A weird output, is it a bug of Gurobi 8.1.1?
AnsweredHi there, I am runing the following simple python code, the m.ObjVal output is 4.0, v.X is 0.01, while obviously, the minimum should be 0 if u is between 1/3 to 2/3?
My Gurobi version is 8.1.1, and there is no any error or warning when running this code, I am wondering why the result is not correct and how to change to make it work? thanks.
import gurobipy as gp
from gurobipy import GRB
def get_factor_from_usage_linear(u):
assert(u >= 0)
factor = 0.0
if u <= 0.333:
factor = 1.0
elif u <= 0.667:
factor = 3.0
elif u <= 0.9:
factor = 10.0
else:
factor = 50.0
return factor
try:
m = gp.Model("gwl")
u = m.addVar(lb=0.01, ub=0.99, vtype=GRB.CONTINUOUS, name="u")
f = get_factor_from_usage_linear(u)
# y = f * u
y = f
z = (y - 3.0) * (y - 3.0)
m.setObjective(sense=GRB.MINIMIZE, expr=z)
m.optimize()
for v in m.getVars():
print('%s %g' % (v.VarName, v.X))
print(m.ObjVal)
except gp.GurobiError as e:
print('Error code ' + str(e.errno) + ':' + str(e))
z = get_factor_from_usage_linear(0.5) - 3.0
print(z * z)
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Gurobi Staff
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You cannot use a variable object in a conditional statement like \( \texttt{if u <= 0.333} \). In a math programming model, the coefficients for variables must be deterministically given when building the model. In other words, the coefficients for a variable cannot conditionally rely on the value of that variable. In the latest version of Gurobi (9.1.1), the code throws the following error:
Constraint has no bool value (are you trying "lb <= expr <= ub"?)Fortunately, there are some modeling tricks and tools you can use to work around this. Here, you are trying to model the following piecewise-linear function:
$$f(u) = \begin{cases}1& \textrm{if }\ \phantom{1/3 \leq }\ u \leq 1/3 \\ 3 & \textrm{if }\ 1/3 < u \leq 2/3 \\ 10 & \textrm{if }\ 2/3 < u \leq 0.9 \\ 50 & \textrm{if }\ 0.9\ < u. \end{cases}$$
Below is a graph of the function:
In Gurobi's Python API, you can add a piecewise-linear constraint to your model with the Model.addGenConstrPWL() method. We introduce a new variable \( y \), then use the points defining the piecewise-linear function to add the piecewise-linear constraint \( y = f(u) \):
y = m.addVar(name='y')
upts = [0, 1/3, 1/3, 2/3, 2/3, 0.9, 0.9, 1 ]
ypts = [1, 1, 3, 3, 10, 10, 50, 50]
m.addGenConstrPWL(u, y, upts, ypts, 'pwl_u_y')With this formulation, we see one optimal solution is \( (u^*, y^*) = (1/3, 3) \). The optimal objective value is \( 0 \).
Note that due to numerical tolerances, Gurobi can pick either \( y \)-value at each "jump" in the piecewise-linear function. You can read more about this in the documentation.
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Dear Eli, thanks for your kind help and very detailed response, it is work if u is defined variable. While in my original problem, the 'u' in my code actually is a combination of other variables, for example, u = (x1 + x2 + x3)/1000, x1, x2,x3, ... are the variables that I have defined before. I have simplified 'u' in the previous code to make it simple. While now it looks like it is not a proper simplification, sorry for that.
I have tried with your suggested way in Gurobi 9.1.1, it is working well if u is a defined variable, but it isn't working if u is a linear combination of other variables, any suggestions on this, many thanks.
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You can explicitly make \( u \) a model variable, then add a constraint to the model setting \( u \) equal to your linear expression. E.g.:
u = m.addVar(name='u')
m.addConstr(u == (x[1] + x[2] + x[3])/1000)Then the piecewise-linear approach I described should work the same way.
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