A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs

Dajun Yue, Jiyao Gao, Bo Zeng and Fengqi You ()
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Dajun Yue: Northwestern University
Jiyao Gao: Cornell University
Bo Zeng: University of Pittsburgh
Fengqi You: Cornell University

Journal of Global Optimization, 2019, vol. 73, issue 1, No 2, 27-57

Abstract: Abstract We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level problems. In particular, we consider MIBLPs with upper-level constraints that involve lower-level variables. We assume that the inducible region is nonempty and all variables are bounded. By using the reformulation and decomposition scheme, an MIBLP is first converted into its equivalent single-level formulation, then computed by a column-and-constraint generation based decomposition algorithm. The solution procedure is enhanced by a projection strategy that does not require the relatively complete response property. To ensure its performance, we prove that our new method converges to the global optimal solution in a finite number of iterations. A large-scale computational study on random instances and instances of hierarchical supply chain planning are presented to demonstrate the effectiveness of the algorithm.

Keywords: Mixed-integer bilevel linear program; Global optimization; Single-level reformulation; Reformulation and decomposition method; Projection; Hierarchical supply chain planning (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (15)

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DOI: 10.1007/s10898-018-0679-1

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