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This paper proposes a novel hybrid algorithm, named Multi-Strategy Hybrid Harris Hawks Tunicate Swarm Optimization Algorithm (MSHHOTSA). The primary objective of MSHHOTSA is to address the limitations of the tunicate swarm algorithm, which include slow optimization speed, low accuracy, and premature convergence when dealing with complex problems. Firstly, inspired by the idea of the neighborhood and thermal distribution map, the hyperbolic tangent domain is introduced to modify the position of new tunicate individuals, which can not only effectively enhance the convergence performance of the algorithm but also ensure that the data generated between the unknown parameters and the old parameters have a similar distribution. Secondly, the nonlinear convergence factor is constructed to replace the original random factor c1 to coordinate the algorithm’s local exploitation and global exploration performance, which effectively improves the ability of the algorithm to escape extreme values and fast convergence. Finally, the swarm update mechanism of the HHO algorithm is introduced into the position update of the TSA algorithm, which further balances the local exploitation and global exploration performance of the MSHHOTSA. The proposed algorithm was evaluated on eight standard benchmark functions, CEC2019 benchmark functions, four engineering design problems, and a PID parameter optimization problem. It was compared with seven recently proposed metaheuristic algorithms, including HHO and TSA. The results were analyzed and discussed using statistical indicators such as mean, standard deviation, Wilcoxon’s rank sum test, and average running time. Experimental results demonstrate that the improved algorithm (MSHHOTSA) exhibits higher local convergence, global exploration, robustness, and universality than BOA, GWO, MVO, HHO, TSA, ASO, and WOA algorithms under the same experimental conditions.