Abstract
By building on earlier established work, a nonrecursive approach to design optimization is proposed. A “fractal” method of design is developed that embraces the entire space of candidate system solutions. It provides for the direct synthesis of optimal system design solutions of complex system implementations with multiple components, embodying different technologies, and with multiple levels of design hierarchy. The derivation and decomposition of comparative evaluation criteria and tradeoff functions, using “mathematical orders” over the space of candidate systems, is explored in detail. An extended form of the Subsystem Tradeoff Functional Equation (i.e., nk‐STFE for n components and k evaluation criteria) is developed, and its application to optimal design of complex systems architectures is presented. In particular, the effect of overall constraints on system implementation—in terms of combinatorial constraints on component choice, and the manner in which this is incorporated into a systems‐theoretic approach to complex system design—is discussed. The development of formal (systems‐theoretic) constructs, theorems, and theorem proofs, are provided where necessary. © 2003 Wiley Periodicals, Inc. Syst Eng 6: 92–105, 2003