2009-05-22Buch DOI: 10.18452/3027
Fenchel Decomposition for Stochastic Mixed-IntegerProgramming
This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. We derive FD cuts based on both the ﬁrst and second stage variables, and devise an FD algorithm for SMIP with binary ﬁrst stage and establish ﬁnite convergence for mixed-binary second stage. We also derive alternative FD cuts based on the second stage variables only and use an idea from disjunctive programming to lift the cuts to the higher dimension space including the ﬁrst stage variables. We then devise an FD-L algorithm based on the lifted FD cuts. Finally, we report on preliminary computational results based on example instances from the literature. The results are promising and show the lifted FD cuts to have better performance than the regular FD cuts. Furthermore, both the FD and FD-L algorithms outperform a standard solver on large-scale instances.
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