Paremini

Paremini is a proposed concept in optimization theory that describes a class of solutions balancing Pareto efficiency with a minimized global objective. In practical terms, Paremini refers to selecting among Pareto-optimal solutions the one that minimizes a predefined scalar function defined on the decision variables or outcomes.

The term appears primarily in informal discussions and heuristic literature and is not standardized in peer-reviewed sources. It is generally regarded as a portmanteau of Pareto and minimum, indicating a desire to obtain a best compromise on the Pareto frontier.

Definition and methods: Paremini solutions are Pareto-optimal with respect to a set of objectives and, among those, minimize a chosen scalar objective. Common approaches to obtain Paremini results include scalarization techniques such as weighted sums and epsilon-constraint methods, as well as lexicographic optimization and certain evolutionary multi-objective algorithms that apply a post hoc selection rule.

Applications: The concept has been discussed in engineering design, logistics, and machine learning model selection, where users seek a single, well-balanced compromise after considering multiple criteria.

Relation to related concepts: Paremini is related to Pareto efficiency and multi-objective optimization but differs by enforcing an explicit minimization of a global objective within the Pareto set. It serves as a practical criterion when one needs a unique representative solution rather than a whole frontier.