""" Created on Sat Feb 24 20:18:05 2019 @author: Raneem """ import numpy import random import time import sys from .solution import solution def crossoverPopulaton(population, scores, popSize, crossoverProbability, keep): """ The crossover of all individuals Parameters ---------- population : list The list of individuals scores : list The list of fitness values for each individual popSize: int Number of chrmosome in a population crossoverProbability: float The probability of crossing a pair of individuals keep: int Number of best individuals to keep without mutating for the next generation Returns ------- N/A """ # initialize a new population newPopulation = numpy.empty_like(population) newPopulation[0:keep] = population[0:keep] # Create pairs of parents. The number of pairs equals the number of individuals divided by 2 for i in range(keep, popSize, 2): # pair of parents selection parent1, parent2 = pairSelection(population, scores, popSize) crossoverLength = min(len(parent1), len(parent2)) parentsCrossoverProbability = random.uniform(0.0, 1.0) if parentsCrossoverProbability < crossoverProbability: offspring1, offspring2 = crossover(crossoverLength, parent1, parent2) else: offspring1 = parent1.copy() offspring2 = parent2.copy() # Add offsprings to population newPopulation[i] = numpy.copy(offspring1) newPopulation[i + 1] = numpy.copy(offspring2) return newPopulation def mutatePopulaton(population, popSize, mutationProbability, keep, lb, ub): """ The mutation of all individuals Parameters ---------- population : list The list of individuals popSize: int Number of chrmosome in a population mutationProbability: float The probability of mutating an individual keep: int Number of best individuals to keep without mutating for the next generation lb: list lower bound limit list ub: list Upper bound limit list Returns ------- N/A """ for i in range(keep, popSize): # Mutation offspringMutationProbability = random.uniform(0.0, 1.0) if offspringMutationProbability < mutationProbability: mutation(population[i], len(population[i]), lb, ub) def elitism(population, scores, bestIndividual, bestScore): """ This melitism operator of the population Parameters ---------- population : list The list of individuals scores : list The list of fitness values for each individual bestIndividual : list An individual of the previous generation having the best fitness value bestScore : float The best fitness value of the previous generation Returns ------- N/A """ # get the worst individual worstFitnessId = selectWorstIndividual(scores) # replace worst cromosome with best one from previous generation if its fitness is less than the other if scores[worstFitnessId] > bestScore: population[worstFitnessId] = numpy.copy(bestIndividual) scores[worstFitnessId] = numpy.copy(bestScore) def selectWorstIndividual(scores): """ It is used to get the worst individual in a population based n the fitness value Parameters ---------- scores : list The list of fitness values for each individual Returns ------- int maxFitnessId: The individual id of the worst fitness value """ maxFitnessId = numpy.where(scores == numpy.max(scores)) maxFitnessId = maxFitnessId[0][0] return maxFitnessId def pairSelection(population, scores, popSize): """ This is used to select one pair of parents using roulette Wheel Selection mechanism Parameters ---------- population : list The list of individuals scores : list The list of fitness values for each individual popSize: int Number of chrmosome in a population Returns ------- list parent1: The first parent individual of the pair list parent2: The second parent individual of the pair """ parent1Id = rouletteWheelSelectionId(scores, popSize) parent1 = population[parent1Id].copy() parent2Id = rouletteWheelSelectionId(scores, popSize) parent2 = population[parent2Id].copy() return parent1, parent2 def rouletteWheelSelectionId(scores, popSize): """ A roulette Wheel Selection mechanism for selecting an individual Parameters ---------- scores : list The list of fitness values for each individual popSize: int Number of chrmosome in a population Returns ------- id individualId: The id of the individual selected """ ##reverse score because minimum value should have more chance of selection reverse = max(scores) reverseScores = reverse - scores.copy() sumScores = sum(reverseScores) pick = random.uniform(0, sumScores) current = 0 for individualId in range(popSize): current += reverseScores[individualId] if current >= pick: return individualId def crossover(individualLength, parent1, parent2): """ The crossover operator of a two individuals Parameters ---------- individualLength: int The maximum index of the crossover parent1 : list The first parent individual of the pair parent2 : list The second parent individual of the pair Returns ------- list offspring1: The first updated parent individual of the pair list offspring2: The second updated parent individual of the pair """ # The point at which crossover takes place between two parents. crossover_point = random.randint(0, individualLength - 1) # The new offspring will have its first half of its genes taken from the first parent and second half of its genes taken from the second parent. offspring1 = numpy.concatenate( [parent1[0:crossover_point], parent2[crossover_point:]] ) # The new offspring will have its first half of its genes taken from the second parent and second half of its genes taken from the first parent. offspring2 = numpy.concatenate( [parent2[0:crossover_point], parent1[crossover_point:]] ) return offspring1, offspring2 def mutation(offspring, individualLength, lb, ub): """ The mutation operator of a single individual Parameters ---------- offspring : list A generated individual after the crossover individualLength: int The maximum index of the crossover lb: list lower bound limit list ub: list Upper bound limit list Returns ------- N/A """ mutationIndex = random.randint(0, individualLength - 1) mutationValue = random.uniform(lb[mutationIndex], ub[mutationIndex]) offspring[mutationIndex] = mutationValue def clearDups(Population, lb, ub): """ It removes individuals duplicates and replace them with random ones Parameters ---------- objf : function The objective function selected lb: list lower bound limit list ub: list Upper bound limit list Returns ------- list newPopulation: the updated list of individuals """ newPopulation = numpy.unique(Population, axis=0) oldLen = len(Population) newLen = len(newPopulation) if newLen < oldLen: nDuplicates = oldLen - newLen newPopulation = numpy.append( newPopulation, numpy.random.uniform(0, 1, (nDuplicates, len(Population[0]))) * (numpy.array(ub) - numpy.array(lb)) + numpy.array(lb), axis=0, ) return newPopulation def calculateCost(objf, population, popSize, lb, ub): """ It calculates the fitness value of each individual in the population Parameters ---------- objf : function The objective function selected population : list The list of individuals popSize: int Number of chrmosomes in a population lb: list lower bound limit list ub: list Upper bound limit list Returns ------- list scores: fitness values of all individuals in the population """ scores = numpy.full(popSize, numpy.inf) # Loop through individuals in population for i in range(0, popSize): # Return back the search agents that go beyond the boundaries of the search space population[i] = numpy.clip(population[i], lb, ub) # Calculate objective function for each search agent scores[i] = objf(population[i, :]) return scores def sortPopulation(population, scores): """ This is used to sort the population according to the fitness values of the individuals Parameters ---------- population : list The list of individuals scores : list The list of fitness values for each individual Returns ------- list population: The new sorted list of individuals list scores: The new sorted list of fitness values of the individuals """ sortedIndices = scores.argsort() population = population[sortedIndices] scores = scores[sortedIndices] return population, scores def GA(objf, lb, ub, dim, popSize, iters): """ This is the main method which implements GA Parameters ---------- objf : function The objective function selected lb: list lower bound limit list ub: list Upper bound limit list dim: int The dimension of the indivisual popSize: int Number of chrmosomes in a population iters: int Number of iterations / generations of GA Returns ------- obj s: The solution obtained from running the algorithm """ cp = 1 # crossover Probability mp = 0.01 # Mutation Probability keep = 2 # elitism parameter: how many of the best individuals to keep from one generation to the next s = solution() if not isinstance(lb, list): lb = [lb] * dim if not isinstance(ub, list): ub = [ub] * dim bestIndividual = numpy.zeros(dim) scores = numpy.random.uniform(0.0, 1.0, popSize) bestScore = float("inf") ga = numpy.zeros((popSize, dim)) for i in range(dim): ga[:, i] = numpy.random.uniform(0, 1, popSize) * (ub[i] - lb[i]) + lb[i] convergence_curve = numpy.zeros(iters) print('GA is optimizing "' + objf.__name__ + '"') timerStart = time.time() s.startTime = time.strftime("%Y-%m-%d-%H-%M-%S") for l in range(iters): # crossover ga = crossoverPopulaton(ga, scores, popSize, cp, keep) # mutation mutatePopulaton(ga, popSize, mp, keep, lb, ub) ga = clearDups(ga, lb, ub) scores = calculateCost(objf, ga, popSize, lb, ub) bestScore = min(scores) # Sort from best to worst ga, scores = sortPopulation(ga, scores) convergence_curve[l] = bestScore if l % 1 == 0: print( [ "At iteration " + str(l + 1) + " the best fitness is " + str(bestScore) ] ) timerEnd = time.time() s.bestIndividual = bestIndividual s.endTime = time.strftime("%Y-%m-%d-%H-%M-%S") s.executionTime = timerEnd - timerStart s.convergence = convergence_curve s.optimizer = "GA" s.objfname = objf.__name__ return s