From dubious construction of objective functions to the application of physical programming

With the increasing availability of computational power, optimization Is be coming a credible and viable option when designing complex multidisciplinar y systems. Computational optimization generally involves three distinct pha ses: 1) model the physical system in terms of design parameters and design metrics, 2) form an aggregate objective function in terms of the design met rics, and 3) minimize the aggregate objective function using an optimizatio n code. Robust analytical and computational tools are available to perform the first and third phases. The analytical tools available for constructing the objective function in phase two are remarkably simplistic and generall y involve difficult-to obtain weights. Because the optimum solution is only as effective as the aggregate objective function, any deficiency in the fo rmation of the latter significantly impacts the ultimate outcome. The multi objective design optimization process is examined from the perspective of c onstructing objective functions. We expose the shortcomings of weight-based methods using analytical and numerical means. Through analytical, graphica l, and computational means, we show how the physical programming approach e ntirely circumvents the reliance on weight, thereby resulting in a new meth od of practical and general applicability.