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Evolutionary Search of Binary Orthogonal Arrays

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11101)


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.


  • Orthogonal arrays
  • Genetic algorithms
  • Genetic programming
  • Boolean functions

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  • DOI: 10.1007/978-3-319-99253-2_10
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This work has been supported in part by Croatian Science Foundation under the project IP-2014-09-4882.

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Correspondence to Luca Mariot .

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Mariot, L., Picek, S., Jakobovic, D., Leporati, A. (2018). Evolutionary Search of Binary Orthogonal Arrays. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11101. Springer, Cham.

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