### Topology Optimization Considering Multiple-Loading Conditions  
Despite the extensive analysis, improvement, and application of various TO methods mentioned above, only a limited number of studies have focused on TO problems under multiple-loading conditions. Moreover, considering multiple-loading conditions is crucial when designing structures for complex systems. In reality, a single structure can experience various loading conditions, and accounting for each scenario is essential to ensuring structural integrity and safety. A multi-load structural TO problem involves determining the optimal distribution of material within a given design space to maximize or minimize certain objective function(s) while considering each of the given loading conditions. Because there are numerous loading conditions that are of interest, the corresponding performance functions associated with each of these conditions must be considered. Therefore, many researchers refer to multi-load problems as multi-objective optimization problems (MOP) [34]. These problems entail seeking processes that aim to discover Pareto solutions [35]. In MOPs, Pareto-optimal solutions are the solutions where it is not possible to improve one objective without worsening one or more other objectives. For an MOP, there might be an infinite set of Pareto solutions that form a Pareto set (known as Pareto front, or Pareto frontier), representingthe trade-offs between different objectives. Generally, when attempting to obtain Pareto solutions for TO problems with multiple-loading conditions, it is required for users to choose a single solution from the Pareto front based on their preferences. When solving a MOP with all objective functions sharing the same unit of measurement, various methods can be used to transform it into a single-objective optimization problem. Thus, it is easier to obtain one or more optimal solutions by solving the transformed problem(s) [35]. Among these methods, the weighted sum (WS) method [29; 34; 35; 36; 37; 38; 39; 40; 41; 42] for multi-objective optimization is widely utilized, which involves assigning weights to each objective and determining a compromised solution. This method not only allows for the generation of multiple solution points by adjusting the weights accordingly but also enables obtaining a single solution point reflecting preferences linked to a specific set of weights. [PERSON] et al., in 1992 [36], used a WS method to optimize the shapes of structures under multiple-loading conditions. They used a homogenization method to formulate and solve the TO problems. A WS method was employed by [PERSON] et al. in 1995 [37] to aggregate the objective functions and find the optimal design when considering simultaneous optimization of material properties and distribution under multiple-loading conditions. In 2000, [PERSON] et al. [34] applied the WS method to optimize the topology of structures for both static and dynamic loading conditions using a genetic algorithm (GA). [PERSON] et al., (2004) [38] employed a WS method to optimize the topology of aircraft wing box ribs utilizing a sequential quadratic programming algorithm. [PERSON] (2006) [39] discussed aspects of three-dimensional (3D) shape and TO with multiple loads. He presented several challenges that are associated with this type of optimization, such as the need to account for the interaction between load cases. In 2020, [PERSON] et al. [35] proposed a new method for multi-load TO based on the WS method. Their method considered the severity and ideality of each load case when assigning weights to the objectives. WS methods have also been widely used in recent studies, particularly in applied articles. For instance, [PERSON] et al. [41] and [PERSON] et al. [42], in 2023, used WS methods to develop 3D real robot structures. [PERSON] et al. [43], in 2023, utilized WS methods in their studies to develop explicit TO for 3D geometrically nonlinear structures.