针对金豺优化算法（golden jackal optimization algorithm, GJO）在求解复杂优化问题时存在收敛速度慢、寻优精度差和易陷入局部极值等缺点，提出一种混合策略改进的金豺优化算法（mixed-strategy improved golden jackal optimization algorithm, MSIGJO）。首先，引入一种Tent映射融合反向学习的初始化策略，增强金豺种群多样性，提高算法初始解的质量；其次，采用一种非线性因子协调算法全局搜索与局部深入开发的能力，再次，在探索阶段融合正弦余弦算法并引入螺旋搜索策略指引机制，提高算法收敛速度；最后，在迭代后期引入反向学习和差分变异策略，避免算法陷入局部最优。使用本文中所提改进算法、基本优化算法及现有改进金豺算法对不同测试函数进行仿真实验，通过仿真结果对比分析可得MSIGJO的收敛性、鲁棒性、Wilcoxon秩和检验及时间复杂度等方面均优于其他算法，具有良好的收敛速度、求解精度和鲁棒性。将MSIGJO用于解决压力容器设计问题，进一步验证了MSIGJO算法在解决实际工程问题时的有效性。

Aiming at the shortcomings of the golden jackal optimization algorithm (GJO) in solving complex optimization problems, such as slow convergence speed, poor optimization accuracy, and easy falling into local extremes, a mixed-strategy improved golden jackal optimization algorithm (MSIGJO) was proposed. Firstly, a Tent mapping fused with inverse learning initialization strategy was introduced to enhance the diversity of the golden jackal population and improve the quality of the initial solution of the algorithm. Secondly, a dynamic adaptive energy factor was used to coordinate the ability of the algorithm to search globally and develop locally in-depth, and once again, a sinusoidal cosine algorithm was fused with a helical search strategy guideline mechanism in the exploration phase to improve the convergence speed of the algorithm. Finally, the algorithm was enhanced with backward learning and differential variation strategies to avoid the algorithm falling into local optimization. Using the improved algorithm proposed the basic optimization algorithm, and the existing improved golden jackal algorithm for simulation experiments on different test functions, through the simulation results of the comparative analysis can be obtained that MSIGJO convergence, robustness, Wilcoxon rank-sum test and time complexity are better than other algorithms, with good convergence speed, solution accuracy, and robustness. MSIGJO was used to solve engineering optimization problems, which verifies the effectiveness and feasibility of MSIGJO algorithm in solving real engineering problems.