Designing the Same, but in Different Ways: Determinism in Graph-Rewriting Systems for Function-Based Design Synthesis

Abstract

This paper compares methods for identifying determinism within graph-rewriting systems. From the viewpoint of functional decomposition, these methods can be implemented to search efficiently for distinct function structures. An additional requirement is imposed on this comparison that stems from a cooperative design application where different organizations contribute to a distributed graph-rewriting system: Inspecting the definitions of production rules is not allowed for identifying determinism because production rules are considered to be confidential corporate knowledge. Under this assumption, two approaches were selected and empirically compared with respect to random search and guided search scenarios. The results suggest that the herein proposed dynamic rule independence analysis outperforms traditional approaches in light of the above restriction.

Graph transformation in engineering design: an overview of the last decade

“…Confluence occurs if the same graph can be created with the application of different rules or rules applied in a different order. To avoid confluence in a collaborative design environment, the dynamic rule independence analysis method has been developed (Eichhoff and Roller, 2016). Generally, the vocabulary and the rules are created by a designer or engineer.…”

“…This analysis method provides the designer with a better understanding of rule matches and allows detecting rules that slow down the search process, because they undo each other or lead to confluence (Königseder et al , 2016). Dealing with confluence is especially important in order to provide an efficient search (Eichhoff and Roller, 2016). For this reason, the “dynamic rule independence analysis” was proposed by Eichhoff and Roller.…”

“…For this reason, the “dynamic rule independence analysis” was proposed by Eichhoff and Roller. Dynamic rule independence analysis can be used to reduce the number of operations and was tested with unordered and partially ordered graph rewriting (Eichhoff and Roller, 2016).

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“…If graph transformation is used for engineering design, the vocabulary and the associated rules contain a significant amount of company knowledge (Eichhoff and Roller, 2016). One resulting challenge is how this knowledge can be protected from clients or competitors in collaborative design environments (Eichhoff and Roller, 2016; Vogel and Arnold, 2020).…”

Modeling for design simplification and power-flow efficiency improvement in an automotive planetary gearbox: A case example

“…Generally, two types of techniques are employed for mechanism synthesis; in many cases, the graph-based methods have been employed [7]. Heuristic synthesis of mechanism, however, can produce better results than graph theorybased methods in the event of specific application orientation such as automotive gearboxes [8,9]. The results of the heuristic or the graph-theoretic solution, obtained in a matrix form, representing the links and joints in a mechanism are used to configure the stick diagram or lever diagram for the mechanism [10].…”