2.4. Application of the Genetic Algorithm to the Q Set
This protocol is extracted from research article:
Multiple Alignment of Promoter Sequences from the Arabidopsis thaliana L. Genome
Genes (Basel), Jan 21, 2021; DOI: 10.3390/genes12020135

To optimize matrices from the Q set, we used a genetic algorithm described in our previous study [25]. The aim was to change each PWM from the Q set to maximize F(L, L), which was considered an objective function. F(L, L) for each matrix was put into vector V(i) (i = 1, 2, …, n1), which was sorted in the ascending order from V(1) (the minimum) to V(n1) (the maximum) and the matrices in the Q set were arranged accordingly. Then, two matrices were randomly selected with the probability of choosing a matrix, which increased with the increase of i from 1 to n1, and the two matrices were used to create a “descendant”, for which any element of the first matrix was selected with an equal probability. Then, rectangles were randomly selected to the right and left above and below the selected element in the first matrix with the probability of 0.25 and the elements within the rectangle were moved from the first to the second matrix to create a descendant, which replaced the PWM with V(1).

Then, we introduced mutations in 10% of the randomly selected matrices from the Q set. To do this, a randomly selected element of the matrix was changed to a random value in the range from −10.0 to +10.0. Usually, less than 104 cycles were required to achieve the moment when V(n1) did not increase, i.e., to reach the maximum designated as maxV(n1). However, in rare cases, more than 105 cycles were performed. At the output of the algorithm (Figure 1), we obtained maxV(n1), two-dimensional alignment of sequences S1 and S, and matrix maxW, which were used to compute the alignment.

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