Abstract
In this paper, we discuss an SLCP algorithm for the solution of Bilevel Linear Programs (BLP) which consists of solving a sequence of Linear Complementarity Problems (LCP) by using a hybrid enumerative method. This latter algorithm incorporates a number of procedures that reduce substantially the search for a solution of the LCP or for showing that the LCP has no solution. Computational experience with the SLCP algorithm shows that it performs quite well for the solution of small- and medium-scale BLPs with sparse structure. Furthermore, the algorithm is shown to be more efficient than a branch-and-bound method for solving the same problems.
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References
F.A. Al-Khayyal, An implicit enumeration procedure for the general linear complementarity problem, Math. Progr. Studies 31(1987)1–20.
G. Anandalingam and D.I. White, A penalty function approach for solving bilevel linear programs, Department of Systems, University of Pennsylvania (1988).
J.F. Bard and J.J. Moore, A branch-and-bound algorithm for the bilevel linear program, SIAM J. Sci. Statist. Comput. 11(1990)281–292.
O. Ben-Ayed, C.E. Blair and D.E. Boyce, Solving a real world highway network design problem using bilevel linear programming, BEBR Faculty Working Paper 1463, University of Illinois at Urbana-Champaign (1988).
W.F. Bialas and M.H. Karwan, Two-level linear programming, Manag. Sci. 30(1984)1004–1020.
R.G. Bland, New finite pivoting rules for the simplex method, Math. Oper. Res. 2(1977)103–107.
P. Hansen, B. Jaumard and G. Savard, A variable elimination algorithm for bilevel linear programming, RUTCOR, Rutgers University (1989).
J.J. Júdice and A.M. Faustino, An experimental investigation of enumerative methods for the linear complementarity problem, Comput. Oper. Res. 15(1988)417–426.
J.J. Júdice and A.M. Faustino, The solution of the linear bilevel linear programming problem by using the linear complementarity problem, Investigação Operacional 8(1988)77–95.
C.D. Kolstad and L.S. Lasdon, Derivate evaluation and computational experience with large bilevel mathematical programs, Faculty Working Paper 1266, College of Commerce and Business Administration, University of Illinois at Urbana-Champaign (1986).
C.D. Kolstad, A review of the literature on bilevel mathematical programming, Technical Report LA-10284-MS, Los Alamos National Laboratory (1985).
P. Marcotte, Network design problem with congestion effects: A case of bilevel programming, Math. Progr. 34(1986)142–162.
K.G. Murty,Linear Programming (Wiley, New York, 1983).
K.G. Murty,Linear Complementarity, Linear and Nonlinear Programming (Heldermann, Berlin, 1988).
J.K. Reid, A sparsity-exploitation variant of the Bartels-Golub decomposition of linear programming bases, Math. Progr. 24(1982)55–69.
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Júdice, J.J., Faustino, A.M. A sequential LCP method for bilevel linear programming. Ann Oper Res 34, 89–106 (1992). https://doi.org/10.1007/BF02098174
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DOI: https://doi.org/10.1007/BF02098174