Pareto optimality

That is why Pareto optimality is often called the “the Pareto frontier” (Sebenius, 2002, p. 237).

the set of all Pareto efficient allocations

The Pareto frontier is the set of all Pareto efficient allocations, conventionally shown graphically.

the set of parameterizations (allocations) that are all Pareto efficient

For a given system, the Pareto frontier or Pareto set is the set of parameterizations (allocations) that are all Pareto efficient.

The set of Pareto-optimal returns and risks

The set of Pareto-optimal returns and risks is called the Pareto efficient frontier for the Markowitz portfolio selection problem.

set of choices that are Pareto efficient

Given a set of choices and a way of valuing them, the Pareto frontier or Pareto set or Pareto front is the set of choices that are Pareto efficient.

the set of maximal elements

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.

a curve line

The Pareto Efficiency Frontier is a curve line that describes cause which is generating the y-axis.

to a set of Pareto Optimal designs that, when combined with a Scoring Algorithm, can be evaluated on how well these designs align with previously determined values

The Pareto Frontier refers to a set of Pareto Optimal designs that, when combined with a Scoring Algorithm, can be evaluated on how well these designs align with previously determined values.

for the Markowitz Portfolio selection problem

The set of Pareto-optimal returns and risks is called the Pareto efficient frontier for the Markowitz portfolio selection problem.

the black curve connecting these two points

Pareto frontier is the black curve connecting these two points.

The collection of yellow points

The collection of yellow points on each method’s graph are known as graph's Pareto frontier.

the set of such payoffs

Such a payoff is described as Pareto efficient, and the set of such payoffs is called the Pareto frontier.

The set of all Pareto efficient networks

The set of all Pareto efficient networks is called the Pareto frontier.

The curve created plotting weight against stiffness of the best designs

The curve created plotting weight against stiffness of the best designs is known as the Pareto frontier.

a tradeoff constraint between two or more variables, time and money in this case

For those of you who are not familiar with the concept, a Pareto frontier represents a tradeoff constraint between two or more variables, time and money in this case.

and the diminishing returns in trading one for the other between performance and cost

The Pareto frontier is convex, showing the trade-offs between performance and cost and the diminishing returns in trading one for the other.

a red dotted line

The Pareto frontier is displayed as a red dotted line.

The top-right boundary of the IPS

The top-right boundary of the IPS is the Pareto frontier – the IPS is the set of all Pareto efficient partitions.

the set of dots that populate the edges where either energy or construction costs, or both, are low

But as with the Mars analysis, the builder need only pay attention to the Pareto frontier: the set of dots that populate the edges where either energy or construction costs, or both, are low.

a compact overview of the potential of the corresponding manufacturing process

The Pareto frontier is of particular importance, as it represents a compact overview of the potential of the corresponding manufacturing process and comprises the parameter combinations of interest for the manufacturing planner.