A multi-strategy crazy sparrow search algorithm (LTMSSA) for logic-tent hybrid chaotic maps is given in the research to address the issues of poor population diversity, slow convergence, and easily falling into the local optimum of the sparrow search algorithm (SSA). Firstly, the LTMSSA employs an elite chaotic backward learning strategy and an improved discoverer-follower ratio factor to improve the population’s quality and diversity. Secondly, the LTMSSA updates the positions of discoverers and followers by the crazy operator and the Lévy flight strategy to expand the selection range of target following individuals. Finally, during the algorithm’s optimization search, the LTMSSA introduces the tent hybrid and Corsi variable perturbation strategies to improve the population’s ability to jump out of the local optimum. Different types and dimensions of test functions are used as performance benchmark functions to test the performance of the LTMSSA with SSA variants and other algorithms. The simulation results show that the LTMSSA can jump out of the optimal local solution, converge faster, and have higher accuracy. Its overall performance is better than the other seven algorithms, and the LTMSSA can find smaller optimal values than other algorithms in the welded beam and reducer designs. The results confirm that the LTMSSA is an effective aid for computationally complex practical tasks, provides high-quality solutions, and outperforms other algorithms.