Abstract
This Chapter describes a specialization of the dual simplex algorithm for the generalized network problem. We use a dual two phase method along with efficient dual partial pricing schemes and specialized routines for the dual ratio test. In comparison with CPLEX 3.0 on a set of ten benchmark problems, we found that our specialized dual code performed 20 times faster than the best CPLEX optimizer. Problems having 10 to 20 thousand arcs are routinely solved in under 10 seconds on a 60MHz DEC Station 5000/260 with our rapid dual generalized network optimizer.
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References
R. Ahuja, T. Magnanti, and J. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Inc., Englewood Cliffs, NJ., 1993.
A. Ali, R. Padman, and H. Thiagarajan. Dual Algorithms for Pure Network Problems. Operations Research, 37 (1): 159–179, 1989.
R. Barr, F. Glover, and D. Klingman. Enhancement of Spanning Tree Labeling Procedures for Network Optimization. INFORS, 17: 66–85, 1979.
K. Belling-Seib. An Improved General Phase-1 Method in Linear Programming. European Journal of Operational Research, 36: 101–106, 1988.
D. Bertsekas and P. Tseng. Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems. Operations Research, 36(1):93–114, 1988!
G. Brown and R. McBride. Solving Generalized Networks. Management Science, 30 (12): 1497–1523, 1984.
R. Clark, J. Kennington, R. Meyer, and M. Ramamurti. Generalized Networks: Parallel Algorithms and an Empirical Analysis. ORSA Journal on Computing, 4 (2): 132–145, 1992.
M. Engquist and M. Chang. New Labeling Procedures for The Basis Graph in Generalized Networks. Operations Research Letters, 4 (4): 151–155, 1985.
J. Forrest and D. Goldfarb. Steepest-edge Simplex Algorithm for Linear Programming. Mathematical Programming, 57: 341–374, 1992.
F. Glover, J. Hultz, D. Klingman, and J. Stutz. Generalized Networks: A Fundamental Computer-Based Planning Tool. Management Science, 24 (12): 1209–1220, 1978.
F. Glover, D. Klingman, and N. Phillips. Network Models in Optimization and Their Applications in Practice. John Wiley & Sons, New York, 1992.
F. Glover, D. Klingman, and J. Stutz. Extensions of the Augmented Predecessor Index Method to Generalized Network Problems. Transportation Science, 7 (4): 377–384, 1973.
D. Goldfarb and J. Reid. A Practicable Steepest-Edge Simplex Algorithm. Mathematical Programming, 12: 361–371, 1977.
P. Harris. Pivot Selection Methods of the DEVEX LP Code. Mathematical Programming, 5: 1–28, 1973.
J. Kennington and R. Helgason. Algorithms for Network Programming. John Wiley & Sons, New York, 1980.
D. Klingman, A. Napier, and J. Stutz. A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems. Management Science, 5(5): 814–821, 1974.
N. Megiddo. On Finding Primal- and Dual-Optimal Bases. ORSA Journal on Computing, 3 (1): 63–65, 1991.
R. Mohamed. Efficient Dual Simplex Optimizers for Generalized Network Models. unpublished dissertation, Department of Computer Science and Engineering, Southern Methodist University, Dallas, TX 75275, 1995.
J. Mulvey and S. Zenios. Solving Large Scale Generalized Networks. Journal of Information and Optimization Sciences, 6 (1): 95–112, 1985.
K. Murty. Linear and Combinatorial Programming. Robert E. Krieger Publishing Company, Malabar, Florida, 1985.
G. Nemhauser and L. Wolsey. Integer and Combinatorial Optimization. John Wiley & Sons, New York, 1988.
W. Nulty and M. Trick. GNO/PC Generalized Network Optimization System. Operations Research Letters, 7 (2): 101–102, 1988.
R. Parker and R. Rardin. Discrete Optimization. Academic Press, New York, 1988.
Using the CPLEX Callable Library Version 3.0. Incline Village, Nevada 89451–9436, 1994.
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Kennington, J.L., Mohamed, R.A. (1997). An Efficient Dual Simplex Optimizer for Generalized Networks. In: Barr, R.S., Helgason, R.V., Kennington, J.L. (eds) Interfaces in Computer Science and Operations Research. Operations Research/Computer Science Interfaces Series, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4102-8_6
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DOI: https://doi.org/10.1007/978-1-4615-4102-8_6
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