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Grammar-Based Evolution of Polyominoes

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Genetic Programming (EuroGP 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14631))

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Abstract

Languages that describe two-dimensional (2-D) structures have emerged as powerful tools in various fields, encompassing pattern recognition and image processing, as well as modeling physical and chemical phenomena. One kind of two-dimensional structures is given by labeled polyominoes, i.e., geometric shapes composed of connected unit squares represented in a 2-D grid. In this paper, we present (a) a novel approach, based on grammars, for describing sets of labeled polyominoes that meet some predefined requirements and (b) an algorithm to develop labeled polyominoes using the grammar. We show that the two components can be used for solving optimization problems in the space of labeled polyominoes, similarly to what happens for strings in grammatical evolution (and its later variants). We characterize our algorithm for developing polyominoes in terms of representation-related metrics (namely, validity, redundancy, and locality), also by comparing different representations. We experimentally validate our proposal using a simple evolutionary algorithm on a few case studies where the goal is to obtain a target polyomino: we show that it is possible to enforce hard constraints in the search space of polyominoes, using a grammar, while performing the evolutionary search.

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Acknowledgements

This research is the result of the collaboration with the Department of Engineering and Architecture of the University of Trieste, Italy; supported by the 2023 SPECIES scholarship. The first author is funded by FCT - Foundation for Science and Technology, under the grant 2022.10174.BD. This work was supported by the Portuguese Recovery and Resilience Plan (PRR) through project C645008882-00000055, Center for Responsible AI, by the FCT, I.P./MCTES through national funds (PIDDAC), by Project No. 7059 - Neuraspace - AI fights Space Debris, reference C644877546-00000020, supported by the RRP - Recovery and Resilience Plan and the European Next Generation EU Funds, following Notice No. 02/C05-i01/2022, Component 5 - Capitalization and Business Innovation - Mobilizing Agendas for Business Innovation, and within the scope of CISUC R &D Unit - UIDB/00326/2020.

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Authors and Affiliations

  1. University of Coimbra, CISUC/LASI - Centre for Informatics and Systems of the University of Coimbra, Department of Informatics Engineering, Coimbra, Portugal

    Jessica Mégane, Nuno Lourenço & Penousal Machado

  2. Department of Engineering and Architecture, University of Trieste, Trieste, Italy

    Eric Medvet

Authors
  1. Jessica Mégane
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  2. Eric Medvet
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  3. Nuno Lourenço
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  4. Penousal Machado
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Correspondence to Eric Medvet .

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Editors and Affiliations

  1. University of Torino, Grugliasco, Italy

    Mario Giacobini

  2. Victoria University of Wellington, Wellington, New Zealand

    Bing Xue

  3. University of Trieste, Trieste, Italy

    Luca Manzoni

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Mégane, J., Medvet, E., Lourenço, N., Machado, P. (2024). Grammar-Based Evolution of Polyominoes. In: Giacobini, M., Xue, B., Manzoni, L. (eds) Genetic Programming. EuroGP 2024. Lecture Notes in Computer Science, vol 14631. Springer, Cham. https://doi.org/10.1007/978-3-031-56957-9_4

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  • DOI: https://doi.org/10.1007/978-3-031-56957-9_4

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