Maximin Latin Hypercube Designs in Two Dimensions

Published Online:https://doi.org/10.1287/opre.1060.0317

References

  • Alam F. M., McNaught K. R., Ringrose T. J. A comparison of experimental designs in the development of a neural network simulation metamodel. Simulation Modelling: Practice and Theory (2004) 12(7–8):559–578CrossrefGoogle Scholar
  • Baer D. Punktverteilungen in Würfeln beliebiger Dimension bezüglich der Maximum-norm. Wiss. Z. Pädagog. Hochsch. Erfurt/Mühlhausen, Math.-Naturwiss. Reihe (1992) 28:87–92Google Scholar
  • Booker A. J., Dennis J. E., Frank P. D., Serafini D. B., Torczon V., Trosset M. W. A rigorous framework for optimization of expensive functions by surrogates. Structural Optim. (1999) 17:1–13CrossrefGoogle Scholar
  • Casado L. G., Garcia I., Szabó P. G., Csendes T., Giannessi F., et al. Packing equal circles in a square II—New results for up to 100 circles using the TAMSASS-PECS algorithm. Optimization Theory (2001) (Kluwer, Dordrecht, The Netherlands) CrossrefGoogle Scholar
  • Dimnaku A., Kincaid R., Trosset M. W. Approximate solutions of continuous dispersion problems. Ann. Oper. Res. (2005) 136(1):65–80CrossrefGoogle Scholar
  • Driessen L. T., Stehouwer H. P., Wijker J. J. Structural mass optimization of the engine frame of the Ariane 5 ESC-B. Proc. Eur. Conf. Spacecraft, Structures, Materials Mechanical Testing (2002) Toulouse, FranceGoogle Scholar
  • Fejes Tóth L. Punktverteilungen in einem Quadrat. Studia Sci. Math. Hung (1971) 6:439–442Google Scholar
  • Florian A. Verteilung von Punkten in einem Quadrat. Sitzungsber., Abt. II, II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. (1989) 198:27–44Google Scholar
  • Hertog D. den, Stehouwer H. P. Optimizing color picture tubes by high-cost nonlinear programming. Eur. J. Oper. Res. (2002) 140(2):197–211CrossrefGoogle Scholar
  • Johnson M. E., Moore L. M., Ylvisaker D. Minimax and maximin distance designs. J. Statist. Planning Inference (1990) 26:131–148CrossrefGoogle Scholar
  • Jones D., Schonlau M., Welch W. Efficient global optimization of expensive black-box functions. J. Global Optim. (1998) 13:455–492CrossrefGoogle Scholar
  • Kirchner K., Wengerodt G. Die dichteste Packung von 36 Kreisen in einem Quadrat. Beiträge Algebra Geom. (1987) 25:147–159Google Scholar
  • Locatelli M., Raber U. Packing equal circles in a square: A deterministic global optimization approach. Discrete Appl. Math. (2002) 122(1–3):139–166CrossrefGoogle Scholar
  • Markót M. Cs., Csendes T. A new verified optimization technique for the “packing circles in a unit square” problems. SIAM J. Optim. (2005) 16:193–219CrossrefGoogle Scholar
  • Melissen J. B. M. Packing and covering with circles. (1997) . Ph.D. thesis, Utrecht University, Utrecht, The NetherlandsGoogle Scholar
  • Montgomery D. C.Design and Analysis of Experiments (1984) 2nd ed.(John Wiley and Sons, New York) Google Scholar
  • Morris M. D., Mitchell T. J. Exploratory designs for computer experiments. J. Statist. Planning Inference (1995) 43:381–402CrossrefGoogle Scholar
  • Myers R. H. Response surface methodology—Current status and future directions. J. Quality Tech. (1999) 31:30–74CrossrefGoogle Scholar
  • Nurmela K. J., Östergård P. R. J. More optimal packings of equal circles in a square. Discrete Computational Geometry (1999) 22:439–547CrossrefGoogle Scholar
  • Oler N. A finite packing problem. Canadian Math. Bull. (1961) 4(2):153–155CrossrefGoogle Scholar
  • Peikert R., Würtz D., Monagan M., den Groot C. Packing circles in a sphere: A review and new results. Proc. 15th IFIP Conf. on System Modeling and Optim. Springer Lecture Notes in Control and Information Sciences (1991) 180:111–124Google Scholar
  • Pintér J. D.LGO: A Model Development and Solver System for Continuous Global Optimization (1995) (Pintér Consulting Services Inc., Halifax, Nova Scotia, Canada) Google Scholar
  • Rikards R., Auzins J. Response surface method for solution of structural identification problems. Inverse Problems Engrg. (2004) 12(1):59–70CrossrefGoogle Scholar
  • Sacks J., Schiller S. B., Welch W. J. Designs for computer experiments. Technometrics (1989a) 31:41–47CrossrefGoogle Scholar
  • Sacks J., Welch W. J., Mitchell T. J., Wynn H. P. Design and analysis of computer experiments. Statist. Sci. (1989b) 4:409–435CrossrefGoogle Scholar
  • Santner T. J., Williams B. J., Notz W. I.The Design and Analysis of Computer Experiments. Springer Series in Statistics (2003) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Specht E. Packomania. (2005) . http://www.packomania.comGoogle Scholar
  • Stinstra E., den Hertog D., Stehouwer H. P., Vestjens A. Constrained maximin designs for computer experiments. Technometrics (2003) 45(4):340–346CrossrefGoogle Scholar
  • Sunset Software Technology XA binary and mixed integer solver. (2003) . http://www.sunsetsoft.com/Google Scholar
  • Trosset M. W. Approximate maximin distance designs. Proc. Section Physical Engrg. Sci. (1999) American Statistical Association, Alexandria, VA:223–227Google Scholar
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