python - 为什么我的模型不尊重约束？

Question

这是我的代码。我尝试按照运输模型优化从供需节点分配的水量。有两个限制条件： 需求必须至少得到供应，并且您的用水量不能超过它能够分配的供应量；但该模型不尊重此约束。

import numpy as np
from scipy.optimize import minimize, LinearConstraint, Bounds

# Data
rho = 1000
g = 9.8
C = 140.0 #roughness coefficient
J = rho*g/(float(1e6)) #constant of function

capacity = [0.3875, 0.607,  0.374,  2.404, 3.614, 2.738, 0.037, 0.17, 0.17, 2.63] #Supply data
demand = [0.768, 0.315, 0.38, 0.463, 0.094, 0.46917, 0.095, 0.129, 0.24057, 0.55, 0.03981, 0.518, 0.5, 0.5, 0.13, 0.021, 0.03721, 0.01346] #Demand data

m= len(capacity)
n = len(demand)

x0 = np.array(m*n*[1]) #Initial point for algorithm


# In[59]:


#READ L and h FROM ARCGIS !!!
L = (314376.57, 277097.9663,    253756.9869 ,265786.5632,   316712.6028,    232857.1468,    112063.9914,    135762.94,  131152.8206,    132323.662, 130317.865, 122075.3889, 19631.25154, 138142.7709, 199325.3382, 84158.4,    235101.9755,    179347.7901,
240720.646, 203442.04,  180101.061, 192130.6375,    243056.677, 159201.2212,    217305.5288,    62107.01542,    57496.89496,    58667.73631,    56661.93936, 48419.46322, 79510.13244,  99019.39624, 154407.9883,   95586.40056,    190184.6256,    134430.4403,
212852.124, 175573.5184,    152232.5389,    164262.1152,    215188.1548,    131332.6989,    189437.0064,    34238.49309,    29628.37263,    30799.21398, 28793.41703, 20761.78967,  115739.8845, 128061.9941,   151819.9124,    131816.1526,    187596.5497,    131842.3643,
156956.6541, 119678.0484,   97801.96823,    108366.6453,    159292.6849,    75437.22891,    131189.4431,    26207.94379,    30046.38946,    30022.33382, 36499.1228, 39154.16025,   165461.956, 173516.5609,    197274.4792,    181538.2241,    233051.1165,    177296.9311,
49979.50696, 36283.5152,    62559.4986, 17708.03221,    53338.17961,    39298.0475, 165299.2185,    133051.7993,    136890.245, 136866.1894,    143342.9784, 145998.0158,   272305.8115,    280360.4165,    304118.3347,    288382.0797,    339894.972, 284140.7867,
52935.33231, 128934.6503,   143847.8851,    99104.57653,    28403.13658,    116496.7582,    153039.7581,    210249.5101,    214087.9557,    214063.9001, 220540.6891,   223195.7265,    262646.9939,    357558.1272,    381316.0454,    365579.7904,    417092.6828,361338.4974,
342896.306, 305617.7003,    291163.1238, 294306.2972,   345232.3368,    261376.8808,    319481.1884,    164282.6751,    159672.5546,    160843.396, 158837.599, 150595.1229,    196032.549, 53287.46567,    18072.73241,    111682.1505,    47867.52331,    13615.3853,
205103.065, 190406.5166,    197459.3, 17835.09, 170439.194, 137982.189, 15022.6557, 168504.7907,    171893.2364,    1711869.181,    178345.9697,    181001.0072, 102411.6421,   206745.8721,    267147.8785,    174880.4788,    302924.5158,    247170.3304,
14088.98864, 175008.1185,   183668.6115, 162951.6989,   106219.1172,    123766.1215,    47423.29471,    188503.6722,    192342.1179,    192318.06,  198794.8512, 201449.8887,   157030.5306,    335812.2893,    359570.2076,    229499.3673,    395346.8449,    33959.65954,
 193562.595,    156698.3255,    120368.67,  145386.92,  197099.806, 112302.1299,    174078.01,  22972.15,   22834.548,  22898.9,    20860.1683, 27742.407,  154363.5577,    139786.9169, 163892.2097, 179394.3768,  199558.9795,    144091.4906)

h= (75, 75, 75, 75, 75, 75, 1320,   75, 75, 75, 75, 75, 898,    75, 75, 665,    75, 75,
1369,   602,    349,    602,    1966,   778,    3837,   0 ,0,   0,  0,  0,  3384,   1602,   423,    2996,   423,    423,
1028,   260,    8,  260,    1624,   437,    3496,   0,  0,  0,  0,  0,  3043,   245,    0,  2655,   0,  0,
1822,   1054,   802,    1054,   2418,   1231,   4290,   0, 0,   0,  27, 0,  3837,   1039,   637,    3449,   637,    637,
893,    0,  0,  0,  1490,   0,  3362,   126,    126,    126,    126,    126,    2908,   126,    126,    2521,   126,    126,
161,    206,    306,    306,    306,    306,    1706,   306,    306,    306,    306,    306,    1325,   306,    306,    781,    306,    306,
1952,   1185,   287,    1185,   2549,   1361,   4421,   767,    767,    767,    767,    767,    3967,   1648,   137,    3674,   585,    0,
303,    758,    758,    758,    303,    758,    842,    758,    758,    758,    758,    758,    564,    168,    168,    1550,   168,    168,
2,  384,    384,    384,    2,  384,    1205,   384,    384,    384,    384, 384,   824,    384,    384,    1829,   384,    384,
1954,   1185,   746,    1185,   2520,   1362,   4401,   466,    466,    466,    437,    437,    3974,   1175,   319,    3790,   574,    319)

K = np.zeros(m*n)
N = np.zeros(m*n)


# In[61]:

#Definition of Objetive function

def objective(x):
    global d
    sum_obj = 0.0
    for i in range(len(L)): 
        if x[i] < 0.01:
          x[i]=0
        if x[i] >= 0.276:
            d= 1.484
        elif 0.276 > x[i] >= 0.212:
            d= 1.299
        elif 0.212 > x[i] >= 0.148:
            d= 1.086
        elif 0.148 > x[i] >= 0.0975:
            d=0.881
        elif 0.0975 > x[i] >= 0.079:
            d = 0.793
        elif 0.079> x[i] >= 0.062:
            d = 0.705
        elif 0.062 > x[i] >= 0.049:
            d= 0.626
        elif 0.049 > x[i] >= 0.038:
            d= 0.555
        elif 0.038 > x[i] >= 0.030:
            d=0.494
        elif 0.030 > x[i] >= 0.024:
            d=0.441
        elif 0.024 > x[i] >= 0.0198:
            d= 0.397
        elif 0.0198 > x[i] >= 0.01565:
            d= 0.353
        elif 0.01565 > x[i] >= 0.0123:
            d= 0.313
        elif 0.0123 > x[i] >=0.0097:
            d= 0.278
        elif 0.0097 > x[i] >= 0.0077:
            d=0.247
        elif 0.0077 > x[i] >= 0.0061:
            d=0.22
        elif 0.0061 > x[i] >= 0.0049:
            d=0.198
        elif 0.0049 > x[i] >= 0.00389:
            d=0.176
        elif 0.00389 > x[i] >= 0.0032:
            d= 0.159
        elif 0.0032 > x[i] >= 0.0025 :
            d= 0.141
        elif 0.0025 > x[i] >= 0:
            d= 0.123
        K[i] = 10.674*L[i]/(C**1.852*d**4.871)
        N[i] = K[i]*x[i]**1.852*J+x[i]*J*h[i]
        sum_obj = sum_obj + N[i]
    return sum_obj

#Definition of the constraints 

GB=[]
for i in range(m):
    GB.append(n*i*[0]+n*[1]+(m-1-i)*n*[0])
P=[]
for i in range(n):
    P.append(m*(i*[0]+[1]+(n-1-i)*[0]))

DU=np.array(GB+P)

lb = np.array(m*[0] + demand) # Supply
ub = np.array(capacity + n*[np.inf]) # Demand


# In[62]:


# show initial objective
print('Initial SSE Objective: ' + str(objective(x0)))


# In[63]:


# optimize
bnds = Bounds(0.00, np.inf, keep_feasible=True)
cons = LinearConstraint(DU,lb,ub)
solution = minimize(objective,x0,method='SLSQP',constraints=cons,bounds=bnds,options={'iprint':2,'disp': True})
x = solution.x

我不知道为什么，但最后我的模型给出了节点需要的更少的水。有什么建议么 ？

标签： pythonnumpyconstraintsnonlinear-optimization