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Non-dominated sorting (also known as non-dominated ranking) is a technique that involves categorizing a set of elements based on their dominance relationship with each other. The purpose of non-dominated sorting is to rank the elements from the best to the worst element according to their dominance relationship. The dominance relationship between elements is determined by comparing their scores on a fixed number of objective functions.[1]
In this context, an element dominates another element if it is better than the other element in at least one objective and no worse in any other objectives[1]. For example, if we have two elements A and B, and A has a better value than B in at least one objective, and no worse value in any other objectives, then A dominates B. On the other hand, if B has a better value than A in at least one objective, and no worse value in any other objectives, then B dominates A. If neither A dominates B nor B dominates A, then A and B are said to be non-dominated or incomparable with respect to each other.
Non-dominated sorting is a technique used to sort elements into different non-dominated fronts. Each front represents a subset of elements that are not dominated by any other elements in the same front. Elements in a given front are dominated by elements in the fronts that come before it, and dominate elements in the front that comes after it.[2]
The first non-dominated front contains the best elements - those that are not dominated by any other elements. In fact the first front corresponds exactly to the maximal elements of the set. The second front contains elements that are dominated only by elements in the first front (an element in the second front is not necessarily dominated by all the elements in the first front, but by at least one of them). The subsequent fronts contain elements that are progressively less optimal with respect to the objective functions.[2]
Non-dominated sorting is used in several multi-objective optimization algorithms.[1][3][2]