Bi-level programming problems (BLPPs) arise very often in areas of engineering, transportation control. A key feature of such problems from a mathematical viewpoint is that even for the simplest linear case, a global optimization approach is typically necessary. In this work, we present two multi-parametric programming based algorithms for the solution of integer and mixed-integer bi-level programming problems. The first algorithm addresses the mixed-integer case of the BLPP and employs a reformulation linearization technique (Sherali and Adams, 1990, 1994; Adams and Sherali, 2005) and continuous multi-parametric programming for the solution of the inner problem. The second algorithm addresses the integer case of the BLPP and approaches the inner problem using global multi-parametric mixed-integer programming (Dua et al. 2004). In both algorithms the solution of the inner problem is embedded in the outer problem to form a set of single-level optimization problems that can be solved to global optimality using a global optimization software.
Bibliographical noteKAUST Repository Item: Exported on 2022-07-01
Acknowledgements: The authors gratefully acknowledge financial support from the Mexican Council for Science and Technology (CONACyT) and the King Abdullah University of Science and Technology (KAUST) for funding part of this research.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- General Chemical Engineering
- Computer Science Applications