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Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions

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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.

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Notes

  1. Retrieved from www.brickset.com

  2. We retrieved the 3D mesh of the giraffe from www.archive3d.net.

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Funding

First author Torkil Kollsker studied as an Industrial Ph.D. student, funded by the Innovation Fund (DK), project number 5189-00095B. LEGO also funded part of the project. Second author, Associate Professor Thomas Stidsen, did not receive any external funding.

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Authors and Affiliations

  1. Technical University of Denmark, Anker Engelunds Vej 1 Bygning 101A, 2800, Kgs. Lyngby, Denmark

    Torkil Kollsker & Thomas J. R. Stidsen

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  1. Torkil Kollsker
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  2. Thomas J. R. Stidsen
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Correspondence to Thomas J. R. Stidsen.

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Kollsker, T., Stidsen, T.J.R. Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions. SN Oper. Res. Forum 2, 21 (2021). https://doi.org/10.1007/s43069-021-00062-3

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