Multiobjective Programming

As diverse as the problems in the previous chapters have been, they share one common feature: they all have one single objective function and the result is an optimal solution (or multiple optima, in case of dual degeneracy). However, the concept of optimality applies only in case of a single objective. If we state that something is “the best” or optimal, we always have an objective in mind: the fastest car, the most comfortable vehicle, the automobile that is cheapest to operate, and so forth. Whenever a second or even more objectives are included in a problem, the concept of optimality no longer applies. For instance, if the top speed of a vehicle and its gas mileage are relevant concerns, then the comparison between a car, whose speed may go up to 110 miles per hour and which gives 20 miles to the gallon (highway rating) and a vehicle that can go up to 90 miles per hour and which gives 25 miles to the gallon is no longer a simple one: the former car is faster at the expense of fuel efficiency. It will now depend on the decision maker which of the two criteria is considered more important. In other words, the decision maker will—sooner or later—have to specify a

tradeoff

between the criteria. This is the type of problems considered in this chapter.