11.2 Example

A very simple example illustrates the mechanics of the algorithm. Figure 11.3 shows the function

for 0 ≤ x < 16. Let the population consist of four units A, B, C, and D with solutions x encoded in 4-bit strings. (A simple function and small population were chosen to provide a clear example. Normal functions are not so simple and populations are larger.)

Units are initialized with random values for the first generation.

After random selection weighted by fitness, the population is A, B, D, D. Unit C with fitness 0 has died and unit D, with the highest fitness, is selected twice.

A mates to D and B mates to D, both with crossover after the 3rd bit.

Mutation flips the 3rd bit in a.

The resulting population after one generation is

Units c and d have already reached the maximum of the function at x = 7 and the average score has increased from 37.75 to 57.75.