currently I'm working on a wind farm layout optimization problem. I found an appropriate model in literature (Fischetti et al.) and now I'm trying to reproduce it using the Python API of cplex with DOCPlex. The model looks like the following:

$\begin{align} \text{max} \ z = \sum_{i \in V} (P_i x_i - w_i) \end{align}$


$\begin{align} N_ {min} \le \sum_{i \in V} x_i \le N_{max} \\\\ x_i + x_j \le 1 \qquad (i,j) \in E_I \tag{eqn of interest}\\\\ \sum_{j \in V} I_{i,j} x_j \le w_i + M_i (1-x_i) \quad i \in V \\\\ w_i \in \{0,1\} \quad i \in V \\\\ w_i \ge 0 \quad i \in V \end{align}$

with the corresponding set $E_I$: $\begin{equation} \{(i,j): i,j \in V, dist(i,j) < D_{min}, i \neq j\} \end{equation}$

From my understanding, this constraint ensures the mininum distance $D_{min}$ is achieved by comparing the current iterator $i$ with all already set locations $x_j$ in the distance of $D_{min}$. If there would be a match, the eqn $x_i + x_j$ would be at least 2 (if the binary at $i$ would be set), violating the constraint. I am currently failing to add this constraint to my model in DOCcplex. If anyone could help my, by giving me a hint I would be glad.

Thank you in advance


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