# Fitness function

A fitness function is the objective function of an evolutionary (optimization) algorithm (EA). Occasionally a fitness function is also described as part of an objective function or vice versa. Like evolutionary algorithms, fitness functions have a biological model, biological fitness , which indicates the degree of adaptation of an organism to its environment. In evolutionary algorithms, the fitness of a candidate describes how well he solves the underlying optimization problem. The fitness function uses the properties of an attempted solution to calculate how well this "individual" is suitable as a solution to the problem posed.

A fitness function does not necessarily have to be able to calculate an absolute value, since it is often enough to compare candidates in order to select the better one. A relative statement of fitness (candidate a is better than b ) is sufficient in some cases, e.g. B. in the tournament selection .

If a solution is sought for several problems at the same time ( multi-objective optimization ) and these cannot be combined, the fitness function does not return a single value , but a tuple .

## Examples

A passenger seat for aircraft is to be optimized, there are various objectives for this:

1. it should be as light as possible;
2. it should be as round as possible and not angular;
3. it should be inexpensive to manufacture;
4. it should use as little material as possible that is difficult to recycle.

The fitness function then uses the geometry parameters to calculate a tuple with four numbers ("the smaller the number, the better"):

{ Weight ; Sum_of_ edge lengths; Manufacturing costs; Mass_bad material}

Different seat geometries can then be classified on the basis of their associated tuples: Which variant is the easiest, which costs the least?

## Individual evidence

1. Thomas Jansen: Analyzing Evolutionary Algorithms: The Computer Science Perspective , page 7.
2. Thomas Baeck, DB Fogel, Z. Michalewicz: Evolutionary Computation 2: Advanced Algorithms and Operators , page 2.