From Dubious Construction of Objective Functions to the Application of Physical Programming

With the increasing availability of computational power, optimization is becoming a credible and viable option when designing complex multidisciplinary systems. Computational optimization generally involves three distinct phases: 1) model the physical system in terms of design parameters and design metrics, 2 ) form an aggregate objective function in terms of the design metrics, and 3 ) minimize the aggregate objective function using an optimization code. Robust analytical and computational tools are available to perform the e rst and third phases. The analytical tools available for constructing the objective function in phase two are remarkably simplistic and generally involve dife cult-to-obtain weights. Because the optimum solution is only as effective as the aggregate objective function, any dee ciency in the formation of the latter signie cantly impacts the ultimate outcome. The multiobjective design optimization process is examined from the perspective of constructing objective functions. We expose the shortcomings of weight-based methods using analytical and numerical means. Through analytical, graphical, and computational means, we show how the physical programming approach entirely circumvents the reliance on weight, thereby resulting in a new method of practical and general applicability.