Question

我有一个约束优化问题，我有很多产品我想花钱并根据模型估算我的总回报我为每个单独的产品而建。

我正在使用scipy.optimzie.minimize找到给出的最佳花费个别型号输出。我遇到的问题是优化器完成“优化器终止成功”标志，但非常清楚找不到最佳解决方案。实际上，输出使用原始 seed / x0优于优化器生成的输出。我打印了一下在目标函数中的语句，你可以看到它只是下降了悬崖。有谁知道为什么会发生这种情况/如何修复它？

我在下面添加了我的代码的简化版本。

如果我的产品是['P1'，'P2'，......'P9']，我每个人都有一个模型

 # estimates returns on spend for each product
  model1 = lambda money : func1(money *betas_a)
  model2 = lambda money : func2(money,*betas_b)
  ... etc

其中func是

之一

def power_curve(x,beta1,beta2):
    return beta1*x**beta2

def mm_curve(x,beta1,beta2):
    "Beta2 >= 0"
    return (beta1*x)/(1+beta2*x)

def dbl_exponential(x,beta1,beta2,beta3,beta4):
    return beta1**(beta2**(x/beta4))*beta3

def neg_exp(x,beta1,beta2):
    "Beta2 > 0"
    return beta1*(1-np.exp(-beta2*x))

我现在想要优化我在每个方面的花费，以便最大化我的总回报。要做到这一点，请使用scipy.optimize.minimize和以下函数的包装器：

def budget(products, budget, betas, models):
  """
  Given a budget distributed across each product, estimate total returns.

  products = str: names of each individual product
  budget = list-floats: amount of money/spend corresponding to each product
  models = list-funcs: function to use to predict individual returns corresponding to each product
  betas = dict: keys are product names - values are list of betas to feed to corresponding model
  """

  results = []
  target_total = 0 # total returns

  assert len(products) == len(budget) == len(betas)

  # for each product, calculate return using corresponding model
  for v,b,m in zip(products,budget,models):
      tpred = m(b,*betas[v])
      target_total+=tpred
      results.append({'val':v,'budget':b, 'tpred':tpred})
  # if you watch this you can see it drops off dramatically towards the end
  print(target_total)
  return results, target_total

最低可重复代码：

import numpy as np
from scipy import optimize

### Setup inputs to the optimizer

vals = ['P1','P2','P3','P4','P5','P6','P7','P8','P9']

funcs = [dbl_exponential,
      mm_curve,
      power_curve,
      mm_curve,
      neg_exp,
      power_curve,
      power_curve,
      mm_curve,
      dbl_exponential]

betas = {'P1': [0.018631215601097723,0.6881958654622713,43.84956270498627,
            1002.1010110475437],
      'P2': [0.002871159199956573, 1.1388317502737174e-06],
      'P3': [0.06863672099961649, 0.7295132426289046],
      'P4': [0.009954885796211378, 3.857169894090025e-05],
      'P5': [307.624705578708, 1.4454030580404746e-05],
      'P6': [0.0875910297422766, 0.6848303282418671],
      'P7': [0.12147343508583974, 0.6573539731442877],
      'P8': [0.002789390181221983, 5.72554293489956e-07],
      'P9': [0.02826834133593836,0.8999750236756555,1494.677373273538,
            6529.1531372261725]
}

bounds = [(4953.474502264151, 14860.423506792453),
       (48189.39647820754, 144568.18943462262),
       (10243.922611886792, 30731.767835660376),
       (6904.288592358491, 20712.865777075473),
       (23440.199762641503, 70320.5992879245),
       (44043.909679905664, 132131.729039717),
       (9428.298255754717, 28284.89476726415),
       (53644.56626556605, 160933.69879669815),
       (8205.906018773589, 24617.718056320766)]

seed = [9906.949005,
     96378.792956,
     20487.845224,
     13808.577185,
     46880.399525,
     88087.81936,
     18856.596512,
     107289.132531,
     16411.812038]

wrapper = lambda b: -budget(vals,b,betas, funcs)[1] # negative to get *maximum* output

## Optimizer Settings
tol = 1e-16
maxiter = 10000
max_budget = 400000
# total spend can't exceed max budget
constraint = [{'type':'ineq', 'fun': lambda budget: max_budget-sum(budget)}]

# The output from the seed is better than the final "optimized" output
print('DEFAULT OUTPUT TOTAL:', wrapper(seed))

res = optimize.minimize(wrapper, seed, bounds = bounds,
                tol = tol, constraints = (constraint),
                options={'maxiter':maxiter})

print("Optimizer Func Output:", res.fun)

Answer 1

与我的大部分问题一样，事实证明是愚蠢的。我传递的种子值之和大于我给它的max_budget约束。因此x0与我的约束不相容。为什么scipy没有产生相应的警告或错误我不确定。但事实证明这是问题所在。

Answer 2

可能你会陷入局部最小值，因为你的函数看起来非常非线性。您是否尝试将优化方法更改为类似BFGS的方法。

res = optimize.minimize(wrapper, seed, bounds = bounds, method='BFGS',
                        tol = tol, constraints = (constraint),
                        options={'maxiter':maxiter})

我尝试使用此算法解决问题，并获得-78464.52052455483。

希望有所帮助

scipy优化最小化无法找到最佳解决方案

2 个答案: