RENS

[nguidotti]

This PR implements RENS (Relaxation Enforced Neighborhood Search, see [1, 2]) heuristic. RENS construct and then solve the following sub-MIP:

$$\begin{align} & z^* = \min \, \vec{c}^T \vec{x} \\ & \text{subject to} & \mathbf{A} \vec{x} = \vec{b} \\ & & l_i \leq x_i \leq u_i, \forall i \in \mathcal{N} \setminus \mathcal{I} \\ & & \lfloor \check{x}_j \rfloor \leq x_i \leq \lceil \check{x}_j \rceil, \forall i \in \mathcal{I} \\ & & \vec{x} \in \mathbb{R}^n \\ & & x_j \in \mathbb{Z}, \forall j \in \mathcal{I} \end{align}$$

where $\mathcal{N}$ is the set of all variables and $\mathcal{I}$ is the set of integer values. In essence, all integer variables with integral values are fixed, while the ones with fractional values are restricted to be rounded up or down.

This re-use the same infrastructure as RINS, i.e., it passes through presolve and can recurse. It requires some refactoring of the sub-MIP code to support these additional features.

Closes #1584.

Refences

[1] T. Berthold, “RENS: The optimal rounding,” Math. Prog. Comp., vol. 6, no. 1, pp. 33–54, Mar. 2014, doi: 10.1007/s12532-013-0060-9.
[2] T. Achterberg, “Constraint Integer Programming,” PhD, Technischen Universität Berlin, Berlin, 2007. doi: 10.14279/depositonce-1634.

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