scipy优化最小化找不到最优解

Question

我有一个约束优化问题，我有很多 我想花钱买的产品，并根据模型估算我的总回报 我为每一个产品设计。在

我在用scipy.optimzie.minimize在给定的 单个模型输出。我遇到的问题是优化器 以“optimizer terminated successfully”标志结束，但非常清楚 找不到最佳解决方案。实际上，输出使用的是原始的 seed/x0比优化器产生的输出更好。我印了个指纹 在目标函数中的语句，你可以看到它在某一点上会消失 悬崖。有没有人知道为什么会发生这种情况/如何解决它？在

我在下面列出了我的代码的简化版本。在

如果我的产品是['P1'，'P2'，…'P9']，我为他们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

^{pr2}$

我现在想优化我在每个方面的支出，以使我的总回报最大化。 要做到这一点，请使用scipy.optimize.minimize和以下函数的包装：

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

最低可复制代码：

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

和我的大多数问题一样，结果都是愚蠢的。我传递的种子值之和大于我给它的最大预算限制。因此x0与我的约束不兼容。为什么scipy没有产生相应的警告或错误，我不确定。但这才是问题所在。在

Answer 2

可能你陷入了一个局部极小值，因为你的函数似乎是非常非线性的。你有没有试过把优化方法改成BFGS。在

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

我尝试用这个算法来解决这个问题，得到了-78464.52052455483。在

希望有帮助