# Selection Criterion of Reanalysis Methods for Plane Truss Optimization
###### Abstract
Global approximation methods, also known as multipoint approximation methods, utilize the calculation information of multiple points after structural changes to construct an approximate function of the structural response with respect to design parameters. Classical global approximation methods mainly include the response surface method [12], the reduced basis method [13; 14], and the polynomial fitting method [15]. Due to the integration of the calculation information of multiple points, global approximation methods normally have higher calculation accuracy than local approximation methods. However, the acquisition and fitting calculation of multiple-point information often make their calculation efficiency relatively low, especially in solving complex structural problems, which can even be lower than that of complete analysis. The idea of iterative approximation methods comes from the iterative method for solving linear equations in mathematics [9]. For example, the Preconditioned Conjugate Gradient (PCG) method [16], which is based on the Conjugate Gradient (CG) method [17], introduces a suitable preconditioning matrix to reduce the condition number of the stiffness matrix, thereby improving the overall calculation efficiency. The PCG method is widely used due to its fast convergence rate and high accuracy. [PERSON] et al. [18] extended the PCG method to solve the topology optimization problems with reduced degrees of freedom (DOFs). Combined with Guyan reduction [19], the PCG method can also handle topology optimization problems with increasing DOFs [20]. The principle of Guyan reduction involves partitioning the stiffness matrix to consolidates the newly added DOFs onto the existing structural DOFs, ensuring that the solution scale remains consistent with the existing structural DOFs. The Combined Approximations (CA) method is a popular and extensively studied method, which is considered to combine the high efficiency of local approximation methods and the high accuracy of global approximation methods. CA was proposed by [PERSON] [21], who applied the reduced basis vector method to represent the approximate solutions of displacements [22]. Furthermore, CA can be derived using binomial series as reduced basis vectors and was successfully applied to topology optimization [23]. To improve the accuracy of CA in solving large-scale modifications, [PERSON] et al. [24] proposed the Iterative Combined Approximations (ICA) method. In addition, scholars such as [PERSON] [25], [PERSON] [26], and [PERSON] [27] also conducted a series of studies on CA. Although the above reanalysis methods have significantly improved structural calculation efficiency, previous studies have mainly focused on innovating or improving single methods. Little research has been done on comparing and exploring the most suitable methods for different structural modification types. The purpose of this paper is three-fold. The first is to investigate the effects of different structural modification types on structures during the structural optimization process. The second is to explore the most suitable method that maintains both accuracy and efficiency under different structural modification types from both qualitative and quantitative perspectives. The third is to develop a selection criterion for reanalysis methods, which is suitable for the structural optimization of plane trusses. The criterion will be combined with the Structural Topology and Shape Annealing (STSA) algorithm [28] to \"draw on the strengths of all\" and further improve the calculation efficiency.