TypeError: 1.0 + 0.0007 <gurobi.Var Awaiting Model Update> is not a variable

回答済み

2023年05月18日 11:24

I want to construct the following constraint:

b_n<=(w_nWtlog2(1+c/w_n))/D_n, where b_n and w_n are decision variables, other notations, such as W, t, are constant.

Considering that the above constraint has an item 1/w_n, we firstly introduce an auxiliary variable z_n, and add a constraint z_n * w_n = 1. Specifically,

# define the decision variable w_n

w = []
for i in range(N):
    name = 'w_' + str(i)
    x = model.addVar(0.1, 1, vtype=GRB.CONTINUOUS, name=name)
    w.append(x)

# define an auxiliary variable z_n

z = []
for i in range(N):
    name = 'z_' + str(i)
    x = model.addVar(1, 10, vtype=GRB.CONTINUOUS, name=name)
    z.append(x)

# add the constraint z_n * w_n = 1, in order to instead 1/w_n with z_n

for i in range(N):
    name = 'c1_' + str(i)
    model.addConstr(z[i] * w[i] == 1, name=name)

In addition, we introduct the variable y_n in order to construct the logarithmic function:

y = []
for i in range(N):
    name = 'y_' + str(i)
    x = model.addVar(vtype=GRB.CONTINUOUS, name=name)
    y.append(x)

# construct the constraint b_n<=(w_nWtlog2(1+c/w_n))/D_n

for i in range(N):
    temp = model.addGenConstrLogA(1 + c * z[i], y[i], 2)
    R = w[i] * W * t * y[i]
    x = R/D[i]
    name = 'c2_' + str(i)
    model.addConstr(b[i] <= x, name=name)

However, the result shows the error as follows:

Great thanks for all recommendations.

7件のコメント

Maliheh Aramon

Gurobi Staff

2023年05月18日 17:21 編集済み
Hi,

A general constraint of type LogA is in the form (Var, Var, a) where Var is a Gurobi variable object and not a Gurobi Linear Expression (LinExpr).

To implement the expression \(\log_2(1+\frac{c}{w_n})\), you need to define three auxiliary variables to represent \(z = \frac{1}{w_n}\), \(v = 1+ cz\), and then \(y=\log_2(v)\).
```
w = m.addVars(N, lb=0.1, ub=1, name="w")
z = m.addVars(N, name="z")
v = m.addVars(N, name="v")
y = m.addVars(N, name="y")

m.addConstrs((z[i] * w[i] == 1 for i in range(N)), name="c_bilinear")
m.addConstrs((v[i] == 1 + c * z[i] for i in range(N)), name="c_linexpr")
for i in range(N):
    m.addGenConstrLogA(v[i], y[i], 2, name="c_log")
```
Best regards,

Maliheh
0

Rabbitutu Yang

2023年05月19日 16:13 編集済み

Hi Maliheh,

your comment helps me a lot, thank you very much!

However, I have a new problem.

The problem can be modeled as follows：

For the problem, only b_n and w_n are decision variables, other notations, such as Q_n, W_n, are constants. We have proven that the objective function and all constraints are convex.

The values of these constants are as follows：

Q = [4200, 3000, 600, 5400, 1700] # each item can be denoted as Q_n
H = [300, 1500, 300, 800, 1100] # each item can be denoted as H_n
M = [200, 300, 120, 300, 200]   # each item can be denoted as M_n
M_e = [100, 50, 70, 260, 80]    # each item can be denoted as M^e_n
M_l = [100, 250, 50, 40, 120]   # each item can be denoted as M^l_n
F_l = [5.5, 3, 7, 8, 10]        # each item can be denoted as F^l_n
D = [10, 15, 20, 25, 30]        # each item can be denoted as D_n
W = 10000
p = [7, 5, 7.5, 6, 8]          # each item can be denoted as p_n
h = [1, 1, 1, 1, 1]           # each item can be denoted as h_n
N_0 = 1

Moreover, the corresponding code is:

# define the decision variable b_n, which is the integer variable
b = W_LP.addVars(N, lb=0, ub=GRB.INFINITY, vtype=GRB.INTEGER, name="b")

# define the decision variable w_n
w = W_LP.addVars(N, lb=0.1, ub=1, vtype=GRB.CONTINUOUS, name="w")

# define the auxiliary variable z_n, so as to add the constraint z_n*w_n=1 and instead 1/w_n with z_n
z = W_LP.addVars(N, lb=1, ub=10, vtype=GRB.CONTINUOUS, name="z")

# define the auxiliary variable v_n, which can be used instead of 1+(p_n*h_n/W*N_0)/w_n in log2(1+(p_n*h_n/W*N_0)/w_n)
v = W_LP.addVars(N, name="v")

# define the auxiliary variable y_n
y = W_LP.addVars(N, name="y")

# define the auxiliary variable tmp_n
tmp = W_LP.addVars(N, name="tmp")

# construct the objective function
obj = LinExpr(0)
for i in range(N):
    a = -Q[i] * M[i] + H[i] * M_e[i]
    obj.addTerms(a, b[i])
W_LP.setObjective(obj, GRB.MINIMIZE)

# add the constraint the sum of w_n is 1 
constr_1 = LinExpr(0)
for i in range(N):
    constr_1.addTerms(1, w[i])
W_LP.addConstr(constr_1 == 1, name="w1")

# add the constraint z_n*w_n=1
W_LP.addConstrs((z[i] * w[i] == 1 for i in range(N)), name="c2_linear")

# add the constraint v_n=1+(p_n*h_n/W*N_0)/w_n
W_LP.addConstrs((v[i] == 1 + (p[i] * h[i] * z[i])/(W * N_0) for i in range(N)), name="c_linexpr")

# log2(1+(p_n*h_n/W*N_0)/w_n)
for i in range(N):
    W_LP.addGenConstrLogA(v[i], y[i], 2, name="c_log")

# b_n=min{F^l_n/M^l_n, (w_n*W*log2(1+(p_n*h_n/W*N_0)/w_n))/D_n},where the two items in min{} must be rounded down
for i in range(N):
    name = 'b_min' + str(i)
    W_LP.addConstr(tmp[i] == W_LP.addGenConstrMin(F_l[i]/M_l[i], (y[i]*w[i]*W)/D[i]), name=name)
W_LP.addConstrs((b[i] == int(tmp[i]) for i in range(N)), name="b2_min")

W_LP.optimize()

print("Obj: ", W_LP.objVal)

the bug shows that

Great thanks for your help!

Huan

Maliheh Aramon

Gurobi Staff

2023年05月20日 00:25 編集済み
Hi,

It seems that you are interested in modeling the constraint below:

\[b_n = \min \Big\{ \big\lfloor \frac{F^l_n}{M^l_n} \big\rfloor, \big\lfloor \frac{w_n W \log_2(1 + \frac{p_nh_n}{w_nWN_0})}{D_n} \big\rfloor \Big \}\]
- You have already defined the auxiliary variables \(y\) to represent \(\log_2(1 + \frac{p_nh_n}{w_nWN_0})\).
- Please note that the Python int() function can only be used on real numbers not on Gurobi expression objects.
  
  The expression \(\frac{w_n W y_n}{D_n}\) is a Gurobi QuadExpr() object. To model \(\lfloor \frac{w_n W y_n}{D_n} \rfloor\), you would need to define new auxiliary variables \(u\).
- See the code snippet below on how to implement this:
  
  The signature for the minimum general constraint is Model.addGenConstrMin(resvar, vars, constant, name)
```
u = W_LP.addVars(N, vtype=gp.GRB.INTEGER, name="u")
# Model u_i to represent the greatest integer less than y[i] * w[i] * W / D[i]
W_LP.addConstrs((u[i] <= y[i] * w[i] * W / D[i] for i in range(N)))
W_LP.addConstrs((u[i] >= y[i] * w[i] * W / D[i] - 1 for i in range(N)))

# Model b = min(int(F^l_n/M^l_n), u)
for i in range(N):
    W_LP.addGenConstrMin(b[i], [u[i]], int(F_l[i] / M_l[i]), name="b_min")
```
Please also note that your model is non-convex because of the following two constraints \(z_i w_i = 1\) and \(u_i \geq \frac{W}{D_i} y_i w_i - 1\). You would need to set the parameter NonConvex to 2.

Best regards,

Maliheh
0
Rabbitutu Yang

2023年05月20日 15:47
Your reply helps me a lot, thank you very much!!

Best regards,

Huan
0

Rabbitutu Yang

2023年08月31日 14:23

Hi Maliheh,

Sorry to disturb you again.

I met a new bug for the above mentioned problem.

During the assignment process, and the constraint with respect to v_n can be written as:

W_LP.addConstrs((v[i] == 1 + (4 * z[i] * 10**11)/(W * N_0) for i in range(N)), name="c_linexpr")

the model is infeasible.

However, if the constraint with respect to v_n is written as:

W_LP.addConstrs((v[i] == 1 + (4 * z[i] * 10**8)/(W * N_0) for i in range(N)), name="c_linexpr")

the model is feasible.

Moreover, the full code is shown as follows:

Q = [4200, 3000, 600, 5400, 1700] # each item can be denoted as Q_n 
H = [300, 1500, 300, 800, 1100] # each item can be denoted as H_n 
M = [200, 300, 120, 300, 200] # each item can be denoted as M_n 
M_e = [100, 50, 70, 260, 80] # each item can be denoted as M^e_n 
M_l = [100, 250, 50, 40, 120] # each item can be denoted as M^l_n 
F_l = [5.5, 3, 7, 8, 10] # each item can be denoted as F^l_n 
D = [10, 15, 20, 25, 30] # each item can be denoted as D_n 
W = 10000 
N_0 = 1

# define the decision variable b_n, which is the integer variable
b = W_LP.addVars(N, lb=0, ub=GRB.INFINITY, vtype=GRB.INTEGER, name="b")

# define the decision variable w_n
w = W_LP.addVars(N, lb=0.1, ub=1, vtype=GRB.CONTINUOUS, name="w")

# define auxiliary variable z_n, so as to add the constraint z_n*w_n=1 and instead 1/w_n with z_n
z = W_LP.addVars(N, vtype=GRB.CONTINUOUS, name="z")

# define the auxiliary variable v_n, which can be used instead of 1+(4*10**11/W*N_0)/w_n in log2(1+(4*10**11/W*N_0)/w_n)
v = W_LP.addVars(N, name="v")

# define the auxiliary variable y_n
y = W_LP.addVars(N, name="y")

# define the auxiliary variable u_n
u = W_LP.addVars(N, vtype=GRB.INTEGER, name="u")

# the objective function
obj = LinExpr(0)
for i in range(N):
   a = Q_t[i] * M[i] - H_t[i] * M_e[i]
   obj.addTerms(a, b[i])
W_LP.setObjective(obj, GRB.MAXIMIZE)

# add the constraint the sum of w_n is 1
constr_1 = LinExpr(0)
for i in range(N):
    constr_1.addTerms(1, w[i])
W_LP.addConstr(constr_1 == 1, name="w1")

# add the constraint z_n*w_n=1
W_LP.addConstrs((z[i] * w[i] == 1 for i in range(N)), name="c2_linear")

# add the constraint v_n=1+(4*10**11/W*N_0)/w_n
W_LP.addConstrs((v[i] == 1 + (4 * z[i] * 10**11)/(W * N_0) for i in range(N)), name="c_linexpr")

# log2(1+(4*10**11/W*N_0)/w_n)
for i in range(N):
    W_LP.addGenConstrLogA(v[i], y[i], 2, name="c_log")

# Model u_i to represent the greatest integer less than y[i] * w[i] * W / D[i]
W_LP.addConstrs((u[i] <= y[i] * w[i] * W / D[i] for i in range(N)))
W_LP.addConstrs((u[i] >= y[i] * w[i] * W / D[i] - 1 for i in range(N)))

# Model b = min(int(F^l_n/M^l_n), u)
for i in range(N):
   W_LP.addGenConstrMin(b[i], [u[i]], int(F_l[i] / M_l[i]), name="b_min")

# set the parameter NonConvex to 2
W_LP.params.NonConvex = 2

W_LP.optimize()
W_LP.computeIIS()
W_LP.write("model.ilp")

the bug shows that:

the model.ilp file shows that:

Great thanks for your help!

Huan

Maliheh Aramon

Gurobi Staff

2023年08月31日 19:10
Hi Huan,

I cannot run your code because some of the input parameters such as \(\texttt{N}\), \(\texttt{Q_t}\), and \(\texttt{H_t}\) are not included.

The IIS indicates that if you relax the upper bound of the variables \(w\) to infinity, the IIS sub-system will be feasible.

I guess the infeasibility occurs because the bounds of the variables participating in the general function constraints is limited to 1e+6 by default to guard against numerical issues. In your current snippet the variables \(v\) are greater than or equal to \(1+4 \times 10^7\) which is greater than the default value for the FuncMaxVal parameter.

Please post the complete code snippet such that I can run it.

Best regards,

Maliheh
0
Rabbitutu Yang

2023年09月01日 09:35
Hi Maliheh,

The reason you guessed that the model is not feasible is completely correct.

Based on this, I first reduced the value of v by a certain multiple, and then increased the value of y by the same multiple as y=log2(v).

In this way, the model becomes feasible and I can obtain the optimal solution.

Thank you very much for your help! ^_^
0

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TypeError: 1.0 + 0.0007 <gurobi.Var *Awaiting Model Update*> is not a variable

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TypeError: 1.0 + 0.0007 <gurobi.Var Awaiting Model Update> is not a variable