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                """Grey wolf optimizer.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                Date: 11.2.2018  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                Author : Iztok Fister Jr.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                License: MIT  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                Reference paper: Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Andrew Lewis.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                "Grey wolf optimizer." Advances in engineering software 69 (2014): 46-61.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                #& Grey Wold Optimizer (GWO) source codes version 1.0 (MATLAB)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                TODO: Validation must be conducted! More tests are required!  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import random  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                __all__ = ['GreyWolfOptimizer']  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                class GreyWolfOptimizer(object):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    # pylint: disable=too-many-instance-attributes  | 
            
            
                                                                                                            
                            
            
                                                                    
                                                                                                        
            
            
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                View Code Duplication | 
                    def __init__(self, D, NP, nFES, Lower, Upper, function):  | 
            
                            
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                        self.D = D  # dimension of the problem  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.NP = NP  # population size; number of search agents  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.nFES = nFES  # number of function evaluations  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Lower = Lower  # lower bound  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Upper = Upper  # upper bound  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Fun = function  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Positions = [[0 for _i in range(self.D)]  # positions of search agents  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                          for _j in range(self.NP)]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.evaluations = 0  # evaluations counter  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        # TODO: "-inf" is in the case of maximization problems  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Alpha_pos = [0] * self.D  # init of alpha  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Alpha_score = float("inf") | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Beta_pos = [0] * self.D  # init of beta  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Beta_score = float("inf") | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Delta_pos = [0] * self.D  # init of delta  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self.Delta_score = float("inf") | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
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                    def init(self):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        # initialization of positions  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        for i in range(self.NP):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                            for j in range(self.D):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                                self.Positions[i][j] = random.random(  | 
            
            
                                                                        
                            
            
                                    
            
            
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                                ) * (self.Upper - self.Lower) + self.Lower  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    def bounds(self, position):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        for i in range(self.D):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            if position[i] < self.Lower:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                position[i] = self.Lower  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            if position[i] > self.Upper:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                position[i] = self.Upper  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return position  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    def move(self):  | 
            
                            
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                        self.init()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        while True:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            if self.evaluations == self.nFES:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                break  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            for i in range(self.NP):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                self.Positions[i] = self.bounds(self.Positions[i])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                Fit = self.Fun(self.D, self.Positions[i])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                self.evaluations = self.evaluations + 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                if Fit < self.Alpha_score:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    self.Alpha_score = Fit  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    self.Alpha_pos = self.Positions[i]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                if ((Fit > self.Alpha_score) and (Fit < self.Beta_score)):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    self.Beta_score = Fit  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    self.Beta_pos = self.Positions[i]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                if ((Fit > self.Alpha_score) and (Fit > self.Beta_score) and  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                        (Fit < self.Delta_score)):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    self.Delta_score = Fit  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    self.Delta_pos = self.Positions[i]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            a = 2 - self.evaluations * ((2) / self.nFES)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            for i in range(self.NP):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                for j in range(self.D):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    r1 = random.random()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    r2 = random.random()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    A1 = 2 * a * r1 - a  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    C1 = 2 * r2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    D_alpha = abs(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                        C1 * self.Alpha_pos[j] - self.Positions[i][j])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    X1 = self.Alpha_pos[j] - A1 * D_alpha  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    r1 = random.random()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    r2 = random.random()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    A2 = 2 * a * r1 - a  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    C2 = 2 * r2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    D_beta = abs(C2 * self.Beta_pos[j] - self.Positions[i][j])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    X2 = self.Beta_pos[j] - A2 * D_beta  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    r1 = random.random()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    r2 = random.random()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    A3 = 2 * a * r1 - a  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    C3 = 2 * r2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    D_delta = abs(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                        C3 * self.Delta_pos[j] - self.Positions[i][j])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    X3 = self.Delta_pos[j] - A3 * D_delta  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                    self.Positions[i][j] = (X1 + X2 + X3) / 3  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self.Alpha_score  | 
            
            
                                                        
            
                                    
            
            
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