Provably near-optimal solutions for very large single-row facility layout problems

References

• Amaral , A. R.S. 2006 . On the exact solution of a facility layout problem . Eur. J. Oper. Res. , 173 ( 2 ) : 508 – 518 .
   Web of Science ®Google Scholar
• Amaral , A. R.S. 2009 . On the exact solution of a facility layout problem . Discrete Appl. Math. , 157 ( 1 ) : 183 – 190 .
   Web of Science ®Google Scholar
• Amaral , A. R.S. 2008 . An exact approach for the one-dimensional facility layout problem . Oper. Res. , 56 : 1026 – 1033 .
   Web of Science ®Google Scholar
• Amaral , A. R.S. and Letchford , A. N. March 2008 . “ A polyhedral approach to the single-row facility layout problem ” . March , Department of Management Science, Lancaster University . Tech. Rep.
   Google Scholar
• Anjos , M. F. 2005 . Semidefinite optimization approaches for satisfiability and maximum-satisfiability problems . J.Satisfiability Boolean Model. Comput. , 1 ( 1 ) : 1 – 47 .
   Google Scholar
• Anjos , M. F. and Vannelli , A. 2008 . Computing globally optimal solutions for single-row layout problems using semidefinite programming and cutting planes . INFORMS J. Comput. , 20 ( 4 ) : 611 – 617 .
   Web of Science ®Google Scholar
• Anjos , M. F. and Wolkowicz , H. 2002 . Semidefinite programming for discrete optimization and matrix completion problems . Discrete Appl. Math. , 123 ( 1–2 ) : 513 – 577 .
   Google Scholar
• Anjos , M. F. , Kennings , A. and Vannelli , A. 2005 . A semidefinite optimization approach for the single-row layout problem with unequal dimensions . Discrete Optim. , 2 ( 2 ) : 113 – 122 .
   Google Scholar
• Borchers , B. 1999 . CSDP, a C library for semidefinite programming . Optim. Methods Softw. , 11/12 ( 1–4 ) : 613 – 623 .
   Web of Science ®Google Scholar
• Çela , E. 1998 . The Quadratic Assignment Problem , Vol. 1 , Dordrecht : Combinatorial Optimization, Kluwer Academic Publishers .
   Google Scholar
• de Alvarenga , A. G. , Negreiros-Gomes , F. J. and Mestria , M. 2000 . Metaheuristic methods for a class of the facility layout problem . J. Intell. Manuf. , 11 : 421 – 430 .
   Web of Science ®Google Scholar
• de Klerk , E. 2002 . Aspects of Semidefinite Programming , Vol. 65 , Dordrecht : Applied Optimization, Kluwer Academic Publishers .
   Google Scholar
• Deza , M. M. and Laurent , M. 1997 . Geometry of Cuts and Metrics , Vol. 15 , Berlin : Algorithms and Combinatorics, Springer-Verlag .
   Google Scholar
• Hall , K. M. 1970 . An r-dimensional quadratic placement algorithm . Manage. Sci. , 17 : 219 – 229 .
   Web of Science ®Google Scholar
• C. Helmberg, Available at http://www-user.tu-chemnitz.de/∼helmberg/semidef.html
   Google Scholar
• Helmberg , C. and Kiwiel , K. C. 2002 . A spectral bundle method with bounds . Math. Program. , 93 ( 2 ) : 173 – 194 . Ser. A
   Google Scholar
• Helmberg , C. and Rendl , F. 2000 . A spectral bundle method for semidefinite programming . SIAM J. Optim. , 10 ( 3 ) : 673 – 696 . (electronic)
   Web of Science ®Google Scholar
• Heragu , S. S. 2006 . Facilities Design , 2 , Bloomington, IN : iUniverse .
   Google Scholar
• Heragu , S. S. and Alfa , A. S. 1992 . Experimental analysis of simulated annealing based algorithms for the layout problem . Eur. J. Oper. Res. , 57 ( 2 ) : 190 – 202 .
   Web of Science ®Google Scholar
• Heragu , S. S. and Kusiak , A. 1988 . Machine layout problem in flexible manufacturing systems . Oper. Res. , 36 ( 2 ) : 258 – 268 .
   Web of Science ®Google Scholar
• Heragu , S. S. and Kusiak , A. 1991 . Efficient models for the facility layout problem . Eur. J. Oper. Res. , 53 : 1 – 13 .
   Web of Science ®Google Scholar
• Karp , R. M. and Held , M. 1967 . Finite-state processes and dynamic programming . SIAM J. Appl. Math. , 15 : 693 – 718 .
   Web of Science ®Google Scholar
• Kumar , K. R. , Hadjinicola , G. C. and Lin , T. 1995 . A heuristic procedure for the single-row facility layout problem . Eur. J. Oper. Res. , 87 ( 1 ) : 65 – 73 .
   Web of Science ®Google Scholar
• Laurent , M. and Rendl , F. 2005 . “ Semidefinite programming and integer programming ” . In Handbook on Discrete Optimization , Edited by: Aardal , K. , Nemhauser , G. and Weismantel , R. 393 – 514 . Amsterdam : Elsevier .
   Google Scholar
• Liu , W. and Vannelli , A. 1995 . Generating lower bounds for the linear arrangement problem . Discrete Appl. Math. , 59 ( 2 ) : 137 – 151 .
   Google Scholar
• Love , R. F. and Wong , J. Y. 1976 . On solving a one-dimensional space allocation problem with integer programming . INFOR , 14 ( 2 ) : 139 – 143 .
   Google Scholar
• Meller , R. D. , Chen , W. and Sherali , H. D. 2007 . Applying the sequence-pair representation to optimal facility layout designs . Oper. Res. Lett. , 35 ( 5 ) : 651 – 659 .
   Web of Science ®Google Scholar
• Murata , H. , Fujiyoshi , K. , Nakatake , S. and Kajitani , Y. 1996 . VLSI module placement based on rectangle-packing by the sequence-pair . IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. , 15 ( 12 ) : 1518 – 1524 .
   Web of Science ®Google Scholar
• Picard , J.-C. and Queyranne , M. 1981 . On the one-dimensional space allocation problem . Oper. Res. , 29 ( 2 ) : 371 – 391 .
   Web of Science ®Google Scholar
• Romero , D. and Sánchez-Flores , A. 1990 . Methods for the one-dimensional space allocation problem . Comput. Oper. Res. , 17 ( 5 ) : 465 – 473 .
   Web of Science ®Google Scholar
• Simmons , D. M. 1969 . One-dimensional space allocation: An ordering algorithm . Oper. Res. , 17 : 812 – 826 .
   Web of Science ®Google Scholar
• Simmons , D. M. 1971 . A further note on one-dimensional space allocation . Oper. Res. , 19 : 249
   Web of Science ®Google Scholar
• Suryanarayanan , J. K. , Golden , B. L. and Wang , Q. 1991 . A new heuristic for the linear placement problem . Comput. Oper. Res. , 18 ( 3 ) : 255 – 262 .
   Web of Science ®Google Scholar
• Whaley , R. , Petitet , A. and Dongarra , J. 2001 . Automated empirical optimizations of software and the ATLAS project . Parallel Comput. , 27 ( 1–2 ) : 3 – 35 .
   Google Scholar
• Wolkowicz , H. , Saigal , R. and Vandenberghe , L. 2000 . Handbook of Semidefinite Programming , Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• Xie , W. and Sahinidis , N. V. 2008 . A branch-and-bound algorithm for the continuous facility layout problem . Comput. Chem. Eng. , 32 : 1016 – 1028 .
   Web of Science ®Google Scholar
• Yen , G. 2008 . “ Cutting-plane separation strategies for semidefinite programming models to solve single-row facility layout problems ” . University of Waterloo . Master's thesis
   Google Scholar