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New Generation

As before, the population is a set of (profile, fitness) tuples. For the present purposes, assume that the profiles in the population are ordered in the decreasing order of their fitness. So let,

When a new generation of the population is created, the fit members of the population are retained and the unfit ones are eliminated. Let be the retention rate, namely the proportion of population members that will be retained in the new generation. The vacancies are proportional to (1 - ). Let be the crossover rate, namely the proportion of vacancies filled in by crossovers. The remaining vacancies are filled in by mutations. The new generation can then be described as follows: where

where is the size of population and and are random numbers between and . The probability that (or ) being some number is proportional to i.e. the fitness of .

Since the members added by mutation and crossover search for newer kinds of information, the serendipity in the system is proportional to the new members added every generation i.e. proportional to . The stability of the system is proportional to , which indicates the proportion of the population that is stable across generations. These values can be appropriately modified to better suit user preferences.


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