scipy.optimize get's trapped in local minima. What can I do?

问题

 from numpy import *; from scipy.optimize import *; from math import *
def f(X):
    x=X[0];    y=X[1]
    return x**4-3.5*x**3-2*x**2+12*x+y**2-2*y

bnds = ((1,5), (0, 2))
min_test = minimize(f,[1,0.1], bounds = bnds); 
print(min_test.x)

My function f(X)has a local minima at x=2.557, y=1 which I should be able to find.

The code showed above will only give result where x=1. I have tried with different tolerance and alle three method: L-BFGS-B, TNC and SLSQP. This is the thread I have been looking at so far: Scipy.optimize: how to restrict argument values

How can I fix this?

I am using Spyder(Python 3.6).

回答1:

You just encounterd the problem with local optimization: it strongly depends on the start (initial) values you pass in. If you supply [2, 1] it will find the correct minima.

Common solutions are:

use your optimization in a loop with random starting points inside your boundaries

import numpy as np
from numpy import *; from scipy.optimize import *; from math import *

def f(X):
    x=X[0];    y=X[1]
    return x**4-3.5*x**3-2*x**2+12*x+y**2-2*y

bnds = ((1,3), (0, 2))

for i in range(100):

    x_init = np.random.uniform(low=bnds[0][0], high=bnds[0][1])
    y_init = np.random.uniform(low=bnds[1][0], high=bnds[1][1])

    min_test = minimize(f,[x_init, y_init], bounds = bnds)

    print(min_test.x, min_test.fun)

use an algorithm that can break free of local minima, I can recommend scipy's basinhopping()
use a global optimization algorithm and use it's result as initial value for a local algorithm. Recommendations are NLopt's DIRECT or the MADS algorithms (e.g. NOMAD). There is also another one in scipy, shgo, that I have no tried yet.

回答2:

Try scipy.optimize.basinhopping. It simply just repeat your minimize procedure multiple times and get multiple local minimums. The minimal one is the global minimum.

minimizer_kwargs = {"method": "L-BFGS-B"}
res=optimize.basinhopping(nethedge,guess,niter=100,minimizer_kwargs=minimizer_kwargs)

来源：https://stackoverflow.com/questions/52438263/scipy-optimize-gets-trapped-in-local-minima-what-can-i-do

标签

python

scipy

spyder

minimization