Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithm
We describe a cutting plane algorithm for solving linear ordering problems. The algorithm uses a primal-dual interior point method to solve the first few relaxations and then switches to a simplex method to solve the last few relaxations. The simplex method uses CPLEX 4.0. We compare the algorithm with one that uses only an interior point method and with one that uses only a simplex method. We solve integer programming problems with as many as 31125 binary variables. Computational results show that the combined approach can dramatically outperform the other two methods.
KeywordsInterior Point Simplex Method Interior Point Method Cutting Plane Current Relaxation
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- Applegate, D., and R. Bixby and V. Chvátal and W. Cook. “The traveling salesman problem”, DIMACS, Rutgers University. New Brunswick, NJ, 1994.Google Scholar
- Czyzyk, J., and S. Mehrotra and M. Wagner and S.J. Wright. “PCx user guide (version 1.1)”, Optimization Technology Center, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois 60439, November 1997. http://www.mcs.anl.gov/otc/Tools/PCx
- Gondzio, J., and R. Sarkissian. “Column generation with a primal-dual method”, Logilab, HEC Geneva, Section of Management Sciences, University of Geneva, 102 Bd Carl Vogt, CH-1211 Geneva 4, Switzerland, June 1996. http://ecolu-info.unige.ch/~logilab/reports/pdcgm.psGoogle Scholar
- Mitchell, J.E. “Computational experience with an interior point cutting plane algorithm”, Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180–3590, February 1997. Revised: April 1997. Available at: http://www.math.rpi.edu/~mitchj/papers/computational.psGoogle Scholar
- Mitchell, J.E. “An interior point cutting plane algorithm for Ising spin glass problems”, Operations Research Proceedings, SOR 1997, Jena, Germany, P. Kischka and H.-W. Lorenz (eds). Springer-Verlag, 114–119, 1998. http://www.math.rpi.edu/~mitchj/papers/isingint.psGoogle Scholar
- Mitchell, J.E., and B. Borchers. “A primal-dual interior point cutting plane method for the linear ordering problem”, COAL Bulletin, 21, 13–18, November 1992.Google Scholar
- Reinelt, G. “The Linear Ordering Problem: Algorithms and Applications”, Heldermann, Berlin, 1995.Google Scholar