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6

If I understand correctly, the following enforces your desired behavior: \begin{align} y_1 &= d_1 \\ y_2 &= d_2 \\ y_3 &= d_3 \\ y_4 &\ge d_1 + d_2 - 1\\ y_5 &\ge d_1 + d_2 + d_3 - 2\\ \end{align} If you also want to enforce $y_4 \implies (d_1 \land d_2)$ and $y_5 \implies (d_1 \land d_2 \land d_3)$, then include these additional ...

5

If I understand correctly, you can obtain the desired linear constraints via conjunctive normal form. Explicitly, suppose $f(\bar{x}_1,\dots,\bar{x}_n)=1$, and let $S_0 = \{j\in\{1,\dots,n\}:\bar{x}_j = 0\}$ and $S_1 = \{j\in\{1,\dots,n\}:\bar{x}_j = 1\}$. You want to enforce \left[\left(\bigwedge_{j\in S_0} \lnot x_j\right) \bigwedge \left(\bigwedge_{j\...

3

You are not going to be able to add these logs and quadratic terms to the model via simple double-sided big-M constraints, as they generate non-convex use of convex quadratics and logs, and CVX does not support that. The use of the squared log is not possible either. I don't think it supports automatic modelling of nonconvex use of abs operator either. Most ...

1

Assuming that the routing of the vehicles is part of the solution, you will likely need a ton of binary variables. The binary variables will determine both which vehicles serve which stations and also the sequencing. There are multiple ways to approach this. For instance, you might have $x_{ij}=1$ if vehicle $i$ serves station $j$ and $y_{jk}=1$ if station \$...

1

{0,1}-ILP can be rewritten as Pseudo-Boolean programming or MAX-Sat. It might be worth to explore alternative solving technologies for your problem.

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