If condition using Addconstrs() function
回答済みHi,
I am trying to write simple conditional constraints in gurobi on python platform as:
for i in range(N=100):
if ( xf1 - x1[i] <= 0 && yf1 - y1[i] <= 0 )
x1[i] - x2[i] < = 3
y1[i] - y2[i] < = 4
Whereas:
xf1 = final state for x1 in x-axis
yf1 = final state for y1 in y-axis
x1[i] = The position of the point 1 on each iteration of "i" on x-axis
y1[i] = The position of the point 1 on each iteration of "i" on y-axis
x2[i] = The position of the point 2 on each iteration of "i" on x-axis
y2[i] = The position of the point 2 on each iteration of "i" on y-axis
How can I convert these conditions into Gurobi constraints form in the python platform?
Kind regards,
Haris
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Hi Haris,
You cannot access the variable values when creating the model. Thus, you have to use MIP modelling techniques to formulate and \(\texttt{if}\)-statements. The stackexchange post How to write if else statement in Linear Programing? explains it very well.
First you have to formulate statement to know whether \(x_{f1} - x_1 \leq 0\) and \(y_{f1}-y_1 \leq 0\). To achieve this you can introduce 2 binary variables
\[\begin{align}
x_{f1} - x_1 &\leq M (1-\delta_x)\\
x_{f1} - x_1 &\geq 0.00001 - M \delta_x \\
y_{f1} - y_1 &\leq M (1-\delta_y)\\
y_{f1} - y_1 &\geq 0.00001 - M \delta_y\\
\delta_x,\delta_y &\in \{0,1\}
\end{align}\]
The above inequalities state that if \(\delta_x=1\), then \(x_{f1} - x_1 \leq 0\) and if \(\delta_x=0\), then \(x_{f1} - x_1 \geq 0.00001\). Same for \(\delta_y\). Note that one has to introduce a small tolerance because it is not possible to model strict inequalities in Gurobi.Next, you want to force the inequalities \(x_1 - x_2 \leq 3, y_1 - y_2 \leq 4\) only if both of the previously introduced binaries \(\delta_x,\delta_y\) equal 1. For this you can introduce a new binary variable \(\delta\) and use the addGenConstrAnd function stating that \(\delta = \delta_x \land \delta_y\). You can then use the binary variable \(\delta\) to introduce indicator constraints stating
\[\begin{align}
\delta = 1 &\rightarrow x_1 - x_2 \leq 3\\
\delta = 1 &\rightarrow y_1 - y_2 \leq 4
\end{align}\]Please note that there is no guarantee that the above formulation is best and there may be a more efficient way of formulating your problem.
Best regards,
Jaromił0 -
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Thank you so much Najman! It is really helpful!
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