# Hybrid Strategy Improved Beetle Antennae Search Algorithm and Application
## 1 Introduction  
Traditional optimization algorithms, such as the steepest descent method and variable metric method, are gradually unable to meet the needs of engineering optimization as the problems faced by the engineering field are becoming increasingly complex [1]. Recently, intelligent optimization algorithms, as a new evolutionary computational tool, have been widely used in engineering optimization problems [2; 3; 4]. As one of the heuristic search algorithms, the Beetle Antennae Search (BAS) algorithm enjoys the advantages of fast convergence, simple model, low computational complexity, and robust searching ability [5; 6], and is widely employed in several engineering optimization problems with high research value [7; 8; 9; 10]. Until now, many researchers have been making efforts to improve the performance of the BAS algorithm further, and mainstream approaches include the search step-size adjustment and algorithm fusion. [PERSON] et al. [11] proposed a BAS algorithm combined with Adaptive Moment Estimation (ADAM), named BAS-ADAM, aiming to avoid falling into the locally optimal solution, which increases the computational complexity at the cost of time. [PERSON] et al. [12] introduced a Beetle Swarm Antennae Search (BSAS) algorithm combined with step-size self-adjustment, reducing the need to update the step iteratively and improving the ability to solve high-dimensional problems. [PERSON] et al. [13] designed a BAS-PSO algorithm combining the BAS algorithm with the Particle Swarm Optimization (PSO)algorithm to enhance the local and global search ability, possibly reducing the convergence rate. [PERSON] et al. [14] proposed a BGWO algorithm that integrates the BAS algorithm with Grey Wolf Optimizer (GWO), which improves the local optimum situation caused by the lack of population diversity and the problem of group hierarchical structure in GWO, thus enhancing search efficiency and robustness. Moreover, there are variations in the algorithm based on Levy flight, adaptive mechanism, quadratic interpolation [15; 16; 17], etc. BAS algorithms are widely used in engineering applications. [PERSON] et al. [18] constructed a multi-objective optimization model for microgrids based on BAS to minimize operation and pollution treatment costs; [PERSON] et al. [19] developed an improved BAS algorithm for collision prediction and obstacle avoidance of underdriven ships; and [PERSON] et al. [20] combined an augmented selection mechanism, a deep learning algorithm, and BAS to improve the accuracy of BAS in the fault diagnosis of rolling bearings. [PERSON] et al. [21] employed the BAS algorithm with Levy flight and inertia weight optimization to tune the hyperparameters in random forests, optimizing the resume design of reinforced concrete beams. [PERSON] et al. [22] investigated a binarized BAS algorithm to increase the diversity of tangential portfolios. [PERSON] et al. [23] combined BAS with the Radial Basis Function Neural Network to model the friction characteristics of robot joints. Based on the No Free Lunch Theorem, no optimization algorithm can solve all optimization problems. For some applications, a metaheuristic may provide prosperous solutions, while it may provide poor performance for other applications [24]. In this paper, a Hybrid Strategy Improved Beetle Antennae Search (HSBAS) algorithm is adopted to solve the multi-dimensional optimization problem in engineering mechanisms. In the initial stage of the algorithm, the step is updated appropriately and explored in multiple directions to strengthen the global optimization ability; meanwhile, the Lens Opposition-Based Learning is interspersed to improve the sample diversity. By comparing and calibrating with other algorithms widely used in engineering structural design, the superiority of HSBAS is verified. Meanwhile, it is further applied to the altitude compensation module of a solar wing-based gravity unloading device to verify its effectiveness in engineering practice.