| ### Chapter 11 - Genetic Algorithms and Neural Networks
Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks
Russell D. Reed and Robert J. Marks II
Copyright © 1999 Massachusetts Institute of Technology

## 11.2 Example

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

Figure 11.3: The function considered in the example.

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.

Generation 1

unit | x | bits | J | fi
A | 1 | 0001 | 28 | 0.1854
B | 9 | 1001 | 60 | 0.3973
C | 15 | 1111 | 0 | 0
D | 6 | 0110 | 63 | 0.4742

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.

New Population

unit
A | 0001
B | 1001
D | 0110
D | 0110

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

Mating results

unit
a | 0000
b | 1000
c | 0111
d | 0111

Mutation flips the 3rd bit in a.

Mutation results

unit
a | 0010
b | 1000
c | 0111
d | 0111

The resulting population after one generation is

Generation 2

unit | x | bits
--- | --- | ---
J | fi
a | 2 | 0010 | 39 | 0.1696
b | 8 | 1000 | 63 | 0.2739
c | 7 | 0111 | 64 | 0.2782
d | 7 | 0111 | 64 | 0.2782

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.