Based on Salp Swarm Algorithm (SSA) and Slime Mould Algorithm (SMA), a novel hybrid optimization algorithm, named Hybrid Slime Mould Salp Swarm Algorithm (HSMSSA), is proposed to solve constrained engineering problems. SSA can obtain good results in solving some optimization problems. However, it is easy to suffer from local minima and lower density of population. SMA specializes in global exploration and good robustness, but its convergence rate is too slow to find satisfactory solutions efficiently. Thus, in this paper, considering the characteristics and advantages of both the above optimization algorithms, SMA is integrated into the leader position updating equations of SSA, which can share helpful information so that the proposed algorithm can utilize these two algorithms’ advantages to enhance global optimization performance. Furthermore, Levy flight is utilized to enhance the exploration ability. It is worth noting that a novel strategy called mutation opposition-based learning is proposed to enhance the performance of the hybrid optimization algorithm on premature convergence avoidance, balance between exploration and exploitation phases, and finding satisfactory global optimum. To evaluate the efficiency of the proposed algorithm, HSMSSA is applied to 23 different benchmark functions of the unimodal and multimodal types. Additionally, five classical constrained engineering problems are utilized to evaluate the proposed technique’s practicable abilities. The simulation results show that the HSMSSA method is more competitive and presents more engineering effectiveness for real-world constrained problems than SMA, SSA, and other comparative algorithms. In the end, we also provide some potential areas for future studies such as feature selection and multilevel threshold image segmentation.

中文翻译：

---

针对约束工程问题的基于突变反对学习的混合 SSA 和 SMA


基于Salp Swarm算法（SSA）和Slime Mold算法（SMA），提出了一种解决约束工程问题的新型混合优化算法——混合Slime Mold Salp Swarm Algorithm（HSMSSA）。 SSA在解决一些优化问题上可以取得很好的效果。然而，它很容易受到局部极小值和人口密度较低的影响。 SMA擅长全局探索，鲁棒性好，但收敛速度太慢，无法有效找到满意的解。因此，本文综合考虑上述两种优化算法的特点和优点，将SMA融入到SSA的引导位置更新方程中，共享有用的信息，使所提出的算法能够利用这两种算法的优点来增强全局优化能力。优化性能。此外，利用Levy飞行来增强探索能力。值得注意的是，提出了一种称为基于突变反对的学习的新策略，以增强混合优化算法在避免过早收敛、探索和利用阶段之间的平衡以及找到令人满意的全局最优方面的性能。为了评估所提出算法的效率，将 HSMSSA 应用于单峰和多峰类型的 23 个不同的基准函数。此外，还利用五个经典的约束工程问题来评估所提出技术的实用能力。仿真结果表明，HSMSSA方法比SMA、SSA和其他对比算法更具竞争力，并且对于现实约束问题表现出更多的工程有效性。 最后，我们还为未来的研究提供了一些潜在的领域，例如特征选择和多级阈值图像分割。