Solving Constraint Integer Programs

Detailed Description

LNS heuristic that tries to delimit the search region to a neighborhood in the constraint graph.

Gregor Hendel

Graph Induced Neighborhood Search (GINS) is a Large Neighborhood Search Heuristic that attempts to improve an incumbent solution by fixing a suitable percentage of integer variables to the incumbent and solving the resulting, smaller and presumably easier sub-MIP.

Its search neighborhoods are based on distances in a bipartite graph \(G\) with the variables and constraints as nodes and an edge between a variable and a constraint, if the variable is part of the constraint. Given an integer \(k\), the \(k\)-neighborhood of a variable \(v\) in \(G\) is the set of variables, whose nodes are connected to \(v\) by a path not longer than \(2 \cdot k\). Intuitively, a judiciously chosen neighborhood size allows to consider a local portion of the overall problem.

An initial variable selection is made by randomly sampling different neighborhoods across the whole main problem. The neighborhood that offers the largest potential for improvement is selected to become the local search neighborhood, while all variables outside the neighborhood are fixed to their incumbent solution values.

GINS also supports a rolling horizon approach, during which several local neighborhoods are considered with increasing distance to the variable selected for the initial sub-problem. The rolling horizon approach ends if no improvement could be found or a sufficient part of the problem component variables has been part of at least one neighborhood.

Definition in file heur_gins.h.

#include "scip/def.h"
#include "scip/type_retcode.h"
#include "scip/type_scip.h"

Go to the source code of this file.