In this system, all modeling related activities, such as model formulation, model instantiation, and model and instance management, are done using simple operations such as selection, projection, and predicated join. A Combined Lagrangian, Linear Programming and Implication Heuristic for Large-Scale Set Partitioning Problems Given a finite ground set, a set of subsets and costs on the subsets, the set partitioning problem is to find 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 feasibility and optimality conditions and reduced cost fixing, with a primal heuristic based on cost perturbations embedded in a Lagrangian dual framework.
Computational experiments illustrate the effectiveness of the approximation algorithm.
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