Aiming at problems such as the dung beetle optimization algorithm's poor global exploration ability and its tendency to fall into local optimization, this paper proposes a hybrid algorithm based on the positive cosine algorithm and the dung beetle optimization algorithm called the SCDBO algorithm. The hybrid algorithm adopts the positive cosine search algorithm instead of the search mechanism of the rolling dung beetle in the dung beetle algorithm, which balances the global search and local exploitation ability of the algorithm. In addition, while introducing the t-distribution perturbation to update the dung beetle population with a certain probability during each iteration, the Levy-Corsi variation operator is introduced to mutate the optimal position. This not only accelerates the convergence speed of the algorithm but also reduces the possibility of falling into the local optimum. Finally, the population diversity of the algorithm is enhanced by initializing the dung beetle population with chaotic mapping. The effectiveness of the SCDBO algorithm is investigated using 23 benchmark functions, and the experimental results show that the algorithm exhibits a better ability to find the optimum compared with other comparative algorithms. To further evaluate the performance of the SCDBO algorithm for practical applications, the algorithm was successfully applied to three engineering design problems. By comparing with other algorithms, the results show that the SCDBO algorithm has high potential in solving practical engineering problems.