Abstract
Reduced-cost-based filtering in constraint programming and variable fixing in integer programming are techniques which allow to cut out part of the solution space which cannot lead to an optimal solution. These techniques are, however, dependent on the dual values available at the moment of pruning. In this paper, we investigate the value of picking a set of dual values which maximizes the amount of filtering (or fixing) that is possible. We test this new variable-fixing methodology for arbitrary mixed-integer linear programming models. The resulting method can be naturally incorporated into existing solvers. Preliminary results on a large set of benchmark instances suggest that the method can effectively reduce solution times on hard instances with respect to a state-of-the-art commercial solver.
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MIPLIB2010. http://miplib.zib.de/miplib2010-benchmark.php
Balas, E., Martin, C.H.: Pivot and complement-a heuristic for 0–1 programming. Manage. Sci. 26(1), 86–96 (1980)
Bergman, D., Cire, A.A., Hoeve, W.-J.: Improved constraint propagation via lagrangian decomposition. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 30–38. Springer, Cham (2015). doi:10.1007/978-3-319-23219-5_3
Bixby, E.R., Fenelon, M., Gu, Z., Rothberg, E., Wunderling, R.: MIP: theory and practice — closing the gap. In: Powell, M.J.D., Scholtes, S. (eds.) CSMO 1999. ITIFIP, vol. 46, pp. 19–49. Springer, Boston, MA (2000). doi:10.1007/978-0-387-35514-6_2
Chvátal, V.: Linear Programming. Freeman, New York (1983). Reprints: (1999), (2000), (2002)
Fahle, T., Sellmann, M.: Cost-based filtering for the constrained knapsack problem. Ann. Oper. Res. 115, 73–93 (2002)
Focacci, F., Lodi, A., Milano, M.: Cost-based domain filtering. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 189–203. Springer, Heidelberg (1999). doi:10.1007/978-3-540-48085-3_14
Focacci, F., Lodi, A., Milano, M., Vigo, D.: Solving TSP through the integration of OR and CP techniques. Electron. Notes Discrete Math. 1, 13–25 (1999)
Focacci, F., Milano, M., Lodi, A.: Solving TSP with time windows with constraints. In: Proceedings of the 1999 International Conference on Logic programming, Massachusetts Institute of Technology, pp. 515–529 (1999)
Klabjan, D.: A new subadditive approach to integer programming. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 384–400. Springer, Heidelberg (2002). doi:10.1007/3-540-47867-1_27
Lodi, A.: Mixed integer programming computation. In: Jünger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.) 50 Years of Integer Programming 1958–2008, pp. 619–645. Springer, Heidelberg (2010)
Mahajan, A.: Presolving mixed-integer linear programs. In: Wiley Encyclopedia of Operations Research and Management Science (2010)
Nemhauser, G.L., Wolsey, L.A.: Integer Programming and Combinatorial Optimization (1988)
Chichester, W., Nemhauser, G.L., Savelsbergh, M.W.P., Sigismondi, G.S.: Constraint Classification for Mixed Integer Programming Formulations. COAL Bulletin, vol. 20, pp. 8–12 (1992)
Refalo, P.: Linear formulation of constraint programming models and hybrid solvers. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 369–383. Springer, Heidelberg (2000). doi:10.1007/3-540-45349-0_27
Sellmann, M.: Theoretical foundations of CP-based lagrangian relaxation. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 634–647. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30201-8_46
Thorsteinsson, E.S., Ottosson, G.: Linear relaxations and reduced-cost based propagation of continuous variable subscripts. Ann. Oper. Res. 115(1), 15–29 (2002)
Wolsey, L.A.: Integer Programming, vol. 4. Wiley, New York (1998)
Yunes, T., Aron, I.D., Hooker, J.N.: An integrated solver for optimization problems. Oper. Res. 58(2), 342–356 (2010)
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Bajgiran, O.S., Cire, A.A., Rousseau, LM. (2017). A First Look at Picking Dual Variables for Maximizing Reduced Cost Fixing. In: Salvagnin, D., Lombardi, M. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017. Lecture Notes in Computer Science(), vol 10335. Springer, Cham. https://doi.org/10.1007/978-3-319-59776-8_18
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DOI: https://doi.org/10.1007/978-3-319-59776-8_18
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