Abstract
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, and cutting planes. Computational experiments illustrate the effectiveness of the approximation algorithm.
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Atamtürk, A., Nemhauser, G.L. & Savelsbergh, M.W.P. A combined Lagrangian, linear programming, and implication heuristic for large-scale set partitioning problems. J Heuristics 1, 247–259 (1996). https://doi.org/10.1007/BF00127080
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DOI: https://doi.org/10.1007/BF00127080