Implementation of transforming a continuous problem to a mixed-integer problem by making some of its variables discrete. The integer variables are considered as bounded (any variable outside the decision space is mapped to the closest boundary point), while the continuous ones are treated as unbounded.
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Implementation of transforming a continuous problem to a mixed-integer problem by making some of its variables discrete. The integer variables are considered as bounded (any variable outside the decision space is mapped to the closest boundary point), while the continuous ones are treated as unbounded.
- Note
- The first problem->number_of_integer_variables are integer, while the rest are continuous.
The discretization works as follows. Consider the case where the interval [l, u] of the inner problem needs to be discretized to n integer values of the outer problem. First, [l, u] is discretized to n integers by placing the integers so that there is a (u-l)/(n+1) distance between them (and the border points). Then, the transformation is shifted so that the optimum aligns with the closest integer. In this way, we make sure that if the optimum is within [l, u], so are all the shifted points.
When evaluating such a problem, the x values of the integer variables are first discretized. Any value x < 0 is mapped to 0 and any value x > (n-1) is mapped to (n-1).
