# Topology Optimization Based on SA-BESO
## 1 Introduction
Therefore, the idea of a simulated annealing algorithm was introduced to gradually delete gray elements and obtain a clear structure. [PERSON] et al. [20] proposed the GESO method by combining the ESO method with the genetic algorithm, and demonstrated with examples that the GESO method has strong global optimization ability and high computational efficiency. The Bi-directional Evolutionary structure Structural Optimization [21; 22] is favored because of its simple concept and high efficiency. Firstly, the contribution degree of the structure is defined as element sensitivity, and the structural elements are sorted in descending order according to element sensitivity. Then, the sensitivity threshold is determined according to the deletion rate and the stage volume. The solid elements whose sensitivity value is lower than the threshold are turned into empty elements. The empty elements whose sensitivity value is higher than the threshold are turned into solid elements. The iteration was stopped when the final volume target and convergence conditions were satisfied, and the optimal topology was finally obtained. When the target volume is satisfied in each iteration, the BESO algorithm will be affected by factors such as the evolution rate, deletion rate, sensitivity calculation and structure target volume. There is a possibility that the structural compliance will suddenly increase due to the accidental deletion of elements, thus falling into a local optimal solution. In order to improve the optimization quality of the BESO algorithm, many scholars have combined the BESO algorithm with intelligent algorithms with strong global search ability, such as the genetic algorithm, discrete particle swarm optimization algorithm, Simulated Annealing Algorithm (SA) and so on. [PERSON] et al. [23] combined the BESO algorithm with the genetic algorithm, entrusting design variables with binary coding, similar to chromosome crossover and mutation, to obtain new coding. [PERSON] et al. [24] also proposed the BESO algorithm with soft deletion based on the improved genetic algorithm to solve the problem that the optimal topology configuration cannot be obtained due to the improper setting of parameters (such as evolution rate) in the traditional BESO algorithm, so as to improve the quality of optimization. [PERSON] [25] proposed a bidirectional asymptotic structure optimization method (IBPSO-BESO) based on improved discrete particle swarm optimization, which effectively improved the quality of the solution and increased the size of the problem. The combination of the above intelligent algorithms and BESO algorithm improves the optimization efficiency. However, it neglects the change in the compliance of the new structure when it is updated randomly, which leads to oscillations in the compliance of the structure during the iteration. The simulated annealing algorithm determines the optimization direction according to the change in the objective function value. Combining it with the BESO algorithm, the change in structural compliance can be judged in the iterative process. The probability of structural compliance mutations can be reduced, thus improving the stability of the iterations and the optimality of the algorithm. Based on this, this paper proposes the SA-BESO joint topology optimization algorithm.