## 1 Introduction
Compared to other swarm intelligence optimization algorithms, the SSA algorithm has the characteristics of short learning time, high optimization accuracy, fast convergence speed, and good stability. However, in some cases, the SSA algorithm exhibits reduced search capability and decreased population diversity during the later stages of iteration, leading to drawbacks such as slow convergence speed, low solution accuracy, and susceptibility to local optima (26). Therefore, improving the SSA algorithm has become a research hotspot. [PERSON] et al. (2020) combined the sparrow search algorithm with the traditional machine learning model Classification and Regression Trees (CART) to establish an SSA-CART optimization model for predicting pork prices. [PERSON] and [PERSON] (2021) proposed an optimization strategy that integrates the butterfly optimization algorithm (BOA). By improving the position updating strategy of the discoverers, the algorithm's global exploration capability is enhanced. [PERSON] et al. (2021) adopted an elite chaotic reverse learning strategy to generate the initial population and proposed an FOC-SSA algorithm. This algorithm improves the quality of initial individuals and population diversity to enhance the algorithm's capability to escape local optima and convergence performance. Based on the above research, it can be observed that with the continuous improvement in and application of metaheuristic algorithms, each algorithm has its unique advantages. Considering the novelty and limitations of the sparrow search algorithm (SSA), this study explored strategies suitable for addressing practical engineering problems and proposes a multi-strategy improved sparrow search algorithm (ISSA) combined with a PID controller to optimize controller gains. Firstly, by introducing tent chaotic mapping for initializing the sparrow population, the algorithm's global search capability is enhanced while maintaining population diversity. Secondly, to tackle the slow convergence speed problem of the SSA algorithm when dealing with high-dimensional complex problems, the concepts of sine and cosine are combined, and a nonlinear learning factor is introduced to dynamically adjust the update mechanism of discoverer positions, thereby accelerating the solution process. Lastly, the Levy flight strategy is employed to update follower positions, introducing perturbations and altering the current optimal solution, thereby enhancing the algorithm's local escape capability. Additionally, addressing the common occurrence of overshoot in practical scenarios, a fitness function incorporating overshoot penalties is proposed to mitigate overshoot issues. This algorithm is then applied to optimize the PID controller parameters of a bridge crane. Through analysis of simulation results, the PID control system optimized by the ISSA algorithm demonstrates superior control performance compared to the SSA, PSO, SA, and WOA algorithms, while also exhibiting robustness and adaptability. The content arrangement of this paper is as follows: Section 1 provides a general introduction. Section 2 elaborates on the theoretical model of the bridge crane, establishing its mathematical model using the Lagrangian equation. Section 3 innovatively introduces the SSA algorithm and its enhancements with multiple strategies. Section 4 describes how the ISSA algorithm is combined with PID controllers and applied to bridge crane control. Section 5 conducts simulations and analyses of the proposed method, examining the control effects of various algorithms on parameter variations and disturbances in bridge crane operations. Finally, conclusions are drawn in Section 6.