Stabilized dynamic constraint aggregation for solving set partitioning problems

Pascal Benchimol, Guy Desaulniers and Jacques Desrosiers

European Journal of Operational Research, 2012, vol. 223, issue 2, 360-371

Abstract: Dynamic constraint aggregation (DCA) and dual variable stabilization (DVS) are two methods that can reduce the negative impact of degeneracy when solving linear programs. The first uses a projection to reduce the primal space whereas the second acts in the dual space. In this paper, we develop a new method, called stabilized dynamic constraint aggregation (SDCA), that combines DCA and DVS for solving set partitioning problems. It allows to fight degeneracy from both primal and dual perspectives simultaneously. To assess the effectiveness of SDCA, we report computational results obtained for highly degenerate multi-depot vehicle scheduling problem instances solved by column generation. These results indicate that SDCA can reduce the average computational time of the master problem by a factor of up to 7 with respect to the best of the two combined methods. Furthermore, they show that its performance is robust with regard to increasing levels of degeneracy in test problems.

Keywords: Primal degeneracy; Set partitioning; Dynamic constraint aggregation; Dual variable stabilization; Column generation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:223:y:2012:i:2:p:360-371

DOI: 10.1016/j.ejor.2012.07.004

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