在scipy中指定fmin_cobyla的约束 [英] Specifying constraints for fmin_cobyla in scipy

问题描述

 
 
我使用Python 2.5。 从numpy import导入numpy 
 asarray 
 
 Initial = numpy.asarray [2，4，5，3]＃以
 $ b开始的初始值$ b＃绑定限制（lower，upper） - 用于可视化
 
 #bounds = [（1,5000），（1,6000），（2，100000），（1,50000）] 
 
＃实际传递边界
 
 b1 = lambda x：5000  -  x [0]＃lambda x：bounds [0] [1]  - 初始[0] 
 
 b2 = lambda x：x [0]  -  2.0＃lambda x：Initial [0]  -  bounds [0] [0] 
 
 b3 = lambda x：6000  -  x [1] ＃同上
 
 b4 =拉姆达x：x [1]  -  4.0 
 
 b5 =拉姆达x：100000  -  x [2] 
 
 b6 = lambda x：x [2]  -  5.0 
 
 b7 = lambda x：50000  -  x [3] 
 
 b8 = lambda x：x [3]  -  3.0 
 
 b9 = lambda x：x [2]> x [3]＃我的问题非常重要！ 
 
 
 opt = optimize.fmin_cobyla（func，Initial，cons = [b1，b2，b3，b4，b5，b6，b7，b8，b9，b10]，maxfun = 1500000） 
  

根据初始值初始值和as每个/在边界内 b1 到 b10 这些值传递给 opt（） code>。但是这些值是有偏差的，特别是 b9 。这是我的问题非常重要的边界条件！ $ b 传递给我的 x [2] 的值函数 opt（）在每次迭代中必须总是大于 x [3] - 怎么可能实现这一点？

在我的界限（ b1 到 b9 <



还是有更好的方法来定义我的边界吗？

请帮助我。

解决方案

fmin_cobyla（）不是内部点方法。也就是说，它会在优化运行过程中将超出界限的点（不可行点）传递给函数。

关于你将要需要解决的是， b9 和 b10 不是 fmin_cobyla（）期望。绑定函数需要返回一个正数，如果它们在边界内，则返回0.0;如果边界正好在边界上，则返回负数;如果超出边界，则返回负数。理想情况下，这些功能应该平稳。 fmin_cobyla（）将尝试取这些函数的数值导数，以便让它知道如何返回到可行区域。

  b9 = lambda x：x [2]  -  x [3] 
  

我不确定如何以 fmin_cobyla（）的方式实现 b10 但是可以使用。

I use Python 2.5.

I am passing bounds to the cobyla optimisation:

import numpy 
from numpy import asarray

Initial = numpy.asarray [2, 4, 5, 3]       # Initial values to start with

#bounding limits (lower,upper) - for visualizing

#bounds = [(1, 5000), (1, 6000), (2, 100000), (1, 50000)] 

# actual passed bounds

b1 = lambda  x: 5000 - x[0]      # lambda x: bounds[0][1] - Initial[0]

b2 = lambda  x: x[0] - 2.0       # lambda x: Initial[0] - bounds[0][0]

b3 = lambda  x: 6000 - x[1]      # same as above

b4 = lambda  x: x[1] - 4.0

b5 = lambda  x: 100000 - x[2]

b6 = lambda  x: x[2] - 5.0

b7 = lambda  x: 50000 - x[3]

b8 = lambda  x: x[3] - 3.0

b9 = lambda  x: x[2] >  x[3]  # very important condition for my problem!


opt= optimize.fmin_cobyla(func,Initial,cons=[b1,b2,b3,b4,b5,b6,b7,b8,b9,b10],maxfun=1500000)

Based on the initial values Initial and as per/within the bounds b1 to b10 the values are passed to opt(). But the values are deviating, especially with b9. This is a very important bounding condition for my problem!

"The value of x[2] passed to my function opt() at every iteration must be always greater than x[3]" -- How is it possible to achieve this?

Is there anything wrong in my bounds (b1 to b9) definition ?

Or is there a better way of defining of my bounds?

Please help me.

解决方案

fmin_cobyla() is not an interior point method. That is, it will pass points that are outside of the bounds ("infeasible points") to the function during the course of the optmization run.

On thing that you will need to fix is that b9 and b10 are not in the form that fmin_cobyla() expects. The bound functions need to return a positive number if they are within the bound, 0.0 if they are exactly on the bound, and a negative number if they are out of bounds. Ideally, these functions should be smooth. fmin_cobyla() will try to take numerical derivatives of these functions in order to let it know how to get back to the feasible region.

b9 = lambda x: x[2] - x[3]

I'm not sure how to implement b10 in a way that fmin_cobyla() will be able to use, though.

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