Solution:

The generation of successors in a GA is determined by a set of operators that recombine and mutate selected members of the current population. These operators correspond to idealized versions of the genetic operations found in biological evolution.

The two most common operators are crossover and mutation.

crossover operator:

The crossover operator produces two new offspring from two-parent strings, by copying selected bits from each parent. The bit at the position I in each offspring is copied from the bit at position i in one of the two parents.

crossover mask:

The choice of which parent contributes the bit for position i is determined by an additional string called the crossover mask.

Single-point crossover operator:

To illustrate, consider the single-point crossover operator at the top of the Table Consider the topmost of the two offspring in this case.

The second offspring uses the same crossover mask, but switches the roles of the two parents. Therefore, it contains the bits that were not used by the first offspring.

In the single-point crossover, the crossover mask is always constructed so that it begins with a string containing n contiguous Is, followed by the necessary number of 0s to complete the string.