population = round_vars(population, self.integer_variables, self.lower_boundary, self.upper_boundary)
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population += perturbation # Add perturbation
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population = np.maximum(np.reshape(self.lower_boundary, (1, self.nvariables)), population)
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population = np.minimum(np.reshape(self.upper_boundary, (1, self.nvariables)), population)
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# Round chromosomes
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new_population = []
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if len(self.integer_variables) > 0:
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new_population = np.copy(population)
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population = round_vars(population, self.integer_variables, self.lower_boundary, self.upper_boundary)
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# Keep the best individual
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population[0, :] = best_individual
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# Evaluate all individuals
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# function_values = self.function(population) we cannot compute in this way to ensure x is one-dim in policy
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n_row, n_dim = population.shape
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function_values = []
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for r in range(n_row):
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function_values.append(self.function(population[r, :]))
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function_values = np.array(function_values)
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if len(function_values.shape) == 2:
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function_values = np.squeeze(np.asarray(function_values))
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# Save the best individual
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ind = np.argmin(function_values)
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best_individual = np.copy(population[ind, :])
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best_value = function_values[ind]
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# Use the positions that are not rounded
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if len(self.integer_variables) > 0:
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population = new_population
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# return best_individual, best_value
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def round_vars(x: np.ndarray, int_var, lb, ub):
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"""Round integer variables to closest integer in the domain.
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:param x: Set of points, of size npts x dim
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:type x: numpy.array
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:param int_var: Set of indices of integer variables
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:type int_var: numpy.array
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:param lb: Lower bounds, of size 1 x dim
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:type lb: numpy.array
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:param ub: Upper bounds, of size 1 x dim
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:type ub: numpy.array
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:return: The set of points with the integer variables
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rounded to the closest integer in the domain
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:rtype: numpy.array
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"""
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# Make sure we don't violate the bound constraints
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for i in int_var:
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ind = np.where(x[:, i] < lb[i])
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x[ind, i] = lb[i]
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ind = np.where(x[:, i] > ub[i])
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x[ind, i] = ub[i]
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if len(int_var) > 0:
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# Round the original ranged integer variables
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x[:, int_var] = np.round(x[:, int_var])
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x = x.astype(numpy.int32, copy=True)
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else:
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x = x.astype(numpy.float64, copy=True)
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return x
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