Crossover

Each feature v_ij of a cluster center is a real number. In order to do crossover the feature value is converted into an integer which captures three decimal places of precision. The integer is then represented as a binary bit string. For example, if the largest value for a feature is 7.999 then it will be converted to 7999 which may be represented by a 13 bit binary number. The binary representation of a V matrix with c clusters and s features each represented by 13 bits requires $c\times s \times 13$ bits (for this example). Crossover is done using 2 point crossover [7]. Each binary string is viewed as a ring. Then 2 cut points are chosen and the bits between the cut points are interchanged to form the two children.

This crossover operation is done on each of the c cluster centers of the mating parents. Crossover produces two children for the next generation which are created by concatenating the results of the c crossovers. It is necessary to do c crossovers to enable each cluster center to move independently of the others. Allowing each cluster center to be adjusted during a generation is important to minimize the number of generations, because each generation requires significant time in the calculation of the R_m value of each population member.