Large Integer Programs: Preprocessing and Cutting Planes
All integer linear programming models are not created equal. Linear programming based branch-and-bound is the most commonly used algorithm for optimizing integer programming models. If the linear programming relaxation of the integer program is naturally integer, then no enumeration is needed. Most interesting integer programming models are not naturally integer, but reformulating or tightening the model so that the convex hull of integer solutions more closely approximates the linear programming relaxation polyhedron will greatly reduce the amount of enumeration. Williams [451, 456] was among the first to stress the importance of correctly formulating an integer program. Consider the following examples.
KeywordsValid Inequality Linear Programming Relaxation Side Constraint Coefficient Reduction Generalize Assignment Problem
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