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# 6 Reinsertion

Once the offspring have been produced by selection, recombination and mutation of individuals from the old population, the fitness of the offspring may be determined. If less offspring are produced than the size of the original population then to maintain the size of the original population, the offspring have to be reinserted into the old population. Similarly, if not all offspring are to be used at each generation or if more offspring are generated than the size of the old population then a reinsertion scheme must be used to determine which individuals are to exist in the new population.

The used selection method determines the reinsertion scheme: local reinsertion for local selection and global reinsertion for all other selection methods.

## 6.1 Global reinsertion

Different schemes of global reinsertion exist:

• produce as many offspring as parents and replace all parents by the offspring (pure reinsertion).
• produce less offspring than parents and replace parents uniformly at random (uniform reinsertion).
• produce less offspring than parents and replace the worst parents (elitist reinsertion).
• produce more offspring than needed for reinsertion and reinsert only the best offspring (fitness-based reinsertion).

Pure Reinsertion is the simplest reinsertion scheme. Every individual lives one generation only. This scheme is used in the simple genetic algorithm. However, it is very likely, that very good individuals are replaced without producing better offspring and thus, good information is lost.

Fig. 6-1: Scheme for elitist insertion

The elitist combined with fitness-based reinsertion prevents this losing of information and is the recommended method. At each generation, a given number of the least fit parents is replaced by the same number of the most fit offspring (see figure ). The fitness-based reinsertion scheme implements a truncation selection between offspring before inserting them into the population (i.e. before they can participate in the reproduction process). On the other hand, the best individuals can live for many generations. However, with every generation some new individuals are inserted. It is not checked whether the parents are replaced by better or worse offspring.

Because parents may be replaced by offspring with a lower fitness, the average fitness of the population can decrease. However, if the inserted offspring are extremely bad, they will be replaced with new offspring in the next generation.

## 6.2 Local reinsertion

In local selection individuals are selected in a bounded neighborhood. (see Section 3.5). The reinsertion of offspring takes place in exactly the same neighborhood. Thus, the locality of the information is preserved.

The used neighborhood structures are the same as in local selection. The parent of an individual is the first selected parent in this neighborhood.

For the selection of parents to be replaced and for selection of offspring to reinsert the following schemes are possible:

• insert every offspring and replace individuals in neighborhood uniformly at random,
• insert every offspring and replace weakest individuals in neighborhood,
• insert offspring fitter than weakest individual in neighborhood and replace weakest individuals in neighborhood,
• insert offspring fitter than weakest individual in neighborhood and replace parent,
• insert offspring fitter than weakest individual in neighborhood and replace individuals in neighborhood uniformly at random,
• insert offspring fitter than parent and replace parent.

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This document is part of version 3.8 of the GEATbx: Genetic and Evolutionary Algorithm Toolbox for use with Matlab - www.geatbx.com.
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