# Multidisciplinary Reliability Design Optimization Modeling Based on SysML
## 3 Representation of Optimization Problems Using SysML  
To integrate MDO models with system design models, it is essential to develop a domain metamodel that is appropriate for expressing MDO-related issues. A metamodel essentially defines a modeling language, and when this language is designed for a specific domain issue like multidisciplinary optimization, it is known as a Domain-Specific Language (DSL). There are three main strategies for constructing a metamodel for a specific DSL: (1) elaborating on an existing DSL metamodel within the same domain to translate more general concepts into detailed ones; (2) extending a generic, domain-neutral modeling language (such as SysML) to incorporate MDO-related concepts; and (3) designing a completely new metamodel for a language from scratch.  
Based on the integration needs of system design and system optimization, the second approach can be chosen--extending the existing general-purpose modeling language SysML to define a metamodel for complex product Multidisciplinary Design Optimization. To extend SysML, two methods can be employed [27]: (1) defining new metaclasses within the SysML metamodel to create new modeling elements with specific attributes, constraints,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Originator** & **Key Contributions** & **Limitations** \\ \hline JPL [16; 17; 18] & Expanded SysML metamodel for trade-off analysis in tiny satellite design and mission architecture optimization & Primarily focused on trade-off analysis, with limited application to comprehensive MDO scenarios \\ [PERSON] [19] & Developed a pattern-based approach to integrate system design and optimization using an extended SysML metamodel Explored CSMOP within SysML, proposing configurations for model variability to solve optimization problems & Limited scalability and effectiveness in highly complex systems with undefined patterns \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main contributions and limitations of references.  
and usages; or (2) extending existing SysML elements using Stereotypes [28] and Tagged Values. The first method allows for precise representation of the new modeling elements and their semantics but may not be supported by existing modeling tools. In contrast, the second method--using Stereotypes to extend the semantics of SysML model elements and Tagged Values to assign attributes not included in the SysML metamodel--offers greater flexibility and generality. Consequently, this paper adopts the latter method to extend SysML to support the expression of elements included in optimization models.  
The process of defining a multidisciplinary optimization metamodel based on the SysML extended version (Stereotype) mainly includes the following steps: (1) extracting MDO domain knowledge and identifying the concepts, relationships, and constraints involved according to MDO definitions and application scenarios; (2) defining the Abstract Syntax of the above concepts using a formal approach; (3) defining the Concrete Syntax, which defines the corresponding SysML representation and notation for all the above-summarized model elements based on the Abstract Syntax, and this process can be realized by extending similar model elements in SysML; (4) describing the model elements and usage methods in the extended MDO metamodel to form the corresponding specification.  
The underlying structure of the Multidisciplinary Design Optimization problem is shown in Figure 2, which is generally divided into a system level and a subsystem level, although of course there may be more layers for complex problems. The optimization model at each level contains parameters, objectives, variables, constraints, and other information. The system level also includes the number of disciplines and disciplinary coupling information. The interdisciplinary coupling information stored at the system level will transmit the coupling information to each discipline when building the multidisciplinary optimization mathematical model.