Collaborative Variable Neighborhood Search

Variable neighborhood search (VNS) is a well-known metaheuristic. Two main ingredients are needed for its design: a collection \(M=(N_1, \ldots , N_r)\) of neighborhood structures and a local search LS (often using its own single neighborhood L). M has a diversification purpose (search for unexplored zones of the solution space S), whereas LS plays an intensification role (focus on the most promising parts of S). Usually, the used set M of neighborhood structures relies on the same type of modification (e.g., change the value of i components of the decision variable vector, where i is a parameter) and they are built in a nested way (i.e., \(N_i\) is included in \(N_{i+1}\)). The more difficult it is to escape from the currently explored zone of S, the larger is i, and the more capability has the search process to visit regions of S which are distant (in terms of solution structure) from the incumbent solution. M is usually designed independently from L. In this paper, we depart from this classical VNS framework and discuss an extension, Collaborative Variable Neighborhood Search (CVNS), where the design of M and L is performed in a collaborative fashion (in contrast with nested and independent), and can rely on various and complementary types of modifications (in contrast with a common type with different amplitudes).