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.

Mariot, L., Picek, S., Jakobovic, D., Leporati, A. (2018). Evolutionary search of binary orthogonal arrays. In Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, Coimbra, Portugal, September 8–12, 2018, Proceedings, Part I (pp.121-133). Springer Verlag [10.1007/978-3-319-99253-2_10].

Evolutionary search of binary orthogonal arrays

Mariot, Luca
;
Leporati, Alberto
2018

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.
slide + paper
Boolean functions; Genetic algorithms; Genetic programming; Orthogonal arrays;
Boolean functions; Genetic algorithms; Genetic programming; Orthogonal arrays; Theoretical Computer Science; Computer Science (all)
English
15th International Conference on Parallel Problem Solving from Nature, PPSN 2018
2018
Fonseca C.M.,Lourenco N.,Machado P.,Paquete L.,Whitley D.,Auger A.
Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, Coimbra, Portugal, September 8–12, 2018, Proceedings, Part I
9783319992525
2018
11101
121
133
https://www.springer.com/series/558
none
Mariot, L., Picek, S., Jakobovic, D., Leporati, A. (2018). Evolutionary search of binary orthogonal arrays. In Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, Coimbra, Portugal, September 8–12, 2018, Proceedings, Part I (pp.121-133). Springer Verlag [10.1007/978-3-319-99253-2_10].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/213970
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