# Multidisciplinary Reliability Design Optimization Modeling Based on SysML
## 2 Related Works
### Integration of System Design and System Optimization  
In model-based system design, system modeling is the primary way to present the outcomes of system design. The International Council on Systems Engineering (INCOSE) first defined \"Model-Based Systems Engineering\" (MBSE) in its \"Vision 2020\" document [12]: MBSE is a formalized approach to modeling that supports system requirements, design, analysis, verification, and validation activities from the conceptual design phase and continues throughout the entire development process and subsequent lifecycle stages. This definition highlights the application of modeling methods, where modeling involves creating models using specific languages and tools. While systems engineering was not the first to adopt modeling methods, MBSE's unique approach involves constructing system architecture models using modeling languages during the conceptual design phase, which is a significant innovation. The three pillars of MBSE are system modeling languages, system modeling methodologies, and system modeling software. SysML has emerged as the standard modeling language for MBSE. SysML [13] is characterized by its object-oriented, graphical, and platform-independent nature, making it suitable for describing, analyzing, designing, and validating complex systems that include both software and hardware aspects. Model-based approaches are tools for system design, but achieving system optimization is the ultimate goal of design. As illustrated in Figure 1, the development of complex products involves an iterative process of continually optimizing design solutions. Advanced system design methods and optimization techniques have always been key drivers in the innovative development of complex products. Efficient integration and application of system design and optimization are crucial for enhancing the design efficiency of complex products [14]. Research on the integration of system design and optimization can be discussed from two perspectives: application platforms and theoretical studies. When using MBSE for system modeling, there may be many design solutions that satisfy system-level requirements that have conflicting objectives at the parameter level, and the existing MBSE does not allow for functional verification and performance optimization of the design solutions. Therefore, MBSE needs to be linked with multidisciplinary design optimization to determine the best design solution [15]. Integrating sys  
Figure 1: The relationship between system design and system optimization. tem design with system optimization has been a hot research topic for scholars in various countries [9; 14]. In recent years, several scholars at home and abroad have developed the SysML language to provide an integrated depiction of design and optimization. NASA's Jet Propulsion Laboratory (JPL) researched an MBSE-based spacecraft-mission operating system architecture to improve the ability to make trade-offs and optimization evaluations of the overall system [16; 17]. The metamodel of SysML was enhanced by JPL in the design of tiny satellites to facilitate the trade-off analysis of solutions [18]. [PERSON] et al. [19] proposed a pattern-based approach for integrating system design and system optimization by extending the SysML metamodel to define a system optimization model and using pattern information containing basic information, problem descriptions, solutions, impacts, and other attributes to find a solution to the optimization problem through semantic matching. [PERSON] et al. [20] explored the constraint satisfaction multicriteria optimization problem (CSMOP) resulting from the SysML model. Several configurations of model variability including continuous and discrete variables have been proposed. Table 1 showcases the key contributions and limitations of the referenced works. Integration of numerical computation programs with system conceptual design modeling tools [21] is another method to integrate system design with system optimization.