PARETO SET Meaning and
Definition
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The Pareto set, also known as the Pareto front or Pareto frontier, is a concept derived from Pareto efficiency in economics. It refers to a set of solutions that represents the best possible outcomes for a given multi-objective optimization problem.
In the context of decision-making, a multi-objective optimization problem involves simultaneously considering multiple criteria or objectives that are often conflicting or mutually exclusive. This could include maximizing efficiency while minimizing cost or maximizing revenue while minimizing risk.
The Pareto set consists of solutions that cannot be improved in any of the objectives without sacrificing the performance in at least one of the other objectives. In other words, any solution outside the Pareto set is considered dominated by at least one solution in the set.
Each solution in the Pareto set is considered non-inferior or Pareto optimal, meaning it is the best achievable outcome in its respective combination of objectives. The Pareto set is often visualized as a convex curve or front in a multi-dimensional objective space, where each point represents a solution.
The Pareto set is widely used in various fields, such as economics, engineering, computer science, and operations research. It helps decision-makers identify the trade-offs between objectives and select the most suitable options based on their preferences. With the Pareto set, decision-makers can explore the range of efficient solutions and make informed choices that align with their desired objectives.
Etymology of PARETO SET
The term "Pareto set" is derived from the name of the Italian economist Vilfredo Pareto (1848-1923), who was one of the pioneers in the field of welfare economics and social choice theory. Pareto is best known for his studies on the distribution of income and the concept of Pareto efficiency.
In economics, Pareto efficiency implies a situation in which it is impossible to make one individual better off without making at least one other individual worse off. The Pareto set refers to the set of all possible allocations or distributions of resources that are Pareto efficient, meaning that any change or redistribution within this set would result in making someone worse off.
Therefore, the term "Pareto set" is named after Vilfredo Pareto due to his significant contributions to the understanding of efficiency and the distribution of resources.
