如何解决为什么代码会以“找不到解决方案”错误和“退出：收敛到局部不可行的点问题可能不可行”而终止？
我似乎无法弄清楚为什么 IPOPT 找不到解决方案。最初，我认为这个问题是完全不可行的，但是当我将 col_total 的值减少到 161000 以下的任何数字或注释掉最后一个约束方程包含 col_total，它使用 Optimal Solution Found and a final objective value function of -161775.256826753 求解和退出。我已经使用 Artificial Bee Colony 和 Particle Swamp Optimization 技术解决了相同的最大化问题，它们分别解决并返回了至少 225000 和 226000 的最优目标值函数.可能需要另一个求解器吗？我还尝试了 APOPT、BPOPT 和 IPOPT 并修改了容差值，但目前还没有任何组合似乎有效。代码贴在下面。任何指导将不胜感激。
from gekko import GEKKO
import numpy as np
distances = np.array([[[0,0],[0,0]],\
[[155,\
[[310,[155,\
[[465,[310,\
[[620,[465,0]]])
alpha = 0.5 / np.log(30/0.075)
diam = 31
free = 7
rho = 1.2253
area = np.pi * (diam / 2)**2
min_v = 5.5
axi_max = 0.32485226746
col_total = 176542.96546512868
rat = 14
nn = 5
u_hub_lowerbound = 5.777777777777778
c_pow = 0.59230249
p_max = 0.5 * rho * area * c_pow * free**3
# Initialize Model
m = GEKKO(remote=True)
#initialize variables,Set lower and upper bounds
x = [m.Var(value = 0.03902278,lb = 0,ub = axi_max) \
for i in range(nn)]
# i = 0
b = 1
c = 0
v_s = list()
for i in range(nn-1): # Loop runs for nn-1 times
# print(i)
# print(i,b,c)
squared_defs = list()
while i < b:
d = distances[b][c][0]
r = distances[b][c][1]
ss = (2 * (alpha * d) / diam)
tt = r / ((diam/2) + (alpha * d))
squared_defs.append((2 * x[i] / (1 + ss**2)) * np.exp(-(tt**2)) ** 2)
i+=1
c+=1
#Equations
m.Equation((free * (1 - (sum(squared_defs))**0.5)) - rat <= 0)
m.Equation((free * (1 - (sum(squared_defs))**0.5)) - u_hub_lowerbound >= 0)
v_s.append(free * (1 - (sum(squared_defs))**0.5))
squared_defs.clear()
b+=1
c=0
# Inserts free as the first item on the v_s list to
# increase len(v_s) to nn,so that 'v_s' and 'x'
# are of same length
v_s.insert(0,free)
gamma = list()
for i in range(len(x)):
bet = (4*x[i]*((1-x[i])**2) * rho * area) / 2
gam = bet * v_s[i]**3
gamma.append(gam)
#Equations
m.Equation(x[i] - axi_max <= 0)
m.Equation((((4*x[i]*((1-x[i])**2) * rho * area) / 2) \
* v_s[i]**3) - p_max <= 0)
m.Equation((((4*x[i]*((1-x[i])**2) * rho * area) / 2) * \
v_s[i]**3) > 0)
#Equation
m.Equation(col_total - sum(gamma) <= 0)
#Objective
y = sum(gamma)
m.Maximize(y) # Maximize
#Set global options
m.options.IMODE = 3 #steady state optimization
#Solve simulation
m.options.soLVER = 3
m.solver_options = ['linear_solver ma27','mu_strategy adaptive','max_iter 2500','tol 1.0e-5' ]
m.solve()
解决方法
在表达式中构建没有 .value 的方程。 x[i].value 仅在解完成后查看解或初始化x[i] 的值时才需要。表达式 m.Maximize(y) 比 m.Obj(-y) 更易读，尽管它们是等价的。
from gekko import GEKKO
import numpy as np
distances = np.array([[[0,0],[0,0]],\
[[155,\
[[310,[155,\
[[465,[310,\
[[620,[465,0]]])
alpha = 0.5 / np.log(30/0.075)
diam = 31
free = 7
rho = 1.2253
area = np.pi * (diam / 2)**2
min_v = 5.5
axi_max = 0.069262150781
col_total = 20000
p_max = 4000
rat = 14
nn = 5
# Initialize Model
m = GEKKO(remote=True)
#initialize variables,Set lower and upper bounds
x = [m.Var(value = 0.03902278,lb = 0,ub = axi_max) \
for i in range(nn)]
i = 0
b = 1
c = 0
v_s = list()
for turbs in range(nn-1): # Loop runs for nn-1 times
squared_defs = list()
while i < b:
d = distances[b][c][0]
r = distances[b][c][1]
ss = (2 * (alpha * d) / diam)
tt = r / ((diam/2) + (alpha * d))
squared_defs.append((2 * x[i] / (1 + ss**2)) \
* m.exp(-(tt**2)) ** 2)
i+=1
c+=1
#Equations
m.Equation((free * (1 - (sum(squared_defs))**0.5)) - rat <= 0)
m.Equation(min_v - (free * (1 - (sum(squared_defs))**0.5)) <= 0 )
v_s.append(free * (1 - (sum(squared_defs))**0.5))
squared_defs.clear()
b+=1
a=0
c=0
# Inserts free as the first item on the v_s list to
# increase len(v_s) to nn,so that 'v_s' and 'x'
# are of same length
v_s.insert(0,free)
beta = list()
gamma = list()
for i in range(len(x)):
bet = (4*x[i]*((1-x[i])**2) * rho * area) / 2
gam = bet * v_s[i]**3
#Equations
m.Equation((((4*x[i]*((1-x[i])**2) * rho * area) / 2) \
* v_s[i]**3) - p_max <= 0)
m.Equation((((4*x[i]*((1-x[i])**2) * rho * area) / 2) \
* v_s[i]**3) > 0)
gamma.append(gam)
#Equation
m.Equation(col_total - sum(gamma) <= 0)
#Objective
y = sum(gamma)
m.Maximize(y) # Maximize
#Set global options
m.options.IMODE = 3 #steady state optimization
#Solve simulation
m.options.SOLVER = 3
m.solve()
这给出了一个具有最大化目标 20,000 的成功解决方案：
Number of Iterations....: 12
(scaled) (unscaled)
Objective...............: -4.7394814741924645e+00 -1.9999999999929641e+04
Dual infeasibility......: 4.4698510326511536e-07 1.8862194343304290e-03
Constraint violation....: 3.8275766582203308e-11 1.2941979026166479e-07
Complementarity.........: 2.1543608536533588e-09 9.0911246952931704e-06
Overall NLP error.......: 4.6245685940749926e-10 1.8862194343304290e-03
Number of objective function evaluations = 80
Number of objective gradient evaluations = 13
Number of equality constraint evaluations = 80
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 13
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 12
Total CPU secs in IPOPT (w/o function evaluations) = 0.010
Total CPU secs in NLP function evaluations = 0.011
EXIT: Optimal Solution Found.
The solution was found.
The final value of the objective function is -19999.9999999296
---------------------------------------------------
Solver : IPOPT (v3.12)
Solution time : 3.210000000399305E-002 sec
Objective : -19999.9999999296
Successful solution
---------------------------------------------------
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