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Finding maximin latin hypercube designs by Iterated Local Search heuristics

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  • Grosso, A.
  • Jamali, A.R.M.J.U.
  • Locatelli, M.

Abstract

The maximin LHD problem calls for arranging N points in a k-dimensional grid so that no pair of points share a coordinate and the distance of the closest pair of points is as large as possible. In this paper we propose to tackle this problem by heuristic algorithms belonging to the Iterated Local Search (ILS) family and show through some computational experiments that the proposed algorithms compare very well with different heuristic approaches in the established literature.

Suggested Citation

  • Grosso, A. & Jamali, A.R.M.J.U. & Locatelli, M., 2009. "Finding maximin latin hypercube designs by Iterated Local Search heuristics," European Journal of Operational Research, Elsevier, vol. 197(2), pages 541-547, September.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:541-547
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    References listed on IDEAS

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    1. den Hertog, Dick & Stehouwer, Peter, 2002. "Optimizing color picture tubes by high-cost nonlinear programming," European Journal of Operational Research, Elsevier, vol. 140(2), pages 197-211, July.
    2. Edwin R. van Dam & Bart Husslage & Dick den Hertog & Hans Melissen, 2007. "Maximin Latin Hypercube Designs in Two Dimensions," Operations Research, INFORMS, vol. 55(1), pages 158-169, February.
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    Cited by:

    1. Jing Zhang & Jin Xu & Kai Jia & Yimin Yin & Zhengming Wang, 2019. "Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes," Mathematics, MDPI, vol. 7(9), pages 1-16, September.
    2. Gao, Yanping & Yi, Siyu & Zhou, Yongdao, 2022. "Maximin L1-distance Range-fixed Level-augmented designs," Statistics & Probability Letters, Elsevier, vol. 186(C).
    3. Vinícius Resende Domingues & Luan Carlos de Sena Monteiro Ozelim & André Pacheco de Assis & André Luís Brasil Cavalcante, 2022. "Combining Numerical Simulations, Artificial Intelligence and Intelligent Sampling Algorithms to Build Surrogate Models and Calculate the Probability of Failure of Urban Tunnels," Sustainability, MDPI, vol. 14(11), pages 1-29, May.
    4. Pengfei Gao & Xinggang Yan & Yao Wang & Hongwei Li & Mei Zhan & Fei Ma & Mingwang Fu, 2023. "An online intelligent method for roller path design in conventional spinning," Journal of Intelligent Manufacturing, Springer, vol. 34(8), pages 3429-3444, December.
    5. Crombecq, K. & Laermans, E. & Dhaene, T., 2011. "Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling," European Journal of Operational Research, Elsevier, vol. 214(3), pages 683-696, November.
    6. A. Jourdan & J. Franco, 2010. "Optimal Latin hypercube designs for the Kullback–Leibler criterion," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(4), pages 341-351, December.
    7. Liuqing Yang & Yongdao Zhou & Min-Qian Liu, 2021. "Maximin distance designs based on densest packings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 615-634, July.
    8. Bozağaç, Doruk & Batmaz, İnci & Oğuztüzün, Halit, 2016. "Dynamic simulation metamodeling using MARS: A case of radar simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 69-86.
    9. János Pintér & Zoltán Horváth, 2013. "Integrated experimental design and nonlinear optimization to handle computationally expensive models under resource constraints," Journal of Global Optimization, Springer, vol. 57(1), pages 191-215, September.
    10. Tonghui Pang & Yan Wang & Jian-Feng Yang, 2022. "Asymptotically optimal maximin distance Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 405-418, May.

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