scipy.optimize 被困在局部最小值中.我能做什么? [英] scipy.optimize get's trapped in local minima. What can I do?

问题描述

 from numpy import *;从 scipy.optimize 导入 *;从数学导入 *定义 f(X):x=X[0];y=X[1]返回 x**4-3.5*x**3-2*x**2+12*x+y**2-2*ybnds = ((1,5), (0, 2))min_test = 最小化(f,[1,0.1], bounds = bnds);打印(min_test.x)

我的函数 f(X) 在 x=2.557, y=1 有一个局部最小值，我应该可以找到.

上面显示的代码只会给出 x=1 的结果.我尝试了不同的公差和所有三种方法:L-BFGS-B、TNC 和 SLSQP.这是到目前为止我一直在看的线程:

解决方案

您刚刚遇到了局部优化的问题:它强烈依赖于您传入的开始(初始)值.如果您提供 [2, 1] 它将找到正确的最小值.

常见的解决方案是:

• 在循环中使用您的优化，在您的边界内具有随机起点

  将 numpy 导入为 np从 numpy 导入 *;从 scipy.optimize 导入 *;从数学导入 *定义 f(X):x=X[0];y=X[1]返回 x**4-3.5*x**3-2*x**2+12*x+y**2-2*ybnds = ((1,3), (0, 2))对于我在范围内(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 = 最小化(f，[x_init，y_init]，边界 = bnds)打印(min_test.x，min_test.fun)

• 使用可以突破局部最小值的算法，推荐scipy的basinhopping()

• 使用全局优化算法并将其结果用作局部算法的初始值.建议是 NLopt 的 DIRECT 或 MADS 算法(例如 NOMAD).scipy 中还有一个，shgo，我还没试过.

 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).

解决方案

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.

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