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Abstract: The field of algorithmic self-assembly is concerned with the design andanalysis of self-assembly systems from a computational perspective, that is,from the perspective of mathematical problems whose study may give insight intothe natural processes through which elementary objects self-assemble into morecomplex ones. One of the main problems of algorithmic self-assembly is theminimum tile set problem MTSP, which asks for a collection of types ofelementary objects called tiles to be found for the self-assembly of anobject having a pre-established shape. Such a collection is to be as concise aspossible, thus minimizing supply diversity, while satisfying a set of stringentconstraints having to do with the termination and other properties of theself-assembly process from its tile types. We present a study of what we thinkis the first practical approach to MTSP. Our study starts with the introductionof an evolutionary heuristic to tackle MTSP and includes results from extensiveexperimentation with the heuristic on the self-assembly of simple objects intwo and three dimensions. The heuristic we introduce combines classic elementsfrom the field of evolutionary computation with a problem-specific variant ofPareto dominance into a multi-objective approach to MTSP.



Autor: Fabio R. J. Vieira, Valmir C. Barbosa

Fuente: https://arxiv.org/



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