Abstract
In this chapter, we describe the most recent advances in the solution of mixed-integer programming problems. The last ten years have seen enormous improvements in the solution of the most difficult mixed-integer programs. The trend towards integration of modeling and optimization now makes it possible to solve the hardest optimization problems arising from electricity generation, such as the unit commitment problem. We report results with a leading software package that was used successfully to solve unit commitment problems in two European utility companies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Balas. Disjunctive programming. Ann. Discrete Math., 5: 3–51, 1979.
E. Balas, S. Ceria, and G. Cornuéjols. Mixed 0-1 programming by lift-and-project in a branch-and-cut framework. Manage. Sci., 42(9): 1229–1246, 1996.
E. Balas, S. Ceria, and G. Cornuéjols. A lift-and-project cutting plane algorithm for mixed 0-1 programs. Math. Prog., 58: 295–324, 1993a.
E. Balas, S. Ceria, and G. Cornuéjols. “Solving Mixed 0-1 Programs by a Lift-and-Project Method.” In Proc. Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, 232–242, 1993b.
J. Batut and R.P. Sandrin. “New Software for the Generation Rescheduling in the Future EDF National Control Center.” In Proc. 10 th PSCC, Graz, Austria, 1990.
Belvaux, G., Solving lot-sizing problems by branch & cut: Basic guide to use of mg-EMOSL. Working paper, CORE, Université catholique de Louvain, February 1998.
A. Caprara and M. Fischetti. Branch-and-Cut Algorithms, in Annotated Bibliographies in Combinatorial Optimization. M. Dell’Amico, F. Maffioli, and S. Martello, eds. Chichester: John Wiley & Sons, Chichester, 45–63, 1997.
S. Ceria. “MIPO: A Mixed-Integer Program Optimizer.” Presented at: 16th International Symposium on Mathematical Programming, Lausanne, August 1996.
C. Cordier, H. Marchand, R.S. Laundy, and L.A. Wolsey. “bc-opt: A branch-and-cut code for mixed integer programs.” Discussion paper DP 9778, CORE, Universite catholique de Louvain, 1997.
H. Crowder, E. Johnson, and M. Padberg. Solving large-scale zero-one linear programming problems. Op. Res., 31: 803–834, 1983.
R. Daniel and J. Tebboth. A tightly integrated modelling and optimisation library: A new framework for rapid algorithm development. Ann. Op. Res., 0: 1–21, 1998.
G.B. Dantzig, D.R. Fulkerson, and S.M. Johnson. Solution of a large-scale traveling salesman problem. Op. Res., 2: 393–410, 1954.
G.B. Dantzig, D.R. Fulkerson, and S.M. Johnson. On a linear programming, combinatorial approach to the traveling salesman problem. Op. Res., 7: 58–66, 1959.
Dash Associates. XPRESS-MP EMOSL Reference Manual, Release 10. Blisworth, Northants NN7 3BX, UK: Blisworth House Church Lane, 1997.
R.S. Garfinkel and G.L. Nemhauser. Merger Programming. New York: John Wiley & Sons, Inc., 1972.
R. Gormory. “An Algorithm for the Mixed-Integer Problem. Technical Report RM-2597, The Rand Corporation, 1960.
R. Gormory. 1958. Outline of an algorithm for integer solutions to linear programs. Bull. Am. Math. Soc., 64: 275–278, 1958.
R. Gormory. “Solving Linear Programming Problems in Integers. In Combinatorial Analysis R.E. Bellman, M. Hall Jr., eds. Providence, RI: American Mathematical Society, 211–216, 1960.
X. Guan, P.B. Luh, and L. Zhang. Non-linear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling. IEEE Trans. Power Syst., 10(2): 772–778, 1995.
H.H. Happ, R.C. Johnson, and W.J. Wright. Large-scale unit commitment method and results. IEEE Trans. PAS, PAS-90: 1373–1383, 1971.
K.L. Hoffman and M. Padberg. Techniques for improving the LP-representation of zero-one linear programming problems. ORSA J. Computing, 3: 121–134, 1991.
K.L. Hoffman and M. Padberg. Solving airline crew scheduling problems by branch-and-cut. Manage. Sci, 39: 657–682, 1993.
E.L. Johnson, G.L. Nemhauser, and M.W.P. Savelsbergh. “Progress in Linear Programming Based Algorithms for Integer Programming: An Exposition.” School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, August 1999.
M. Jünger and S. Thienel. Introduction to ABACUS — A branch-and-cut system. Op. Res. Lett., 22: 83–95, 1998.
H.A. Land and A.G. Doig. An automatic method for solving discrete programming problems. Econometrica 28: 497–520, 1960.
T. Lekane and J. Ghuery. “Short Term Operation of an Electric Power System.” Tractebel Energy Engineering, Brussels, Belgium.
L. Lovasz and A. Schrijver. Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optimization, 1: 166–190, 1990.
G.L. Nemhauser, M.W.P. Savelsbergh, and G.C. Sigismondi. MINTO, a Mixed INTeger Optimizer. Op. Res. Lett., 15: 47–58, 1993.
G.L. Nemhauser and L.A. Wolsey. Integer and Combinatorial Optimization. New York: John Wiley & Sons, 1988.
S.O. Orero and M.R. Irving. Large-scale unit commitment using a hybrid genetic algorithm. Elec. Power Energy Syst., 19(1): 45–55, 1997.
M.W. Padberg and G. Rinaldi. A branch-and-cut algorithm for the resolution of largescale symmetric traveling salesman problems. SIAM Rev., 33: 60–100, 1991.
M.W. Padberg and G. Rinaldi. Optimization of a 532 city symmetric traveling salesman problem by branch-and-cut. Op. Res. Lett., 6: 1–7, 1987.
C.K. Pang, G.B. Sheblé, and F. Albuyeh. Evaluation of dynamic programming based methods and multiple area representation for thermal unit commitments. IEEE Trans. PAS, PAS 100(3): 1212–1218, 1981.
M.W.P. Savelsbergh and G.L. Nemhauser. Functional description of MINTO, a mixed integer optimizer, version 2.3. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, November 1996.
A. Schrijver. Theory of Linear and Integer Programming. Chichester: John Wiley & Sons, 1986.
H. Sherali and W. Adams. A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Disc. Math., 3: 411–430, 1990.
T.J. Van Roy and L.A. Wolsey. Solving mixed-integer programming problems using automatic reformulation. Op. Res., 35: 45–57, 1987.
T.J. Van Roy and L.A. Wolsey, Solving mixed 0-1 programs by automatic reformulation. Op. Res. 35: 145–163, 1987.
S.J. Wand, S.M. Shahidehpour, D.S. Kirschen, S. Mokhtari, and G.D. Irisarri. Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation. IEEE Trans. Power Syst., 10(3): 1294–1301, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic Publishers
About this chapter
Cite this chapter
Ceria, S. (2002). Solving Hard Mixed-Integer Programs for Electricity Generation. In: Hobbs, B.F., Rothkopf, M.H., O’Neill, R.P., Chao, Hp. (eds) The Next Generation of Electric Power Unit Commitment Models. International Series in Operations Research & Management Science, vol 36. Springer, Boston, MA. https://doi.org/10.1007/0-306-47663-0_9
Download citation
DOI: https://doi.org/10.1007/0-306-47663-0_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-7334-6
Online ISBN: 978-0-306-47663-1
eBook Packages: Springer Book Archive