## Genetic Algorithm Terminology

### Fitness Functions

The *fitness function* is the function you
want to optimize. For standard optimization algorithms, this is known
as the objective function. The toolbox software tries to find the
minimum of the fitness function.

Write the fitness function as a file or anonymous function, and pass it as a function handle input argument to the main genetic algorithm function.

### Individuals

An *individual* is any point to which you
can apply the fitness function. The value of the fitness function
for an individual is its score. For example, if the fitness function
is

$$f\left({x}_{1},{x}_{2},{x}_{3}\right)={\left(2{x}_{1}+1\right)}^{2}+{\left(3{x}_{2}+4\right)}^{2}+{\left({x}_{3}-2\right)}^{2},$$

the vector (2, -3, 1), whose length is the number of variables
in the problem, is an individual. The score of the individual (2,
–3, 1) is *f*(2, –3,
1) = 51.

An individual is sometimes referred to as a *genome* and
the vector entries of an individual as *genes*.

### Populations and Generations

A *population* is an array of individuals.
For example, if the size of the population is 100 and the number of
variables in the fitness function is 3, you represent the population
by a 100-by-3 matrix. The same individual can appear more than once
in the population. For example, the individual (2, -3, 1) can appear
in more than one row of the array.

At each iteration, the genetic algorithm performs a series of
computations on the current population to produce a new population.
Each successive population is called a new *generation*.

### Diversity

*Diversity* refers to the average distance
between individuals in a population. A population has high diversity
if the average distance is large; otherwise it has low diversity.
In the following figure, the population on the left has high diversity,
while the population on the right has low diversity.

Diversity is essential to the genetic algorithm because it enables the algorithm to search a larger region of the space.

### Fitness Values and Best Fitness Values

The *fitness value* of an individual is the
value of the fitness function for that individual. Because the toolbox
software finds the minimum of the fitness function, the *best* fitness
value for a population is the smallest fitness value for any individual
in the population.

### Parents and Children

To create the next generation, the genetic algorithm selects
certain individuals in the current population, called *parents*,
and uses them to create individuals in the next generation, called *children*.
Typically, the algorithm is more likely to select parents that have
better fitness values.