Fuzzy Logic Constraints in Gurobi
AnsweredDear All,
I'm trying to insert the trapezoidal fuzzy logic as the capacity constraints in my VRP code. The initial Python code is like this:
def f(r):
a,b,c,d = (20, 30, 40, 50)
if a <= r <= b:
return ((r-a)/(b-a))
if b <= r <= c:
return 1
if c <= r <= d:
return (1-((r-a)/(b-a)))
Then the problem appeared because we have to do vectorization rather than a <= r <= b.
I'm still stuck in the vectorization for this fuzzy logic modelling.
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Official comment
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Gurobi Staff
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Hi Putri,
It is not clear to me what exactly you are trying to achieve. Could you please elaborate more on what exactly you are trying to model/implement in Gurobi?
Best regards,
Jaromił0 -
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Hi, sorry for the unclear question. I want to ask how to model the membership value of fuzzy logic in Gurobi. In my case, I want to assign the membership value (mv) based on the current quantity (x) with the parameter (a) = desired capacity and (b) = maximum capacity.
if the current quantity in vehicle <=a, then mv = 1
if the current quantity in vehicle < b, then mv = 1/ ((b-x)/(b-a))
then the mv will be included in the obj function:
mdl.setObjective(quicksum(y[i,j,k]*traveltime[i,j]*mv[k] for i,j,k in q))
note: I have 4 vehicles; i,j represent the nodes and k represent the vehicle
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Hi Putri,
Thank your for the clarification. What you are trying to model is the piecewise-linear function
\[\begin{align*}
z = \begin{cases} \frac{r-a}{b-a}&, a \leq r \leq b \\ 1&, b \leq r \leq c\\ 1 - \frac{r-a}{b-a} &, c \leq r \leq d\end{cases}
\end{align*}\]This can be implemented using the addGenConstrPWL method. I would recommend having a look at our documentation on piecewise-linear objectives where we explain modeling piecewise-linear functions.
In general, you will have to add an auxiliary variable \(z\) and compute values at the border points of the segments of the above piecewise-linear function and feed this information to the addGenConstrPWL method.
Best regards,
Jaromił0 -
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Hi Jaromil, thank you for your answer. I found this page https://stackoverflow.com/questions/64265698/add-constraint-in-gurobipy-using-conditional-decision-variable and followed the suggestion there.
It works well until I modified the code for my research and I got this error:
I've been using 'mdl' for the whole code, and this is the only error. Could you please help me?
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Hi Putri,
Python's error messages can be a bit cryptic here, and often point to the code after the issue, not the issue itself. In this case it looks like you just have a mismatched bracket at this line which causes the syntax error:
mdl.addConstr((quicksum(x[i,k]) <= z.prod([3000, 3500]))
# ^ this second bracket isn't neededBest regards,
Simon0 -
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Hi Simon,
It works! Thank you.
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Hi Putri,
Please note that with the constraints from the stackexchange post, you are modeling nothing different than a piecewise-linear function, which can be modeled automatically using Gurobi's addGenConstrPWL method. In case that you are going to model this logic more often, I would recommend having a closer look at piecewise-linear functions and their modeling in Gurobi to make your model construction easier and less error prone.
Best regards,
Jaromił0 -
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Hi Jaromil,
I think so. I revised the constraints into the following:
but I encountered a problem to define this. The x[i,k] is the current capacity and m[k] will be the returned value according to the position of x[i,k] .
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Hi Putri,
Your input does not work because you have to provide real values for x points and y points of the PWL function, i.e., no optimization variables are allowed as input for the 3rd and 4th arguments, see addGenConstrPWL documentation.
Adding your function as a PWL constraint would look something like
mdl.addGenConstrPWL(r, x, [20,30,40,40,50], [(20-20)/(30-20),(30-20)/(30-20),1,1-(40-20)/(30-20),1-(40-20)/(30-20)])
Note that I added two values for the point \(r=40\), because there is a jump at \(r=40\) from \(1\) to \(1-\frac{40-20}{30-20} = -1\). You can find all details in our documentation on piecewise-linear objectives.
Best regards,
Jaromił0 -
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Hi Jaromil,
Thank you for your great help! It's much simpler and it works!
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