Abstract
Abstract : A primary focus of this project is on how to find quickly good solutions and tight bounds on their quality for hard combinatorial optimization and integer programming problems. One of the basic ideas is to do repeated local search by solving small integer programs defined by fixing many of the variables. We demonstrate the effectiveness of such an approach by developing and testing such an algorithm for large-scale fixed-charge network flow (FCNF) problems [1]. The solution approach combines mathematical programming algorithms with heuristic search techniques. To obtain high-quality solutions, it relies on local search with carefully chosen neighborhoods derived from the arc-based formulation of FCNF. To obtain lower bounds, the linear programming relaxation of the path-based formulation of FCNF is used and strengthened with cuts discovered during the neighborhood search.
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