### Topology Optimization Considering Multiple-Loading Conditions
[PERSON] et al., in 2023 [44], employed WS methods to address TO in dual-material design problems with multiple load cases. Additionally, [PERSON] et al., (2024) [45] used WS methods for solving TO problems of joints in truss structures considering multiple load cases. The advantages of the WS method include its simplicity and ease of implementation. However, the effectiveness of this method may depend on the accuracy of assigning severity degrees and ideality values to the load cases. In other words, WS methods can be sensitive to the subjective choice of weights and may not be able to obtain the global optimum solution for the original MOPs. Other researchers adopted an approach when considering multiple load cases, referred to as the worst-case design [46; 47; 48; 49; 50; 51; 52; 53; 54]. In 1998, [PERSON] [47] used this approach to carry out multiple-load truss topology and sizing optimization to determine the optimal discrete or discretized mechanical structures with respect to maximal stiffness. In the article, the feasible structures that are best able to withstand their worst loading condition were considered. The definition of the \"worst loading\" condition is given as the loading condition where maximal compliance occurs among all compliances, associated with each loading condition. However, in TO incorporated with multiple-loading conditions, defining the \"worst loading\" becomes challenging as it changes together with the change in the topology of the structure. Hence, the min-max concept was introduced in the same study to address the uncertain \"worst loading\" condition depending on the design itself. The min-max formulation of MOPs was first proposed in a linear model by [PERSON] and [PERSON] and was further extended by [PERSON] [48] and [PERSON] et al. [49]. In 1998, [PERSON] [50] applied the min-max strategy to solve engineering optimization problems using a GA. The method includes giving a reasonably small number of weight combinations, making it a subjective approach that requires a better understanding of each problem. Consequently, the min-max formulation itself remains unsolved. The min-max compliance formulation was also introduced in [PERSON] et al., (2018) [53] together with an alternative bound formulation. The alternative bound formulation was solved using a \"parametric level\" technique in [PERSON]'s paper. In 2020, [PERSON] et al. [54] adopted the min-max compliance formulation in a biomimetic approach, where it is combined with the weighted sum method to handle TO problems under multiple loads. However, the min-max compliance formulation was not directly handled in the aforementioned papers, and its true solution remains ambiguous. Another method for solving MOPs is the epsilon-constraint method [55; 56; 57; 58], which is mainly used to generate Pareto fronts for MOPs. This method consists of the optimization of only one objective as a single-objective function (single-objective problems), while the other remaining objectives are considered as constraints. The epsilon-constraint method was first introduced by [PERSON] et al. in 1971 [55]. The method was designed to address MOPs where one objective function was optimized and the remaining objective functions were constrained to avoid exceeding the given target values. This method was successfully implemented for various multi-objective mathematical programming problems in 2009 by [PERSON] [56]. In 2013, [PERSON] et al. [57] used the epsilon-constraint method to generate Pareto frontiers in MOPs. The application of this method to TO was proposed by [PERSON] in 2015 [58]. In a recent study from 2023, [PERSON] et al. [59] employed the epsilon-constraint method to solve multi-objective two-scale sizing optimization problems. However, in the epsilon-constraint method, the necessity of giving the epsilon values by users, which requires a certain understanding of all scenarios of the problems, leads to difficulty in method implementation, and the method remains somewhat subjective.