A recursive procedure to generate all cuts for 0-1 mixed integer programs
Mathematical Programming: Series A and B
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Cutting planes for mixed-integer knapsack polyhedra
Mathematical Programming: Series A and B - Special issue on computational integer programming
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
TSP Cuts Which Do Not Conform to the Template Paradigm
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Lifted Cover Inequalities for 0-1 Integer Programs: Computation
INFORMS Journal on Computing
Aggregation and Mixed Integer Rounding to Solve MIPs
Operations Research
Operations Research
Dynamic Programming
K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau
INFORMS Journal on Computing
Optimizing over the split closure
Mathematical Programming: Series A and B
Exact solutions to linear programming problems
Operations Research Letters
Two-Step MIR Inequalities for Mixed Integer Programs
INFORMS Journal on Computing
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During the last decades, much research has been conducted deriving classes of valid inequalities for single-row mixed integer programming polyhedrons. However, no such class has had as much practical success as the MIR inequality when used in cutting plane algorithms for general mixed integer programming problems. In this work we analyze this empirical observation by developing an algorithm which takes as input a point and a single-row mixed integer polyhedron, and either proves the point is in the convex hull of said polyhedron, or finds a separating hyperplane. The main feature of this algorithm is a specialized subroutine for solving the Mixed Integer Knapsack Problem which exploits cost and lexicographic dominance. Separating over the entire closure of single-row systems allows us to establish natural benchmarks by which to evaluate specific classes of knapsack cuts. Using these benchmarks on Miplib 3.0 instances we analyze the performance of MIR inequalities. Computations are performed in exact arithmetic.