Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes

References

• Amaral A. R. S. On the exact solution of a facility layout problem. Eur. J. Oper. Res. (2006) 173:508–518Crossref, Google Scholar
• Anjos M. F. Semidefinite optimization approaches for satisfiability and maximum-satisfiability problems. J. Satisfiability, Boolean Model. Comput. (2005) 1:1–47Crossref, Google Scholar
• Anjos M. F., Vannelli A. On the computational performance of a semidefinite programming approach to single row layout problems. Proc. Oper. Res. 2005 (2006) (Springer-Verlag, Berlin) 277–282Crossref, Google Scholar
• Anjos M. F., Wolkowicz H. Semidefinite programming for discrete optimization and matrix completion problems. Discrete Appl. Math. (2002) 123:513–577Crossref, Google Scholar
• Anjos M. F., Kennings A., Vannelli A. A semidefinite optimization approach for the single-row layout problem with unequal dimensions. Discrete Optim. (2005) 2:113–122Crossref, Google Scholar
• Borchers B. CSDP, a C library for semidefinite programming. Optim. Methods Software (1999) 11:613–623Crossref, Google Scholar
• Çela E.The Quadratic Assignment Problem, Combinatorial Optimization (1998) 1(Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
• de Alvarenga A. G., Negreiros-Gomes F. J., Mestria M. Metaheuristic methods for a class of the facility layout problem. J. Intell. Manuf. (2000) 11:421–430Crossref, Google Scholar
• de Klerk E.Aspects of Semidefinite Programming, Applied Optimization (2002) 65(Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
• Deza M. M., Laurent M.Geometry of Cuts and Metrics, Algorithms and Combinatorics (1997) 15(Springer-Verlag, Berlin) Crossref, Google Scholar
• Goemans M. X., Williamson D. P. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. Assoc. Comput. Mach. (1995) 42:1115–1145Crossref, Google Scholar
• Grötschel M., Jünger M., Reinelt G. A cutting plane algorithm for the linear ordering problem. Oper. Res. (1984) 32:1195–1220Link, Google Scholar
• Heragu S. S., Alfa A. S. Experimental analysis of simulated annealing based algorithms for the layout problem. Eur. J. Oper. Res. (1992) 57:190–202Crossref, Google Scholar
• Heragu S. S., Kusiak A. Machine layout problem in flexible manufacturing systems. Oper. Res. (1988) 36:258–268Link, Google Scholar
• Heragu S. S., Kusiak A. Efficient models for the facility layout problem. Eur. J. Oper. Res. (1991) 53:1–13Crossref, Google Scholar
• Kumar K. R., Hadjinicola G. C., Lin T. A heuristic procedure for the single-row facility layout problem. Eur. J. Oper. Res. (1995) 87:65–73Crossref, Google Scholar
• Laurent M., Rendl F., Aardal K., Nemhauser G., Weismantel R. Semidefinite programming and integer programming. Handbook on Discrete Optimization (2005) (Elsevier, Amsterdam) 393–514Crossref, Google Scholar
• Liu W., Vannelli A. Generating lower bounds for the linear arrangement problem. Discrete Appl. Math. (1995) 59:137–151Crossref, Google Scholar
• Mitchell J. E., Borchers B., Frenk H., Roos K., Terlaky T., Zhang S. Solving linear ordering problems with a combined interior point/simplex cutting plane algorithm. High Performance Optimization (2000) 33(Kluwer Academic Publishers, Dordrecht, The Netherlands) 349–366Crossref, Google Scholar
• Nugent C. E., Vollmann T. E., Ruml J. An experimental comparison of techniques for the assignment of facilities to locations. Oper. Res. (1968) 16:150–173Link, Google Scholar
• Picard J.-C., Queyranne M. On the one-dimensional space allocation problem. Oper. Res. (1981) 29:371–391Link, Google Scholar
• Reinelt G.The Linear Ordering Problem: Algorithms and Applications, Research and Exposition in Mathematics (1985) 8(Heldermann Verlag, Berlin) Google Scholar
• Romero D., Sánchez-Flores A. Methods for the one-dimensional space allocation problem. Comput. Oper. Res. (1990) 17:465–473Crossref, Google Scholar
• Simmons D. M. One-dimensional space allocation: An ordering algorithm. Oper. Res. (1969) 17:812–826Link, Google Scholar
• Whaley R., Petitet A., Dongarra J. Automated empirical optimizations of software and the ATLAS project. Parallel Comput. (2001) 27:3–35Crossref, Google Scholar
• Wolkowicz H., Saigal R., Vandenberghe L.Handbook of Semidefinite Programming (2000) (Kluwer Academic Publishers, Boston) Crossref, Google Scholar