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Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions

Author

Listed:
  • Torkil Kollsker

    (Technical University of Denmark)

  • Thomas J. R. Stidsen

    (Technical University of Denmark)

Abstract

Combinatorial optimisation can be applied in a multitude of areas, and this article presents its application to the optimisation of LEGO constructions. Building LEGO constructions is an inherently combinatorial problem, with a large but finite number of possible brick combinations. The objective was to make an aesthetically pleasing construction which is cheap and is structurally stable. Through the application of an adaptive large neighbourhood search metaheuristic, in combination with a mixed integer programming model neighbourhood search procedure and a quadratic programming model ensuring static equilibrium, this article demonstrates how to optimise LEGO constructions with up to 77.000 brick positions.

Suggested Citation

  • Torkil Kollsker & Thomas J. R. Stidsen, 2021. "Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions," SN Operations Research Forum, Springer, vol. 2(2), pages 1-52, June.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:2:d:10.1007_s43069-021-00062-3
    DOI: 10.1007/s43069-021-00062-3
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    References listed on IDEAS

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    1. Pierre de la Poix de Fréminville & Guy Desaulniers & Louis-Martin Rousseau & Sylvain Perron, 2015. "A column generation heuristic for districting the price of a financial product," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(6), pages 965-978, June.
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