Materials selection and design
You want to minimize two objectives at once, the mass and the cost of a part, but lighter materials are more expensive and no material is best on both. Which is an appropriate way to choose a material in this case?
- AChoosing the best material on the mass index guarantees it is also the best on cost, so comparing one objective is enough
- BCollect 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
- CAdd the performance indices for mass (kg) and cost (yen) directly without making the units consistent, and choose the one with the smallest sum
Show answer and explanation
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.