test_functions/CantileverBeam.py

import torch
import numpy as np


#
#
#   CantileverBeam: 10D objective, 11 constraints
#
#   Reference:
#     Yang XS, Hossein Gandomi A (2012) Bat algo-
#      rithm: a novel approach for global engineer-
#      ing optimization. Engineering computations
#      29(5):464–483
#
#








def CantileverBeam(individuals):

    assert torch.is_tensor(individuals) and individuals.size(1) == 10, "Input must be an n-by-10 PyTorch tensor."
    
    fx = []
    gx1 = []
    gx2 = []
    gx3 = []
    gx4 = []
    gx5 = []
    gx6 = []
    gx7 = []
    gx8 = []
    gx9 = []
    gx10 = []
    gx11 = []
    
    

    n = individuals.size(0)

    for i in range(n):
        
        x = individuals[i,:]

        
        x1 = x[0]
        x2 = x[1]
        x3 = x[2]
        x4 = x[3]
        x5 = x[4]
        x6 = x[5]
        x7 = x[6]
        x8 = x[7]
        x9 = x[8]
        x10 = x[9]
        
        P = 50000
        E = 2*107
        L = 100
        
        
        
        ## Negative sign to make it a maximization problem
        test_function = - ( x1*x6*L + x2*x7*L + x3*x8*L + x4*x9*L + x5*x10*L )
        fx.append(test_function) 
        
        ## Calculate constraints terms 
        g1 = 600 * P / (x5*x10*x10) - 14000
        g2 = 6 * P * (L*2) / (x4*x9*x9) - 14000
        g3 = 6 * P * (L*3) / (x3*x8*x8) - 14000
        g4 = 6 * P * (L*4) / (x2*x7*x7) - 14000
        g5 = 6 * P * (L*5) / (x1*x6*x6) - 14000
        g6 = P* L**3 * (1/L + 7/L + 19/L + 37/L + 61/L) / (3*E) -2.7
        g7 = x10/x5 - 20
        g8 = x9/x4 - 20
        g9 = x8/x3 - 20
        g10 = x7/x2 - 20
        g11 = x6/x1 - 20

        
        
        gx1.append( g1 )       
        gx2.append( g2 )    
        gx3.append( g3 )            
        gx4.append( g4 )
        gx5.append( g5 )       
        gx6.append( g6 )    
        gx7.append( g7 )            
        gx8.append( g8 )
        gx9.append( g9 )
        gx10.append( g10 )
        gx11.append( g11 )
    

    fx = torch.tensor(fx)
    fx = torch.reshape(fx, (len(fx),1))

    gx1 = torch.tensor(gx1)  
    gx1 = gx1.reshape((n, 1))

    gx2 = torch.tensor(gx2)  
    gx2 = gx2.reshape((n, 1))
    
    gx3 = torch.tensor(gx3)  
    gx3 = gx3.reshape((n, 1))
    
    gx4 = torch.tensor(gx4)  
    gx4 = gx4.reshape((n, 1))
    
    gx5 = torch.tensor(gx5)  
    gx5 = gx1.reshape((n, 1))

    gx6 = torch.tensor(gx6)  
    gx6 = gx2.reshape((n, 1))
    
    gx7 = torch.tensor(gx7)  
    gx7 = gx3.reshape((n, 1))
    
    gx8 = torch.tensor(gx8)  
    gx8 = gx4.reshape((n, 1))
    
    gx9 = torch.tensor(gx9)  
    gx9 = gx4.reshape((n, 1))
    
    gx10 = torch.tensor(gx10)  
    gx10 = gx4.reshape((n, 1))
    
    gx11 = torch.tensor(gx11)  
    gx11 = gx4.reshape((n, 1))
    
    

    gx = torch.cat((gx1, gx2, gx3, gx4, gx5, gx6, gx7, gx8, gx9, gx10, gx11), 1)

    
    
    return gx, fx




def CantileverBeam_Scaling(X):

    assert torch.is_tensor(X) and X.size(1) == 10, "Input must be an n-by-10 PyTorch tensor."
    
    x1 = (X[:,0] * (5-1) + 1).reshape(X.shape[0],1)
    x2 = (X[:,1] * (5-1) + 1).reshape(X.shape[0],1)
    x3 = (X[:,2] * (5-1) + 1).reshape(X.shape[0],1)
    x4 = (X[:,3] * (5-1) + 1).reshape(X.shape[0],1)
    x5 = (X[:,4] * (5-1) + 1).reshape(X.shape[0],1)
    x6 = (X[:,5] * (65-30) + 30).reshape(X.shape[0],1)
    x7 = (X[:,6] * (65-30) + 30).reshape(X.shape[0],1)
    x8 = (X[:,7] * (65-30) + 30).reshape(X.shape[0],1)
    x9 = (X[:,8] * (65-30) + 30).reshape(X.shape[0],1)
    x10 = (X[:,9] * (65-30) + 30).reshape(X.shape[0],1)
    
    X_scaled = torch.cat((x1, x2, x3, x4, x5, x6, x7, x8, x9, x10), dim=1)
    return X_scaled