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3

Depending on the solver used, you may be able to prioritize the $x$ variables so that variables with higher indices are branched on before variables with lower indices (and elements of $x$ are branched on before any other integer variables). You may also be able to instruct the solver, after branching on $x_i$, to prioritize the child with $x_i=1$ over the ...

3

Without the entire problem description it is hard to provide a complete answer, but you will probably need a variable $x_t \in \mathbb{N}$ for the number of operators hired at time period $t$. With these variables, and taking into account the fact that once an operator is hired, he is hired for the entire time period, the extra cost at a given time $t$ ...

1

The first thing that comes to mind, is, to try to model the process in something like (timed?) colored Petri nets. Then, perhaps do some process mining and network partitioning and shortest path tree computations. As long as the search converges to a local minimum, it would be locally non-dominated. So, if you add a dimension for every position in the space, ...

2

As a partial answer, Equation 16 is a condition that leads to convergence. The replacement follows from maximization by a method that seems similar to LP rounding. I have not ran the numbers, but a factor of 3/2 seems plausible for that technique. I suppose convergence is chosen as a criterion because it doesn't know where to optimize to. I think it related ...

8

Suppose your two arrays are indexed by $I$ and $J$, and let $x_i$ be the binary variable. zero or one elements may be selected from first array: $$\sum_{i\in I} x_i \le 1 \tag1$$ zero, one, or many elements may be selected from second array: no constraint needed here if no element is selected from first array, then no element should be selected from ...

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