Very Large-Scale Neighborhood Search

Very Large-Scale Neighborhood Search is not an algorithm or a class of algorithms, but rather a conceptual framework which can be used for solving combinatorial optimization problems. The approach “concentrates on neighborhood search algorithms where the size of the neighborhood is ‘very large’ with respect to the size of the input data.” Typically, the searched neighborhoods are exponentially large, but the term has come to be used more generally to describe algorithms working on neighborhoods that are too large to explicitly search in practice. The search of the large neighborhood has often been made by dedicated mathematical programming modules, deriving from different techniques. This chapter reports on the rich literature following this approach and proposes a possible implementation for the GAP.