使用GpyOpt时如何添加限制条件?

问题描述

当前，我尝试使用GPyOpt来最小化功能并获得优化的参数.

Currently I try to minimize the function and get optimized parameters using GPyOpt.

import GPy
import GPyOpt
from math import log
def f(x):
    x0,x1,x2,x3,x4,x5 = x[:,0],x[:,1],x[:,2],x[:,3],x[:,4],x[:,5],
    f0 = 0.2 * log(x0)
    f1 = 0.3 * log(x1)
    f2 = 0.4 * log(x2)
    f3 = 0.2 * log(x3)
    f4 = 0.5 * log(x4)
    f5 = 0.2 * log(x5)
    return -(f0 + f1 + f2 + f3 + f4 + f5) 

bounds = [
    {'name': 'x0', 'type': 'discrete', 'domain': (1,1000000)},
    {'name': 'x1', 'type': 'discrete', 'domain': (1,1000000)},
    {'name': 'x2', 'type': 'discrete', 'domain': (1,1000000)},
    {'name': 'x3', 'type': 'discrete', 'domain': (1,1000000)},
    {'name': 'x4', 'type': 'discrete', 'domain': (1,1000000)},
    {'name': 'x5', 'type': 'discrete', 'domain': (1,1000000)}
]

myBopt = GPyOpt.methods.BayesianOptimization(f=f, domain=bounds)
myBopt.run_optimization(max_iter=100)
print(myBopt.x_opt) 
print(myBopt.fx_opt) 

我想为此功能添加限制条件.这是一个例子.

I want to add limiting conditions to this function.Here is an example.

x0 + x1 + x2 + x3 + x4 + x5 == 100000000

我应该如何修改此代码?

How should I modify this code?

推荐答案

GPyOpt仅支持c(x0, x1, ..., xn) <= 0形式的约束，因此，您最好的做法是选择一个足够小的值，并将约束表达式夹在中间"，以便你有它.假设0.1足够小，那么您可以执行以下操作:

GPyOpt only supports constrains in a form of c(x0, x1, ..., xn) <= 0, so the best you can do is to pick a small enough value and "sandwich" the constrain expression that you have with it. Let's say 0.1 is sufficiently small, then you could do this:

(x0 + x1 + x2 + x3 + x4 + x5) - 100000000 <= 0.1
(x0 + x1 + x2 + x3 + x4 + x5) - 100000000 >= -0.1

然后

(x0 + x1 + x2 + x3 + x4 + x5) - 100000000 - 0.1 <= 0
100000000 - (x0 + x1 + x2 + x3 + x4 + x5) - 0.1 <= 0

API看起来像这样:

The API would look like that:

constraints = [
    {
        'name': 'constr_1',
        'constraint': '(x[:,0] + x[:,1] + x[:,2] + x[:,3] + x[:,4] + x[:,5]) - 100000000 - 0.1'
    },
    {
        'name': 'constr_2',
        'constraint': '100000000 - (x[:,0] + x[:,1] + x[:,2] + x[:,3] + x[:,4] + x[:,5]) - 0.1'
    }
]

myBopt = GPyOpt.methods.BayesianOptimization(f=f, domain=bounds, constraints = constraints)

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