Search Methods
       Adaptive
           Converging Set Methods
                Genetic Algorithms

Genetic algorithms (GA) are an adoption of biological evolution theories to global optimization [Holland 1975]. Starting from a randomly generated initial sample (population) S, the basic idea is to select a subset for which mutations and crossovers are used to obtain new sample points. New sample points are kept only if they are "fit enough", i.e., have low enough function value.

The traditional way to represent the population is to encode each individual as a string of 0's and 1's, by using a 10-bit binary number (suitably scaled) for each coordinate.

In the selection step the subset is biased towards the best individuals.

The crossover operation is achieved by taking two individuals from the subset, cutting the strings at a random index (or several) and exchanging parts.

Mutation is achieved by simply flipping a 0 for a 1 or vice versa at some random index. Mutations are usually given low occurrence probability per iteration.

Among the newly created individuals only the best are kept and will replace the worst in S. Those that are worse than their parents are thrown away.