Optimization with Vector — Valued Cost

Abstract

Up till now we have considered problems involving a single performance index or cost, namely, a scalar-valued functional. This is predicated on the supposition that one can select a single, overriding criterion in the form of a functional whose value is to be extremized. However, as we have observed a long time ago (Ref. 17.1), “one person’s optimum may well be another’s pessimum.” For example, in designing a product the engineers may wish to maximize strength or durability, the environmentalists may strive for minimum pollution, while the managers may desire to minimize cost or to maximize profit, and so on. In general these goals are not compatible; that is, one would not expect to be able to arrive at a design that results in the simultaneous satisfaction of all parties who can influence the design.