A two-phase path-relinking algorithm for the Generalized Assignment Problem

We propose a two-phase Path-Relinking (PR) heuristic for the NP-hard Generalized Assignment Problem. The first phase of the algorithm combines LP-solving, cuts and local search for obtaining a population of solutions with guided diversity. The second phase applies the PR template to the population built at phase one. Both feasible and infeasible solutions are inserted in the reference set during combinations of PR. The trade-off between feasibility and infeasibility is controlled through a penalty coefficient for infeasibility which is dynamically updated throughout the search for maintaining a balance between feasible and infeasible solutions in the reference set. Numerical experiments on classical testbed instances of the OR-library show the practical efficiency of the method. Key-words : combinatorial optimization, assignment, heuristics.