Science Forum - Pareto Optimality, criterion space, multiple objective fcns

rick.taiwan

One naive definition of engineering is the art of making technical tradeoffs. E.g., one can make the bridge lighter if one doesn't mind making it less strong, etc.

Assume we have n many design variables and we have m many objective functions.

The values of the design variables can be graphed in n-space. However, the objective functions can be made the axes of a "criterion space." This seems a bit "gee-whiz" to me because I just found out about it. (The authors later say that only 2-space and 3-space are practical, so perhaps my use of m-space is a little too broad.)

A simple case is if one has two design variables and two objective functions. Then it's easy to draw 2-D graphs of ordinary space and criterion space. Sometimes one can see obvious points of interest on the criterion space graph that wouldn't be apparent on the normal graph.

I got this from a book I don't much enjoy, namely Belegundu and Chandrupatla's "Optimization Concepts and Applications in Engineering." There are probably better books that deal with this kind of problem.