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Models and algorithms for optimising two-dimensional LEGO constructions

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  • Kollsker, Torkil
  • Malaguti, Enrico

Abstract

The LEGO Construction Problem is the problem of deciding which bricks to place where in a predefined LEGO construction. The input consists of coloured voxels that each correspond to the size of a LEGO unit, such that all LEGO bricks are multiples of this LEGO unit. A solution to the LEGO Construction Problem is feasible if all bricks are within the design domain, the bricks do not overlap, the bricks satisfy the colour constraints, and all bricks connect into a stable construction.

Suggested Citation

  • Kollsker, Torkil & Malaguti, Enrico, 2021. "Models and algorithms for optimising two-dimensional LEGO constructions," European Journal of Operational Research, Elsevier, vol. 289(1), pages 270-284.
    • Handle: RePEc:eee:ejores:v:289:y:2021:i:1:p:270-284
    DOI: 10.1016/j.ejor.2020.07.004
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    References listed on IDEAS

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    1. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
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    3. Charles Fleurent & Fred Glover, 1999. "Improved Constructive Multistart Strategies for the Quadratic Assignment Problem Using Adaptive Memory," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 198-204, May.
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    2. Wang, Qianqing & Pantoja-Rosero, Bryan German & Santos, Ketson R.M. dos & Beyer, Katrin, 2024. "An image convolution-based method for the irregular stone packing problem in masonry wall construction," European Journal of Operational Research, Elsevier, vol. 316(2), pages 733-753.

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