Tree-Seed Algorithm (TSA) is a meta-heuristic optimization algorithm with good performance in solving continuous optimization problems. However, there is an imbalance between its exploration and exploitation when solving complex problems, mainly lack exploration. To overcome this problem, this paper proposes two tree migration mechanisms: triple-learning-based migration mechanism and sine-random-distribution migration mechanism. The target tree position is migrated by learning from the first three trees in the current iteration. The sine function is added to the tree migration formula to enhance the randomness of tree distribution. In order to verify these migration mechanisms, Triple Tree-Seed Algorithm (TriTSA) has been proposed and compared with TSA on 30 well-known test functions from IEEE CEC 2014. In addition, STSA, SCA, PSO, ABC, Jaya, and TLBO are adopted in some comparative experiments on different dimensions. The experiments show that the tree migration mechanism can improve the optimization capability of the original algorithm effectively. On all 30 benchmark test functions, TriTSA outperforms TSA on 10, 30, 50, and 100 dimensions by 70%, 90%, 90%, and 97% respectively. Finally, the proposed TriTSA is compared with TSA, ABC, PSO, and SCA on solving two classical engineering design problems. It is proved that the proposed algorithm is more applicable in solving practical problems.

Tree-Seed Algorithm (TSA) 是一种元启发式优化算法，在解决连续优化问题方面具有良好的性能。然而，在解决复杂问题时，其探索性和开发性之间存在不平衡，主要是缺乏探索性。为了克服这个问题，本文提出了两种树迁移机制：基于三重学习的迁移机制和正弦随机分布迁移机制。通过从当前迭代中的前三棵树中学习来迁移目标树位置。树迁移公式中加入正弦函数，增强树分布的随机性。为了验证这些迁移机制，在 IEEE CEC 2014 的 30 个著名测试函数上提出了三重树种子算法 (TriTSA) 并与 TSA 进行了比较。 此外，STSA、SCA、PSO、ABC、Jaya、和 TLBO 在一些不同维度的对比实验中被采用。实验表明，树迁移机制可以有效提高原算法的优化能力。在所有 30 个基准测试函数中，TriTSA 在 10、30、50 和 100 个维度上分别优于 TSA 70%、90%、90% 和 97%。最后，将提出的 TriTSA 与 TSA、ABC、PSO 和 SCA 在解决两个经典工程设计问题上进行比较。证明该算法更适用于解决实际问题。和 100 个维度分别为 70%、90%、90% 和 97%。最后，将提出的 TriTSA 与 TSA、ABC、PSO 和 SCA 在解决两个经典工程设计问题上进行比较。证明该算法更适用于解决实际问题。和 100 个维度分别为 70%、90%、90% 和 97%。最后，将提出的 TriTSA 与 TSA、ABC、PSO 和 SCA 在解决两个经典工程设计问题上进行比较。证明该算法更适用于解决实际问题。