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Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.
Point C is not on the Pareto frontier because it is dominated by both point A and point B. Points A and B are not strictly dominated by any other, and hence lie on the frontier. A production-possibility frontier. The red line is an example of a Pareto-efficient frontier, where the frontier and the area left and below it are a continuous set of ...
The set of all Pareto-optimal solutions, also called Pareto set, represents the set of all optimal compromises between the objectives. The figure below on the right shows an example of the Pareto set of two objectives and to be maximized. The elements of the set form the Pareto front (green line).
In Pareto efficiency, a Pareto optimum is a maximal element with respect to the partial order of Pareto improvement, and the set of maximal elements is called the Pareto frontier. In decision theory , an admissible decision rule is a maximal element with respect to the partial order of dominating decision rule .
In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions.It is often used to model the tails of another distribution. It is specified by three parameters: location , scale , and shape
Constrained Pareto efficiency is a weakening of Pareto optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual ...
All the points on this locus are Pareto efficient allocations, meaning that from any one of these points there is no reallocation that could make one of the people more satisfied with his or her allocation without making the other person less satisfied. The contract curve is the subset of the Pareto efficient points that could be reached by ...
Ordinal Pareto efficiency refers to several adaptations of the concept of Pareto-efficiency to settings in which the agents only express ordinal utilities over items, but not over bundles. That is, agents rank the items from best to worst, but they do not rank the subsets of items.