A branch and bound algorithm for the bilevel programming problem
SIAM Journal on Scientific and Statistical Computing
Algorithms for solving the mixed integer two-level linear programming problem
Computers and Operations Research
The mixed integer linear bilevel programming problem
Operations Research
New branch-and-bound rules for linear bilevel programming
SIAM Journal on Scientific and Statistical Computing
Discrete linear bilevel programming problem
Journal of Optimization Theory and Applications
Exact and inexact penalty methods for the generalized bilevel programming problem
Mathematical Programming: Series A and B
Parametric global optimisation for bilevel programming
Journal of Global Optimization
A mixed-integer optimization framework for the synthesis and analysis of regulatory networks
Journal of Global Optimization
Model building using bi-level optimization
Journal of Global Optimization
Fuzzy Equilibrium Logic: Declarative Problem Solving in Continuous Domains
ACM Transactions on Computational Logic (TOCL)
Analysis of different approaches to cross-dock truck scheduling with truck arrival time uncertainty
Computers and Industrial Engineering
Proceedings of the Ninth IEEE/ACM/IFIP International Conference on Hardware/Software Codesign and System Synthesis
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In this article, we propose a new algorithm for the resolution of mixed integer bi-level linear problem (MIBLP). The algorithm is based on the decomposition of the initial problem into the restricted master problem (RMP) and a series of problems named slave problems (SP). The proposed approach is based on Benders decomposition method where in each iteration a set of variables are fixed which are controlled by the upper level optimization problem. The RMP is a relaxation of the MIBLP and the SP represents a restriction of the MIBLP. The RMP interacts in each iteration with the current SP by the addition of cuts produced using Lagrangian information from the current SP. The lower and upper bound provided from the RMP and SP are updated in each iteration. The algorithm converges when the difference between the upper and lower bound is within a small difference 驴. In the case of MIBLP Karush---Kuhn---Tucker (KKT) optimality conditions could not be used directly to the inner problem in order to transform the bi-level problem into a single level problem. The proposed decomposition technique, however, allows the use of KKT conditions and transforms the MIBLP into two single level problems. The algorithm, which is a new method for the resolution of MIBLP, is illustrated through a modified numerical example from the literature. Additional examples from the literature are presented to highlight the algorithm convergence properties.