Comparison of global and local treatment for coupling variables into multidisciplinary problems

Nowadays products become more and more complex and their design is usually of large scale, characterized by an important number of design variables, constraints and objectives. Besides the traditional economic point of view, more recent industrial requirements, such as robustness and performance of the design, but also marketing criteria have appeared and quickly become important characteristics of the design and of the optimization process. In the same time, the structure in which the design process takes place has evolved a lot. Enterprises have grown in complexity. The increasing economic competition has led to a specialization and distribution of knowledge, expertise, tools and work sites. Enterprises have reduced their competencies to be finally specialized in one (or several) discipline(s); in this context, the use of subcontractors is now really common and the extended enterprise is the common companies’ structure model. Such a structure requires efficient optimization methodologies that take into account the decomposition of the product into several disciplines that are simultaneously optimized in different structures (team, division, subcontractors) and places. This kind of structures can be considered as complex systems and defined as assemblies of interacting members that are difficult to understand as a whole. Such complex systems can be decomposed by several ways: object, aspect, sequential and model-based. Object decomposition divides a system by physical components. Aspect (or discipline) decomposition divides the system according to different disciplines or specialities. Object and aspect partitioning are ”natural” partitions and typically large companies employ both types of partitions simultaneously (mixed partition) in a matrix management organization. Sequential decomposition is applicable when partitioned sub-problems are organized by work-flow or process logic and presumes unidirectionality of design information. Hierarchical decomposition: Complex systems are composed of several sub-systems that form subsystems and multilevel: Figure 1 on the following page shows the structural decomposition of a plane. Such decomposition can be pursued until the basic members of the system appear. Actually, basic members are either components or disciplines that can be more easily optimized that the complex system. Interaction between sub-systems: Interactions betweens sub-systems exist at any level of the decomposition. However, they do not appear at the system level (level zero). Such interactions are usually called ”coupling functions”. They are output data for one of the sub-systems that are needed as input data by one or several others sub-systems. They ensure the system’s coherence and synergy between members. Non-hierarchical systems: Frequently, complex systems are non-hierarchical what means that there is no reason to process the optimization of one sub-system before another. In the optimization process of such systems, the presence of coupling functions and their recognition constitutes a real challenge for researchers.