Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions

Torkil Kollsker and Thomas J. R. Stidsen ()
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Torkil Kollsker: Technical University of Denmark
Thomas J. R. Stidsen: Technical University of Denmark

SN Operations Research Forum, 2021, vol. 2, issue 2, 1-52

Abstract: 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.

Keywords: Combinatorial optimisation (90C27); Mixed integer programming (90C11); Combinatorics and topology (37F20); Approximation methods and heuristics (90C59) (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s43069-021-00062-3

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