Genetic crossover

Crossover, which is also called recombijiation, follows the idea that aji offspring in natiu c always holds genes from both its parents. Accordingly, the genetic crossover operator takes parts of two parent chromosomes to create a new offspring. 

Step 4 Randomly pairing up the chromosomes in the new population, apply the genetic crossover operator to each pair. That is, randomly select a bit-position, say k, for each pair of chromosomes, say and and replace this pair with two new pairs - and - constructed via genetic < rossover C, consists of the first k bits of C,i, and the last N — k) bits of and C, consists of the first k bits of and the last N — k) bits of. ... 

Next, we randomly pair up the new chromosomes, and perform the genetic crossover operation at randomly selected bit-positions -- chromosomes C and C4 exchange their last three bits, C2 and Cg exchange their last four bits, and C3 and C5 exchange their last bit ... 

The nature of the mutational event which could lead to a peptide chain extension can only be guessed at. A mutation in an initiation codon or in the recognition site in the intercistronic region could have been sufficient to form the first zymogen. Alternatively a partial genetic crossover could lead to such an extension. 

It is noted that mutant or wild-type phages or viruses may occur (Voet and Voet, 1995, p. 842). Thus, we may be speaking of genetic crossovers, such as for influenza viruses that invade humans as weU as animals, and even of such incidences as of the Marburg and Ebola viruses. 

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 genetic crossover operator adopted here is the k-point crossover. The mutation operator is based on a random sort of a procedure to guarantee the diversity of the explored solutions (random gene replacement, gene permutation. ..). The classical Goldberg s biased roulette wheel is used for selection. 

Fig. 2 Illustration of the most basic genetic crossover operations, i.e. single point (top line) and two point crossover. Horizontal bars represent parent (left) and children trial solution vectors.

The evolutionary process of a genetic algorithm is accomplished by genetic operators which translate the evolutionary concepts of selection, recombination or crossover, and mutation into data processing to solve an optimization problem dynamically. Possible solutions to the problem are coded as so-called artificial chromosomes, which are changed and adapted throughout the optimization process until an optimrun solution is obtained. 

Selection alone cannot achieve an optimization towards the solution With mere scicction performed over a number of generations, one would get a population which comprises only the best chromosome of the original population. Therefore, an operator has to be applied which causes variance within the population, This is achieved by the application of genetic operators such as the crossover and the mutation operators. 

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.

Figure 11.11 shows examples of the three basic genetic operations of reproduction, crossover and mutation, as applied to a population of 8-bit chromosomes. Reproduction makes a set of identical copies of a given chromosome, where the number of copies depends on the chromosome s fitness (see below). The crossover operator exchanges subparts of two chromosomes, where the position of the crossover is randomly selected, and is thus a crude facsimile of biological sexual recombination between two single-chromosome organisms. The mutation operator randomly flips one or more bits in the chromosome, where the bit positions are randomly chosen. 

Fig. 11.11 Schematic representation of the basic genetic operations of reproduction, crossover and mutation.

Table 11.3 One pass (read left to right) through the step.s of a basic genetic algorithm scheme to maximize the fitness function f x) = using a population of six 6-bit chromosomes. The crossover notation aina2) means that chromosomes Ca, and Ca2 exchange bits beyond the bit. The underlined bits in the Mutation Operation column are the only ones that have undergone random mutation. See text for other details.

Besides unequal crossover and transposition, a third mechanism can effect rapid changes in the genetic material. Similar sequences on homologous or nonhomol-ogous chromosomes may occasionally pair up and eliminate any mismatched sequences between them. This may lead to the accidental fixation of one variant or another throughout a family of repeated sequences and thereby homogenize the sequences of the members of repetitive DNA families. This latter process is referred to as gene conversion. 

The mechanism for accomplishing this is crossover. In one-point crossover (Figure 5.14), two strings chosen at random from the freshly created parent pool are cut at the same randomly chosen position into a head section and a tail section. The heads are then swapped, so that two offspring are created, each having genetic material from both parents. 

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