Setting the Goals

Historically, optimizers have solved this problem by forcing the user to decide from the start which goals are more important, and by how much. Then the optimization algorithms look for designs that support this particular trade-off. To better understand what this is like, suppose that you want to design an engine with a large torque, but with good fuel economy too. And assume also that you have a software tool that, for any given design, will tell you the expected torque (expressed in Nm) and the expected fuel economy (expressed in mpg or l/100Km). Your task is than to write a mathematical expression for a single measure to be maximized (or minimized). If the fuel economy is for you as important as the maximum torque, how would you express it? And if one were twice as important as the other?

As you can see, this approach is clearly flawed, as it is virtually impossible to assign numbers to our intuitions of what is a better design (i.e., to convert a trade-off into a mathematical expression). On the other hand, when we are faced with two design alternatives, it is far easier to pick what we consider the best.
Accordingly, modeFRONTIER's multi-objective search algorithms aim to identify the set of designs that are on, or near, the Pareto Frontier. This mathematical construct identifies the set of designs (called the Pareto Set) that cannot be improved with regard to one goal without moving farther away from the others. The final selection will then be based on these designs.

With modeFRONTIER defining the goals is then very easy, as the user only needs to list the measures describing the business effectiveness of a design. The problem of selecting the appropriate trade-off between these goals is pushed to a later time, when it is much more manageable.