Space-filling Latin hypercube designs for computer experiments

Alam FM, McNaught KR, Ringrose TJ (2004) A comparison of experimental designs in the development of a neural network simulation metamodel. Simul Model Pract Theory 12(7–8):559–578

Audze P, Eglais V (1977) New approach for planning out of experiments. Probl Dyn Strengths 35:104–107

Baer D (1992) Punktverteilungen in Würfeln beliebiger Dimension bezüglich der Maximum-norm. Wissenschaft. Z. Pädagog. Hochschule Erfurt/Mühlhausen, Mathematisch-Naturwissenschaftliche Reihe 28:87–92

Barthelemy JFM, Haftka RT (1993) Approximation concepts for optimum structural design—a review. Struct Multidiscip Optim 5(3):129–144

Bates RA, Buck RJ, Riccomagno E, Wynn HP (1996) Experimental design and observation for large systems. J R Stat Soc B 58:77–94

Bates SJ, Sienz J, Toropov VV (2004) Formulation of the optimal Latin hypercube design of experiments using a permutation genetic algorithm. In: 45th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, pp 1–7

Bulik M, Liefvendahl M, Stocki R, Wauquiez C (2004) Stochastic simulation for crashworthiness. Adv Eng Softw 35(12):791–803

Crary SB (2002) Design of computer experiments for metamodel generation. Analog Integr Circuits Signal Process 32(1):7–16

Crary SB (2008) WebDOE™. http://www.webdoe.cc . January 2008

Crary SB, Cousseau P, Armstrong D, Woodcock DM, Mok EH, Dubochet O, Lerch P, Renaud P (2000) Optimal design of computer experiments for metamodel generation using I-OPT™. Comput Model Eng Sci 1(1):127–139

van Dam ER (2008) Two-dimensional minimax Latin hypercube designs. Discrete Appl Math 156(18):3483–3493

van Dam ER, Husslage BGM, den Hertog D, Melissen JBM (2007) Maximin Latin hypercube designs in two dimensions. Oper Res 55(1):158–169

van Dam ER, Rennen G, Husslage BGM (2009) Bounds for maximin Latin hypercube designs. Oper Res 57:595–608

Dimnaku A, Kincaid R, Trosset MW (2005) Approximate solutions of continuous dispersion problems. Ann Oper Res 136(1):65–80

Driessen LT, Stehouwer HP, Wijker JJ (2002) Structural mass optimization of the engine frame of the Ariane 5 ESC-B. In: Proceedings of the European conference on spacecraft, structures, materials & mechanical testing, Toulouse, France, pp 1–9

Erkut E (1990) The discrete p-dispersion problem. Eur J Oper Res 46(1):48–60

Fejes Tóth L (1971) Punktverteilungen in einem Quadrat. Studia Sci Math Hung 6:439–442

Florian A (1989) Verteilung von Punkten in einem Quadrat. Sitzungsberichte, Abteilung II, Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse 198:27–44

Forrester AIJ, Keane AJ, Bressloff NW (2006) Design and analysis of “noisy” computer experiments. AIAA J 44(10):2331–2339

Giunta AA, Wojtkiewicz SF, Eldred MS (2003) Overview of modern design of experiments methods for computational simulations. In: AIAA 2003, vol  649, pp 1–17

den Hertog D, Stehouwer HP (2002) Optimizing color picture tubes by high-cost nonlinear programming. Eur J Oper Res 140(2):197–211

Hino R, Yoshida F, Toropov VV (2006) Optimum blank design for sheet metal forming based on the interaction of high-and low-fidelity FE models. Arch Appl Mech 75(10):679–691

Husslage BGM (2006) Maximin designs for computer experiments. PhD thesis, CentER for Economic Research, Tilburg University, Tilburg, The Netherlands

Husslage BGM, Rennen G, van Dam ER, den Hertog D (2006) Space-filling Latin hypercube designs for computer experiments. CentER Discussion Paper 2006-18, pp 1–11. Tilburg University, Tilburg, The Netherlands

Jin R, Chen W, Sudjianto A (2005) An efficient algorithm for constructing optimal design of computer experiments. J Stat Plan Inference 134(1):268–287

Johnson ME, Moore LM, Ylvisaker D (1990) Minimax and maximin distance designs. J Stat Plan Inference 26:131–148

Kirchner K, Wengerodt G (1987) Die dichteste Packung von 36 Kreisen in einem Quadrat. Beitrage Algebra Geom 25:147–159

Koehler JR, Owen AB (1996) Computer experiments. In: Ghosh S, Rao CR (eds) Design and analysis of experiments. Handbook of Statistics, vol 13. North-Holland, Amsterdam, pp 261–308

Liefvendahl M, Stocki R (2006) A study on algorithms for optimization of Latin hypercubes. J Stat Plan Inference 136(9):3231–3247

Locatelli M, Raber U (2002) Packing equal circles in a square: a deterministic global optimization approach. Discrete Appl Math 122(1–3):139–166

Markót MC, Csendes T (2005) A new verified optimization technique for the “packing circles in a unit square” problems. SIAM J Control Optim 16(1):193–219

McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239–245

Melissen JBM (1997) Packing and covering with circles. PhD thesis, Utrecht University, Utrecht, The Netherlands

Morris MD, Mitchell TJ (1995) Exploratory designs for computer experiments. J Stat Plan Inference 43:381–402

Nurmela KJ, Östergård PRJ (1999) More optimal packings of equal circles in a square. Discrete Comput Geom 22:439–547

Palmer K, Tsui KL (2001) A minimum bias Latin hypercube design. IIE Trans 33(9):793–808

Peikert R, Würtz D, Monagan M, den Groot C (1991) Packing circles in a sphere: a review and new results. In: Proceedings of the 15th IFIP conference on system modeling and optimization. Springer lecture notes in control and information sciences, vol 180, pp 111–124

Rennen G, Husslage BGM, van Dam ER, den Hertog D (2010) Nested maximin Latin hypercube designs. Struct Multidiscip Optim 46(2):287–306

Rikards R, Auzins J (2004) Response surface method for solution of structural identification problems. Inverse Probl Eng 12(1):59–70

Rikards R, Chate A, Gailis G (2001) Identification of elastic properties of laminates based on experiment design. Int J Solids Struct 38(30–31):5097–5115

Santner TJ, Williams BJ, Notz WI (2003) The design and analysis of computer experiments. Springer Series in Statistics. Springer, New York

Simpson TW, Booker AJ, Ghosh D, Giunta AA, Koch PN, Yang R-J (2004) Approximation methods in multidisciplinary analysis and optimization: a panel discussion. Struct Multidiscip Optim 27(5):302–313

Simpson TW, Peplinski J, Koch PN, Allen JK (2001) Metamodels for computer-based engineering design: survey and recommendations. Eng Comput 17:129–150

Sobieszczanski-Sobieski J, Haftka RT (1997) Multidisciplinary aerospace design optimization: survey of recent developments. Struct Multidiscip Optim 14(1):1–23

Specht E (2008) Packomania. http://www.packomania.com . January 2008

Stinstra ED, den Hertog D, Stehouwer HP, Vestjens A (2003) Constrained maximin designs for computer experiments. Technometrics 45(4):340–346

Stocki R (2005) A method to improve design reliability using optimal Latin hypercube sampling. Comput Assist Mech Eng Sci 12(4):393–412

Trosset MW (1999) Approximate maximin distance designs. In: Proceedings of the section on physical and engineering sciences, Alexandria, VA, USA, pp 223–227

Ye KQ, Li W, Sudjianto A (2000) Algorithmic construction of optimal symmetric Latin hypercube designs. J Stat Plan Inference 90(1):145–159