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2. BACKGROUNDConfiguration design problems are generally exponentially complex, that is, they suffer from a combinatorial explosion of parts and their possible interactions. Parts have ports that limit the ways they can be connected or interact, which reduces the problem combinatorics. In addition, functional decompositions are used to identify one-to-one mappings from parts to the functions they perform in the design. Functional decompositions reduce the combinatorics by limiting candidate parts to those that implement low-level functions, thus reducing the allowable combinations of parts. The sum total of the individual low-level functions implemented by the parts in the configuration is the functionality desired of the complete designed artifact by the user. A variety of techniques have been developed to manage the complexity of configuration design. In early work, the problem was viewed as the selection of given parts from parts libraries that would be properly combined to obtain the functionality specified by their use, satisfy constraints, and achieve optimality goals (Mittal and Frayman, 1989). Early design applications include: paper-handling system design (Mittal, Dym, et al., 1986), elevator design (Marcus, Stout, et al., 1988), and computer design (Birmingham, Gupta, et al., 1992). The most common technique utilized in these early systems was a centralized system that maps functions into parts that perform those functions. Configurations are then formed by selecting parts to implement functions, and the design is then extended by eliminating the remaining choices according to: (1) the functions that have already been implemented, (2) the allowed connectivity of the configuration, (3) design constraints, and (4) optimality criteria. Now, when parts implement more than one function, termed the multifunction part problem, configuration design is further complicated. Similarly, when parts require additional functions for their correct operation -- the support-function problem -- additional complications ensue. In both cases, the increased complexity results from the need to consider the topology of the selected parts in solving the problem. In multifunction part problems, parts can implement more than one function (Mittal and Frayman, 1989; Haworth, Birmingham et al., 1993), so a designer must take into account two major issues when selecting a set of parts to achieve the functionality desired by the user: minimizing the number of extraneous or redundant functions implemented by the selected parts, and minimizing the number of selected parts. Minimizing the number of extraneous or redundant functions eliminates waste, since all the functions implemented by a part are used. Minimizing the number of selected parts tends to minimize performance attributes of the final solution (e.g., cost, power consumption, area, weight) because multifunction parts tend to behave better than a set of single-function parts that implement the same functions (e.g., cost less, consume less power, etc.). The GOPS algorithm solves the multifunction part problem optimally in a centralized, nondistributed way (Haworth, Birmingham, et al., 1993). Support functions are functions that are required for the correct operation of a part (Mittal and Frayman, 1989; Gupta, Birmingham, et al., 1993; Haworth, Birmingham, et al., 1993). These functions are needed in addition to the original functions specified by the designer. With support functions, a designer must keep track of which functions are needed at any point in the design process, based on the current set of selected parts.
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