pg. 214

[alextzik]

The criterion space is defined as the image of X through the objective function. It is thus evident that the utopia point does not need to be in the criterion space. However, in the definition of the utopia point it is described as a point of the criterion space.

[tawheeler]

@mykelk Alex brings up a good technicality here. We use the criterion space to refer to the projection of the design into the objective-space. However, when we define the utility point, we should be referring to objective-space, and not the image of all possible designs into the objective space. (The utility point is typically not feasible, and thus is not in the image).

Here are some possible alternatives: We define the utopia point to be the point in the objective space consisting of the component-wise optima:

or: We define the utopia point to be the point in the objective function space consisting of the component-wise optima:

or: We define the utopia point to be the point in the space of objective function values consisting of the component-wise optima:

What do you prefer?

[mykelk]

Ah! Good point. Let's go with the first one. Thanks!

[tawheeler]

done!