# Topology Optimization Based on SA-BESO
## 1 Introduction  
Topology optimization is used during the design process to solve the problems of weight restriction and material distribution in a specific design space under certain constraints. At present, structural topology optimization has become a hot topic in current academic research due to its wide application in many related technical fields, such as aerospace [1], automobile manufacturing [2], architectural design, additive manufacturing [3], 3D printing [4], etc. Hence, more and more structural topology optimization methods have been proposed, such as the variable density method [5], progressive structural optimization method, topological derivative method [6], proportional-integral-derivative control algorithm [7], feature-driven method [8], level set method [9], etc. The variable density method uses variable cell density values as design variables for the algorithm by relating densities to structural materials. Although it makes the mathematics model of the topological optimization more concise and easy to understand, density values are discrete. The Solid Isotropic Material With Penalization method (SIMP) [10; 11] applies the interpolation function to the material density of each element. SIMP transforms the topology optimization problem of discrete integers into one based on continuous design variables. However, the larger displacement may make the stiffness matrix of the low density element too uncertain or even negatively determined in the later iteration period of the SIMP method. The Evolutionary Structure Optimization method (ESO) [12], which can delete low density elements, has the potential to solve this problem. The topology structure obtained by the topology optimization method based on density variation usually has a sawtooth boundary. In order to obtain a smooth boundary of the topology structure, some methods using boundary information as design variables are proposed. For example, the level set topology optimization method [13] uses the implicit function of the level set to express the geometric boundary of the structure. It also can control the output of thefunction according to the optimization conditions so as to modify the boundary shape. Additionally, using the implicit level set function modeling is a feature-driven method [14], which transforms the structure from a single component of materials into an organic whole composed of interconnected features, and transforms topological optimization into an optimization problem based on the number, shape and layout of features. In addition, the topological derivative method [15], topological optimization method based on principal component analysis [16], proportional integral-differential control method [17] and other numerical solution methods have been proposed. The core idea of the numerical solution method is to simplify the topology optimization problem to obtain the approximate solution, but it is easy to fall into the local solution. On this basis, more and more scholars have introduced an intelligent optimization algorithm with a strong global optimization ability. To optimize the wing structure and reduce the displacement variation range of the wing structure, [PERSON] et al. [18] proposed an aircraft wing structure topology optimization method based on the genetic algorithm. The key to solving topology optimization problems by the intelligent algorithm lies in the mechanism of structure random updating. The intelligent optimization algorithm regards the structure as a population and needs to randomly update the population to form a new structure in each iteration. This process requires a large amount of calculation and has low solving efficiency, so it is not suitable for solving complex engineering problems. Therefore, the idea of an intelligent method is commonly integrated into the numerical solution method to improve the quality of structural topology optimization. [PERSON] [19] could not obtain a satisfactory structure because the medium density region of the topology obtained by the SIMP method lacked physical meaning.