Integer and combinatorial optimization
Integer and combinatorial optimization
Optimal solution of set covering/partitioning problems using dual heuristics
Management Science
Solving airline crew scheduling problems by branch-and-cut
Management Science
Modern heuristic techniques for combinatorial problems
Tighter representations for set partitioning problems
Discrete Applied Mathematics
The C++ Programming Language, Third Edition
The C++ Programming Language, Third Edition
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Constraint Handling in Genetic Algorithms: The Set Partitioning Problem
Journal of Heuristics
A Heuristic Method for the Set Covering Problem
Operations Research
A Parallel, Linear Programming-based Heuristic for Large-Scale Set Partitioning Problems
INFORMS Journal on Computing
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Relax-and-Cut algorithms offer an alternative to strengthen Lagrangian relaxation bounds. The main idea behind these algorithms is to dynamically select and dualize inequalities (cuts) within a Lagrangian relaxation framework. This paper proposes a Relax-and-Cut algorithm for the Set Partitioning Problem. Computational tests are reported for benchmark instances from the literature. For Set Partitioning instances with integrality gaps, a variant of the classical Lagrangian relaxation is often used in the literature. It introduces a knapsack constraint to the standard formulation of the problem. Our results indicate that the proposed Relax-and-Cut algorithm outperforms the latter approach in terms of lower bound quality. Furthermore, it turns out to be very competitive in terms of CPU time. Decisive in achieving that performance was the implementation of dominance rules to manage inequalities in the cut pool. The Relax-and-Cut framework proposed here could also be used as a preprocessing tool for Linear Integer Programming solvers. Computational experiments demonstrated that the combined use of our framework and XPRESS improved the performance of that Linear Integer Programming solver for the test sets used in this study.