There is, indeed, a difficulty about part and whole … whether the part and the whole are one or more than one, and how they can be one or many, and, if they are more than one, in what sense they are more than one.
The system concept was the very first one introduced in Chapter 1. We argued that using the word “design” instead of “system” allows us to make use of the extensive work done on studying systems. In this chapter, we take up the system discussion again and assert that every design is a system.What is the exact “system” is a matter of subjective perspective and focus of the design effort. Following the discussion in Section 1.2, our working concept of a system is that the system comprises elements, probably interacting with each other, that function together. A system can be partitioned into its elements (system partitioning), and its overall function is achieved through properly tracking how the elements function together (system coordination). The elements can be physical parts (object partitioning) or function disciplines (aspect partitioning).
System optimization acknowledges this partitioning and coordination character and follows the basic principle of decomposition: break the problem into simpler problem pieces (subproblems), solve each subproblem separately, and coordinate the subproblem solutions so that you obtain the solution to the original problem. This decomposition-based optimization strategy is useful if: (i) the effort for partitioning, subproblem solution, and coordination is less than the effort required to solve the original problem; or (ii) the original problem is simply not solvable without decomposition; and (iii) the decomposition-based solution is indeed the same as the solution to the original nonpartitioned problem. The first two cases are a practical matter for when to use decomposition strategies. The third one is both practical and theoretical; it requires a mathematical convergence proof that the decomposition strategy will yield solutions within the solution set of the original problem. This mathematical requirement turns out to be quite demanding, as many strategies developed for solving practical system design problems tend to be heuristic with no convergence proofs. Still, getting a good answer for a complex problem is better than no answer.