A state in which improving any one of several objectives necessarily worsens another. For competing objectives, candidates are chosen from the Pareto front using an exchange constant.
Japanese name: パレート最適
Pareto optimality appears in 1 practice question across 1 topic, including Materials selection and design.
In materials selection with two or more objectives, a candidate is said to dominate another if it is equal or better in every objective and strictly better in at least one. Candidates that are not dominated by any other are Pareto-optimal, named after the Italian economist Pareto. When mass and cost are plotted on the horizontal and vertical axes, the Pareto-optimal candidates line up along the lower-left edge, called the Pareto front (trade-off curve). Dominated candidates lying to the upper right of the front are never chosen whatever the weighting, so they can be removed at the start.
To choose one candidate on the front, a rate of exchange between objectives is set. For mass m and cost C, the candidate minimizing the penalty function Z = αm + C is chosen, where α is the amount one is willing to pay to save 1 kg of mass (the exchange constant). For example, among three candidates, A (10 kg, 2000 yen), B (6 kg, 4000 yen) and C (4 kg, 20000 yen), A is the minimum for α = 300 yen/kg, B for 2000 yen/kg and C for 10000 yen/kg. α is set by the nature of the product and is far larger for aircraft and spacecraft, where lightness translates directly into fuel savings, than for cars.
Pareto-optimal does not mean best but rather that neither objective can be improved further without the other getting worse, and usually there is more than one candidate. Where on the front to choose is decided only by adding a value judgment such as an exchange constant. Adding objectives in different units without normalizing them lets the result be driven by the size of the numbers. Selection by a weighted sum also has the property that when the front has a dented shape, candidates in the dent are never chosen however the weights are changed. Incidentally, the Pareto principle, that the top 20% account for 80% of the whole, is a different concept named after the same person.
On materials selection charts, two performance indices are plotted on logarithmic axes, candidate materials are plotted and the Pareto front is drawn. On logarithmic charts, lines of constant Z = αm + C are curves rather than straight lines, so reading the points where they touch the front for several values of α shows how the choice changes with the exchange constant. In materials informatics, which searches alloy compositions and process conditions, competing objectives such as strength and ductility or performance and cost are often handled together, and methods are used that find the Pareto front by multi-objective optimization such as genetic algorithms and choose the candidates to test experimentally from it.
Answer: B. Collect the Pareto-optimal candidates, which no other candidate beats on both objectives at once, then choose by setting an exchange rate between mass and cost
When objectives compete, first pick out the candidates that are not simultaneously beaten on both objectives by any other candidate. These lie on a trade-off curve (the Pareto front), along which improving one objective worsens the other. The final choice is made by deciding an exchange constant, how much money you are willing to pay to save 1 kg, and combining mass and cost into a single evaluation function (penalty function). This is why expensive but light materials are chosen for products where lightness is highly valued, such as aircraft, and cheap materials for ordinary products. The material best for one objective is not necessarily best for the other, so the choice saying the best for one is always the best for the other is wrong. Adding quantities with different units directly makes the result depend on the choice of units, so it is not a meaningful comparison.
It is the line (a surface for three or more objectives) joining the Pareto-optimal candidates, those not dominated by any other. When both objectives are to be minimized, it is the lower-left edge of the chart. Along the front, improving one objective always worsens the other.
It is set by converting the value gained from saving 1 kg of mass into money, from fuel savings, extra payload and the like. It varies greatly with the type of product, being larger for aircraft than for ordinary cars and larger for spacecraft than for aircraft. If its value is uncertain, check whether the chosen candidate changes as α is varied.
The name comes from the same Pareto, but the content is different. The Pareto principle is a rule of thumb that a small number of factors account for most of the whole, as in the distribution of income. Pareto optimality is an optimization concept referring to a state in which one objective cannot be improved without worsening another.
These lie on a trade-off curve (the Pareto front), along which improving one objective worsens the other.
You want to minimize two objectives at once, the mass and t…Ashby chart (materials selection chart) Life cycle assessment Material index (performance index) Specific stiffness Tramp elements Yield before fracture