Evolutionary Search of Binary Orthogonal Arrays

Balanced crossover operators in Genetic Algorithms

“…In this section, we discuss the main findings that can be deduced from the results reported in the previous section, especially with respect to the research hypotheses laid out in Section 4.2. Additionally, we compare our results with those obtained by two recent works in the literature, namely [17] for the balanced Boolean functions and bent functions problems and [12] for the orthogonal arrays problem. Best fitness at the last generation Figure 9: Results of the OA problem, (16,15,2,4) instance.…”

“…The third and fourth columns report, for each problem instance, the size of the corresponding search space respectively when one-point crossover is used (UNB Size) and when balanced crossover operators are adopted (BAL size). The details for the computation of the search space sizes can be found in [12]. It can be remarked from Table 1 that for the two Boolean functions problems (Bal-NL and Bent) the use of balanced crossover operators yields a reduction of the search space between one and two orders of magnitude.…”

“…On the other hand the map-of-ones crossover performs slightly worse than the other considered methods on the bent functions problem, with a more pronounced difference in the median fitness for higher number of variables. Table 3 compares the success rates for the OA problem between our mapof-ones crossover and the Genetic Algorithms with counter-based crossover (GA-CB) and Genetic Programming (GP) proposed in [12]. One can remark that over the smallest problem instance the map-of-ones crossover converges more frequently than the GA-CB algorithm.…”

“…The first researchers who pioneered this approach in the area of cryptography were Millan et al [14], who proposed a counter-based crossover operator to evolve balanced Boolean functions, which was later adapted to evolve plateaued functions in [10]. Similar operators have been later proposed for GA applied to combinatorial designs problems [11,12], portfolio optimization [2,3], multiobjective k-subset selection [13] and disease classification [18,19].…”

On the Difficulty of Evolving Permutation Codes

“…Apart from algebraic constructions, for which the reader may find a survey in [3], a few heuristic algorithms have also been developed to construct large permutation codes [22,19], mostly based on branch and bound and iterative clique search approaches. As far as we know, up to now, there have been no attempts in the literature to employ Evolutionary Algorithms (EA) to address this problem, although some authors used EA in the past to evolve other kinds of combinatorial designs, such as orthogonal Latin squares [17], orthogonal arrays [18] and disjunct matrices [15].…”