2009, Vol.12, No.3, pp.211-231

Integrated product development requires that decomposition and integration schemes be congruent and in harmony with each other. This harmony marks a product development project with success. In domain of problem solving one needs to resort to simulation based techniques to gain insight into problem structure, its underlying couplings and complexity. The core idea, however, is around the fact that by using an arbitrary complexity measure that satisfies primary criteria of representing the complexity of a graph, general and useful results may be concluded with regard to problem classification. Here, we refer to the problem structure as the self map of the system. Usually for large scale problems the self needs to be decomposed for tractability purposes the structure of the problem after decomposition is the real structure to be dealt with. We refer to complexity of the system/problem before decomposition as self complexity and complexity of system after decomposition as real complexity. It is reasoned that regardless of type of complexity measure, the real complexity cannot be less than the self complexity. Furthermore, it is noted that emergence laws of weak emergence and strong emergence can be explained by using a justified complexity measure. This would have important implications in problem classification and choosing the right design process that is in congruence with complexity of the problem.
Key words: complexity, emergence, decomposition, spectral partitioning, chaos, multi agent system

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