Multilayer variable neighborhood search for two-level uncapacitated facility location problems with single assignment

We develop a variant of the variable neighborhood search (VNS) metaheuristic called the multilayer VNS (MLVNS). It consists in partitioning the neighborhood structures into multiple layers. For each layer l , a VNS defined on the associated neighborhood structures is invoked, each move being evaluated and completed by a recursive call to the MLVNS at layer l − 1 . A specific MLVNS is developed to solve approximately a class of two‐level uncapacitated facility location problems with single assignment (TUFLPS), when only mild assumptions are imposed on the cost functions. Two special cases are used to illustrate the efficiency of the MLVNS: the classical TUFLPS and a problem with modular costs derived from a real‐life case. To assess the efficiency of the MLVNS, computational results on a large set of instances are compared with those obtained by slope scaling heuristic methods and by solving integer programming models using a state‐of‐the‐art commercial solver.