In the modern engineering domain, the design and optimization of complex systems have become increasingly significant topics. With the rapid advancements in technology, the scale and complexity of engineering systems continue to escalate, leading to system performance being influenced by various uncertain factors. These uncertainties may stem from multiple sources, such as material properties, manufacturing processes, operational environments, and human interventions. Therefore, it is essential to adequately consider these uncertainties when modeling and optimizing complex systems to ensure their stability, reliability, and performance. Traditional modeling and design optimization methods are typically based on deterministic assumptions, which presume that there is an exact relationship between the system inputs and outputs. However, in practical applications, uncertainties are often inevitable and may significantly impact system performance. Consequently, addressing uncertainties in the modeling and design optimization process has emerged as one of the critical challenges in the engineering field. This study systematically recalls the theoretical basis and recent progress in this field, and ends with discussions as well as conclusions and future prospect.
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