Fitness function

Got its name from genetics . Allows you to assess the degree of fitness of specific individuals in the population and choose from them the most adapted (that is, having the maximum values ​​of the fitness function) in accordance with the evolutionary principle of survival of the "strongest" (best adapted)

In the field of genetic programming and genetic algorithms, each solution studied is usually represented as a string of numbers or characters (called a chromosome ). The main idea is to remove n worst-case solutions (chromosomes) after each round of testing or modeling and introduce n new solutions (chromosomes) into the population. To implement this method, each solution studied must correspond to a certain value that indicates how close the solution is to the desired value, the specified value is obtained by applying the fitness function . Despite the fact that the algorithm is engaged in the search for the optimal solution, the main direction in the search is set by the person who must determine the fitness function . If it is poorly designed, the algorithm will either converge on a non-optimal solution, or will hardly converge to a solution in general.

The fitness function should not only closely correlate with the desired solution, but also be quickly calculated. Speed ​​of execution is very important, since a typical genetic algorithm must be repeated many times (from 1000 iterations (generations)) in order to find a solution for a non-trivial task.

The fitness function has a strong influence on the operation of genetic algorithms and must have an accurate and correct definition. In optimization problems , the fitness function is usually optimized (maximized) and is called the objective function . In minimization problems, the objective function is transformed, and the problem is reduced to maximization.

In control theory , it can take the form of an error function , and in game theory it can take the value function . At each iteration of the genetic algorithm, the fitness of each individual of a given population is evaluated using the fitness function, and based on this assessment, the following population is created, which constitute a set of potential solutions ^[1] .

1. The function must be adequately defined. This means that for a successful search it is necessary that the distribution of values ​​coincides with the distribution of the real quality of the solutions.
2. The function should have a diverse relief, without large "flat" sections. That is, despite the fact that the solutions differ, they have the same score, which means the algorithm does not have the ability to choose the best solution, choose the direction of further development. This problem is also referred to as the “ golf course problem ”, where the entire space is exactly the same, with the exception of only one point, and is the optimal solution - in this case, the algorithm will simply stop or wander completely by accident.
3. The fitness function should require a minimum of resources. Since this is the most frequently used detail of the algorithm, it has a significant impact on its speed ^[2] .

The fitness function turns the state space into a fitness landscape (adaptive landscape) ^{[ unknown term ]} , where each point in space has a certain "height", in accordance with the value of its fitness.

• Genetic algorithm