A certain goal program I've been working on has three goals that each operate at different scales.

Two of the goals stay between 0-10, so any deviation from the goal is generally only a couple of "points" away from the goal.

The third goal has a much larger scale (its a measure of distance travelled), so the deviations from the goal can range from 10s of "points" away to 100s, depending on the solution.

Because of this difference in magnitude of the deviations derived from each goal, the model has an implicit bias towards satisfying the third goal as closely as possible.

I suppose one could normalize all the goals such that they're on the same scale or maybe weight the goals such that the larger magnitude one gets truncated down to be comparable to the others.

Is there a standard practice for dealing with these scale differences in a goal program?


1 Answer 1


I'm not sure I would use the word "standard", but a common practice is to scale the goals so that they are commensurable.

There are also multiobjective approaches that are less affected by scaling. For instance, if you use preemptive priorities, the solution approach is to optimize the highest priority objective, lock in its value via a constraint, optimize the second highest priority objective, etc. The scales of the objectives are irrelevant with that method. If you assign goals for each objective and prioritize them, a similar approach applies, with the difference that rather than locking in the attained value of a higher priority objective you lock in the smaller of the attained value or the goal (assuming more is better for that objective; use the higher value if less is better). The catch with either of these is that an absolute prioritization is required.

Yet another possibility, albeit a costly one in many cases, is to enumerate the Pareto frontier (or at least the extreme points of the Pareto frontier), then let the decision maker pick a winner. That too makes no assumptions about scaling.


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