## 1 Introduction  
In practical engineering problems, various uncertainties exist in terms of the operating environment, manufacturing process, material properties, etc. Under the combined action of these uncertainties, the performance of engineering structures or products may fluctuate greatly. Robustoptimization [1; 2] is a methodology, and its fundamental principle is to improve the performance of a product by minimizing the effects of uncertainties without eliminating these causes. The concept of robustness optimization has long been embedded in engineering design. In recent years, thanks to the rapid development of computer technology, it has been widely applied to many engineering fields, such as electronic [3], vehicle [4], aerospace [5], and civil engineering [6]. The core of robustness optimization lies in understanding, measuring, and controlling the uncertainty in the product design process. In mechanical engineering disciplines, uncertainty is usually differentiated into objective and subjective from an epistemological perspective [7]. The former, also called aleatory uncertainty, comes from an inherently irreducible physical nature, e.g., material properties (elasticity modulus, thermal conductivity, expansion coefficient) and operating conditions (temperature, humidity, wind load). A probabilistic model [8; 9; 10] is an appropriate way to describe such uncertain parameters, provided that sufficient samples are obtained for the construction of accurate random distribution. Conventional robustness optimization methods [11; 12; 13] are based on probabilistic models, in which the statistical moments (e.g., mean, variance) are employed to formulate the robustness function for the performance assessment under uncertainties. On the other hand, designers may lack knowledge about the issues of concern in practice, which leads to subjective uncertainty, also known as epistemic uncertainty. The uncertainty is caused by cognitive limitation or a lack of information, which could be reduced theoretically as effort is increased. At present, the methods of dealing with epistemic uncertainty mainly include possibility theory [14; 15], the fuzzy set [16; 17], convex model [18; 19], and evidence theory [20; 21]. Among them, evidence theory is an extension of probability theory, which can properly model the information of incompleteness, uncertainty, unreliability and even conflict [22]. When evidence theory treats a general structural problem, all possible values of an uncertain variable are assigned to several sub-intervals, and the corresponding probability is assigned to each sub-interval according to existing statistics and expert experience. After synthesizing the probability of all the sub-intervals, the belief measure and plausibility measure are obtained, which constitute the confidence interval of the proposition and show that the structural performance satisfies a given requirement. Compared with other uncertainty analysis theories, evidence theory may be more general. For example, when the sub-interval of each uncertain variable is infinitely small, evidence theory is equivalent to probability theory; when the sub-interval is unique, it is equivalent to convex model theory; when no conflict occurs to the information from different sources, it is equivalent to possibility theory [23]. In the past decade, some progress has been made in evidence-theory-based robust optimization (EBRO). For instance, [PERSON] [24] employed evidence theory to model the uncertainties of spacecraft subsystems and trajectory parameters in the robust design of space trajectory and presented a hybrid co-evolutionary algorithm to obtain the optimal results. For the preliminary design of a space mission, [PERSON] et al. [25] formulated the robust optimization model using evidence theory and proposed three practical solving technologies. Their features of efficiency and accuracy were discussed through the application of a space mission. [PERSON] et al.