## Abstract

Orthogonal Arrays (OA) represent an interesting breed of combinatorial designs that finds applications in several domains such as statistics, coding theory, and cryptography. In this work, we address the problem of constructing binary OA through evolutionary algorithms, an approach which received little attention in the combinatorial designs literature. We focus on the representation of a feasible solution, which we encode as a set of Boolean functions whose truth tables are used as the columns of a binary matrix, and on the design of an appropriate fitness function and variation operators for this problem. We finally present experimental results obtained with genetic algorithms (GA) and genetic programming (GP) on optimizing such fitness function, and compare the performances of these two metaheuristics with respect to the size of the considered problem instances. The experimental results show that GP outperforms GA at handling this type of problem, as it converges to an optimal solution in all considered problem instances but one.

Original language | English |
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Title of host publication | Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, 2018, Proceedings |

Editors | A. Auger, C.M. Fonseca, N. Lourenço, P. Machado, L. Paquete, D. Whitley |

Place of Publication | Cham |

Publisher | Springer |

Pages | 121-133 |

Number of pages | 13 |

Edition | 1 |

ISBN (Electronic) | 978-3-319-99253-2 |

ISBN (Print) | 978-3-319-99252-5 |

DOIs | |

Publication status | Published - 2018 |

Event | 15th International Conference on Parallel Problem Solving from Nature, PPSN 2018 - Coimbra, Portugal Duration: 8 Sep 2018 → 12 Sep 2018 Conference number: 15 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Publisher | Springer |

Volume | 11101 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th International Conference on Parallel Problem Solving from Nature, PPSN 2018 |
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Country | Portugal |

City | Coimbra |

Period | 8/09/18 → 12/09/18 |

## Keywords

- Boolean functions
- Genetic algorithms
- Genetic programming
- Orthogonal arrays