Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions

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. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.