如何解决如何使用 Google 的 CP-SAT 求解器计算“AddAbsEquality”或“AddMultiplicationEqualit”进行非线性优化?
我的目标是根据预测序列恢复数据序列。假设原始数据序列是 x_org = [10,20,30,40,50] 但我收到的随机数据为 x_ran = [50,10,30]。现在,我的目标是通过让它们最接近原始模式来恢复模式(最小化恢复损失)。
我使用了与 Google OR-tool 网站 [https://developers.google.com/optimization/assignment/assignment_teams] 上提供的“Assignment with Teams of Workers”和“Solving an Optimization Problem”几乎相似的方法,以及[https://developers.google.com/optimization/cp/integer_opt_cp]。
我可以最小化损失的总和(误差),但无法计算平方和/绝对和。
from ortools.sat.python import cp_model
x_org = [10,50]
x_ran = [50,30]
n = len(x_org)
model = cp_model.CpModel()
# Defidning recovered data
x_rec = [model.NewIntvar(0,10000,'x_rec_%i') for i in range(n)]
# Defidning recovery loss
x_loss = [model.NewIntvar(0,'x_loss_%i' % i) for i in range(n)]
# Defining a (recovery) mapping matrix
M = {}
for i in range(n):
for j in range(n):
M[i,j] = model.NewBoolVar('M[%i,%i]' % (i,j))
# -----------------Constraints---------------%
# Each sensor is assigned one unique measurement.
for i in range(n):
model.Add(sum([M[i,j] for j in range(n)]) == 1)
# Each measurement is assigned one unique sensor.
for j in range(n):
model.Add(sum([M[i,j] for i in range(n)]) == 1)
# Recovering the remapped data x_rec=M*x_ran (like,Ax =b)
for i in range(n):
model.Add(x_rec[i] == sum([M[i,j]*x_ran[j] for j in range(n)]))
# Loss = orginal data - recovered data
for i in range(n):
x_loss[i] = x_org[i] - x_rec[i]
# minimizing recovery loss
model.Minimize(sum(x_loss))
#--------------- Calling solver -------------%
# Solves and prints out the solution.
solver = cp_model.cpsolver()
status = solver.solve(model)
print('Solve status: %s' % solver.StatusName(status))
if status == cp_model.OPTIMAL:
print('Optimal objective value: %i' % solver.ObjectiveValue())
for i in range(n):
print('x_loss[%i] = %i' %(i,solver.Value(x_loss[i])))
那么没有绝对误差和的输出是:
Solve status: OPTIMAL
Optimal objective value: 0
x_loss[0] = -10
x_loss[1] = -30
x_loss[2] = 0
x_loss[3] = 30
x_loss[4] = 10
这表明即使损失总和为零,恢复也不正确。但是,当我尝试添加另一个int变量来存储损失的绝对值时[如下图],编译器报错。
# Defidning abs recovery loss
x_loss_abs = [model.NewIntvar(0,'x_loss_abs_%i' % i) for i in range(n)]
# Loss = orginal data - recovered data
for i in range(n):
model.AddAbsEquality(x_loss_abs[i],x_loss[i])
#model.AddMultiplicationEquality(x_loss_abs[i],[x_loss[i],x_loss[i]])
回溯的错误是:
TypeError Traceback (most recent call last)
<ipython-input-42-2a043a8fef8b> in <module>
3 # Loss = orginal data - recovered data
4 for i in range(n):
----> 5 model.AddAbsEquality(x_loss_abs[i],x_loss[i])
~/anaconda3/envs/tensorgpu/lib/python3.7/site-packages/ortools/sat/python/cp_model.py in AddAbsEquality(self,target,var)
1217 ct = Constraint(self.__model.constraints)
1218 model_ct = self.__model.constraints[ct.Index()]
-> 1219 index = self.GetorMakeIndex(var)
1220 model_ct.int_max.vars.extend([index,-index - 1])
1221 model_ct.int_max.target = self.GetorMakeIndex(target)
~/anaconda3/envs/tensorgpu/lib/python3.7/site-packages/ortools/sat/python/cp_model.py in GetorMakeIndex(self,arg)
1397 else:
1398 raise TypeError('NotSupported: model.GetorMakeIndex(' + str(arg) +
-> 1399 ')')
1400
1401 def GetorMakeBooleanIndex(self,arg):
TypeError: NotSupported: model.GetorMakeIndex((-x_rec_%i + 10))
您能否建议如何最小化恢复损失的绝对和/平方和?谢谢。
解决方法
AddAbsEquality
要求参数是变量(不是诸如 x_org[i] - x_rec[i]
之类的表达式。因此必须在使用它之前创建一个临时决策变量(此处为 v
)。以下似乎是工作:
# ...
x_loss_abs = [model.NewIntVar(0,10000,'x_loss_abs_%i' % i) for i in range(n)]
# ...
for i in range(n):
# x_loss[i] = x_org[i] - x_rec[i] # Original
v = model.NewIntVar(-1000,1000,"v") # Temporary variable
model.Add(v == x_org[i] - x_rec[i] )
model.AddAbsEquality(x_loss_abs[i],v)
# ....
model.Minimize(sum(x_loss_abs))
解决方案是(我改变了输出):
Optimal objective value: 0
x_org: [[10,20,30,40,50]]
x_rec: [10,50]
x_loss: [0,0]
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