Chromosome crossover points

Figure 2 Genetic operators used to create a population of children chromosomes from a population of parent chromosomes, (a) Single-point mutation. A gene to he mutated is selected at random, and its value is modified, (b) One-point crossover. The crossover point is selected randomly, and the genes are exchanged between the two parents. Two children are created, each having genes from both parents.

In this step, recombination (crossover) and mutation operators are applied to the individuals selected for reproduction in the previous step. The number of chromosomes, which will be reproduced by crossover operation, as well as, crossover points, can be determined either deterministically by the user or randomly. For example, in case of one-point crossover (see for example in Fig. 11.4) the chromosomes of the parents are cut at some randomly chosen point and the resulting subchromosomes are swapped. As far as the mutation operator is concerned, the user gives the number of genes to be changed per generation. The points to be mutated are chosen either randomly or deterministically according to the accident scenario considered (see for example in Fig. 11.4). 

In metaphase of melosis I, both sister chromatids In one (replicated) chromosome associate with microtubules emanating from the same spindle pole, rather than from opposite poles as they do In mitosis. Two physical links between homologous chromosomes are thought to resist the pulling force of the spindle until anaphase (a) crossing over between chromatids, one from each pair of homologous chromosomes, and (b) cohesin cross-links between chromatids distal to the crossover point. 

In case of crossover, randomly, a father and mother are selected. Also, a crossover position is fixed in the chromosome or in the bit character string, which is used to derive the aggregation of the genes of the parents. All bits left of the crossover point are transferred to the child from the father and all bits right of the point are given by the mother and vice versa. 

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. 

In uniform crossover, a coin is flipped for each bit of the chromosome. If it is heads, the first child gets this bit from the first parent, and the second child gets this bit from the second parent If it is tails, then the first child gets this bit from the second parent, and the second child gets this bit from the first parent. Hence, uniform crossover is similar to n-point crossover, except the number of crossover points changes with each new pair of children. Uniform crossover is demonstrated in Figure 6.17. The two parents are both automatically replaced by their children, or of the four individuals, the two most fit are kept and the other two discarded. ... 

For the so-called one-point crossover a position within the chromosomes is randomly picked at the same position in both parents and the chromosomes are both cut at this position. Then the first part of chromosome 1 is concatenated with the second part of chromosome 2, and vice versa. This procedure is shown in Figure 9-29. 

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). 

There is no single point at which these two chromosomes can be cut to crossover and form the all-zero string. However, a two-point crossover scheme would work. Imagine making cuts between bit pairs [3,4] and [9,10]. The first child gets the first and fourth segments of parent 1, and the second and third of... 

The uniform crossover n ethod will allow (in principle) any pair of schemata to be combined. In one-point crossover, schemata nearby on the chromosome tend to stay together, so that if two parameters tend to behave in a correlated fashion, crossover is most helpful (or least harmful) if those parameters are coded within nearby regions of the chromosome. However, one typically does not know about these correlations beforehand, and in taa. these correlations may be precisely what one wishes to discover. Uniform crossover minimizes this need to carefully order the parameters. 

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, in principle, is a simple cut and swap operation. Due to the nature of constraints, a modified crossover operation is required. In this study, to make sure the offspring chromosomes are feasible, crossover operation is not applied to feasible chromosome, but to the corresponding initial chromosome. After crossover operation, the corresponding off-springs will be cut to satisfy constraints and to ensure all offsprings are feasible. This study uses one-point crossover, illustrated as follows ... 

Each chromosome of the bivalent divides into two chromatids, and the bivalent is now composed of four chromatids. But, in contrast to chromatid separation in mitotic prophase, these chromatids are held together in some points of their structure. These points of attachment are referred to as chiasmata. At the chias-mata, two of the four chromatids form an x. The chiasmata provide for genetic crossover and probably result from the breaking followed by the refusion of the chromatids. 

The others genetic operators, rather then selection, are crossover and mutation. A crossover operation, as it is performed in this work, interchange genetic information, which are crossedover at random points of the chromosome. This genetic operation is executed according to equation (7). 

A uniform crossover is the generalized form of crossover where chromosomal exchanges happen between parents, across multiple (the number chosen randomly) cut-points. The recombination operator has a probability associated with it which dictates how often it is used. The probability of crossover is typically set to a high value (around 99%) for binary coded representation. A random number is drawn and whenever it falls below the crossover probability, two individuals (selected using one of the selection schemes described in the previous section) are allowed to undergo crossover. If the random number test fails, the chosen individuals are duplicated and placed in the offspring population. 

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