Single point crossover

To determine the optimal number of cut points, it is necessary to return to the balance of exploration and exploitation. Uniform crossover is more exploratory than single-point crossover because the number of schema that can be sampled increases (Spears, 1993). However, the exploration comes at the cost of exploitation because more of the schema are disrupted (Eschelman et al., 1989). The specific balance between these effects will depend on the sampling ability of the library, the structure of the schema, and the ruggedness of the fitness landscape. 

The mating procedure is performed by a single-point crossover, i.e., the chromosomes of the two parents are cut in a single position and the cut segments are swapped. 

The remainder of the new population is filled in via single-point crossover, which is a type of sexual reproduction. A pair of individuals (the parents) is chosen from the mating pool, and their chromosomes are lined up, split at a single point, and the left and right halves are swapped, producing two new individuals (the children) (Figure 3). 

Single-point crossover as used by the SGA has the problem that it is often difficult to quickly recombine some good building blocks into an optimal individual, turning to the four-word problem from above, imagine the following pair of individuals ... 

Single point crossover follows the procedures below. 

The two offspring each inherit some genes from each parent fi om this single point crossover. Figure 8.2 shows a single point crossover that occurs after the third bits of two ten-bit parental chromosomes. 

Crossover Form two offspring candidate solutions (trees) from each randomly selected pair of parent trees from the parent pool. Crossover can be performed multiple ways. For example, in the single-point crossover shown in Fig. 3.59c, a location is selected randomly within the stractnre of each parent tree. Next, the respective trees are spliced at that location and offspring candidate solntions are created by mutually exchanging and combining the spliced segments of the parent trees. 

Once two parents are selected, they must be recombined to form two new children. Single point crossover is the simplest recombination method. If the length of the chromosome (the string of I s and O s representing each individual) is m, then some point p between 1 and m - 1 is chosen as the crossover point. To create the first child, the first p bits of the first parent are combined with the last m - p bits of the second parent. The second child is created by attaching the first p bits of the second parent to the last m- p bits of the first parent. Alternatively, with n-point crossover, n crossover points are selected and the children are produced analogously. This process is demonstrated in Figure 6.16. 

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