Automatic integer programming reformulation using variable neighborhood search.
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Date
2017
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Abstract
Chvatal-Gomory cuts are well-known cutting planes for Integer Programming problems.
As shown in previous works, the inclusion of these cuts allows to significantly
reducing the integrality gap. This work presents a Local Search heuristic approach
based on Variable Neighborhood Search to discover violated Chv`atal-Gomory inequalities.
Since this problem is known to be NP-hard, this approach was designed
to generate violated inequalities in restricted amounts of time. Constraints are
grouped in several sets, considering the amount of common variables. These sets
are processed in parallel in order to obtain the best multipliers and produce violated
cuts. We report some preliminary results obtained for MIPLIB 3.0 and 2003
instance sets, comparing our approach with an integer programming based separation
method. Our algorithm was able to separate many violated inequalities,
reducing the duality gap. Furthermore, it uses an extended numerical precision
implementation, since it is not specifically bound to simplex based solvers.
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Keywords
Integer programs, Separation problems, Chvatal-Gomory cuts
Citation
BRITO, S. S.; SANTOS, H. G. Automatic integer programming reformulation using variable neighborhood search. Electronic Notes in Discrete Mathematics, v. 58, p. 7-14, 2017. Disponível em: <http://www.sciencedirect.com/science/article/pii/S1571065317300380>. Acesso em: 02 out. 2017.