A combined Lagrangian, linear programming, and implication heuristic for large-scale set partitioning problems

Given a nite ground set a set of subsets and costs on the subsets the set partitioning problem is to nd a minimum cost partition of the ground set Many combinatorial optimization problems can be formulated as set partitioning problems We present an approximation algorithm that produces high quality solutions in an acceptable amount of computation time The algorithm is iterative and combines problem size reduction techniques such as logical implications derived from feasibil ity and optimality conditions and reduced cost xing with a primal heuristic based on cost perturbations embedded in a Lagrangian dual framework Computational experiments illustrate the e ectiveness of the approximation algorithm