pso_examples.py

import numpy as np
from pyswarm import pso

###############################################################################

print('*'*65)
print('Example minimization of 4th-order banana function (no constraints)')
def myfunc(x):
    x1 = x[0]
    x2 = x[1]
    return x1**4 - 2*x2*x1**2 + x2**2 + x1**2 - 2*x1 + 5

lb = [-3, -1]
ub = [2, 6]

xopt1, fopt1 = pso(myfunc, lb, ub)

print('The optimum is at:')
print('    {}'.format(xopt1))
print('Optimal function value:')
print('    myfunc: {}'.format(fopt1))

###############################################################################

print('*'*65)
print('Example minimization of 4th-order banana function (with constraint)')
def mycon(x):
    x1 = x[0]
    x2 = x[1]
    return [-(x1 + 0.25)**2 + 0.75*x2]

xopt2, fopt2 = pso(myfunc, lb, ub, f_ieqcons=mycon)

print('The optimum is at:')
print('    {}'.format(xopt2))
print('Optimal function value:')
print('    myfunc: {}'.format(fopt2))
print('    mycon : {}'.format(mycon(xopt2)))

###############################################################################

print('*'*65)
print('Engineering example: minimization of twobar truss weight, subject to')
print('  Yield Stress <= 100 kpsi')
print('  Yield Stress <= Buckling Stress')
print('  Deflection   <= 0.25 inches')
def weight(x, *args):
    H, d, t = x  # all in inches
    B, rho, E, P = args
    return rho*2*np.pi*d*t*np.sqrt((B/2)**2 + H**2)
    
def stress(x, *args):
    H, d, t = x  # all in inches
    B, rho, E, P = args
    return (P*np.sqrt((B/2)**2 + H**2))/(2*t*np.pi*d*H)

def buckling_stress(x, *args):
    H, d, t = x  # all in inches
    B, rho, E, P = args
    return (np.pi**2*E*(d**2 + t**2))/(8*((B/2)**2 + H**2))

def deflection(x, *args):
    H, d, t = x  # all in inches
    B, rho, E, P = args
    return (P*np.sqrt((B/2)**2 + H**2)**3)/(2*t*np.pi*d*H**2*E)

def mycons(x, *args):
    strs = stress(x, *args)
    buck = buckling_stress(x, *args)
    defl = deflection(x, *args)
    return [100 - strs, buck - strs, 0.25 - defl]

B = 60  # inches
rho = 0.3  # lb/in^3
E = 30000  # kpsi
P = 66  # lb (force)
args = (B, rho, E, P)
lb = [10, 1, 0.01]
ub = [30, 3, 0.25]
xopt4, fopt4 = pso(weight, lb, ub, f_ieqcons=mycons, args=args)

print('The optimum is at:')
print('    {}'.format(xopt4))
print('Optimal function values:')
print('    weight         : {}'.format(fopt4))
print('Constraint functions:')
print('    stress         : {}'.format(stress(xopt4, *args)))
print('    buckling stress: {}'.format(buckling_stress(xopt4, *args)))
print('    deflection     : {}'.format(deflection(xopt4, *args)))