Landscape of values
A value landscape is the somewhat flowery expression for a mathematical function , where is a (freely selectable) set. Usually a value landscape function is needed in connection with optimization problems , where a (global) optimum of such a function is sought. In such contexts, a value landscape is often assigned a neighborhood function.
If a global optimum, i.e. a global minimum or a global maximum , is sought, then mountains and valleys are often used as an illustration . This corresponds precisely to the maxima and minima of the value landscape , which is why landscape is a very suitable term for it. In the imagination of one's value system the potential surface not dissimilar.
When looking for mountains or valleys in the value landscape , the mountaineer is often referred to . It symbolizes a (current) location in the value landscape (i.e. a position in the function ). Since many optimization methods choose a location from the surroundings of the previous location as the next location in each case, the mountaineer can often also hike .
Terms such as a value landscape help to better imagine and thus understand abstract mathematical relationships and processes.
In the case of genetic algorithms , the value landscape is also called the fitness landscape , since in this case an individual is assigned to each genome and a fitness to each individual.
Landscape types
Some value landscapes correspond to certain types for which certain properties apply. The following types exist: