This paper proposes a novel sine–cosine and Nelder–Mead (SCANM) algorithm which hybridizes the sine–cosine algorithm (SCA) and Nelder–Mead (NM) local search method. The original version of SCA is prone to early convergence at the local minimum. The purpose of the SCANM algorithm is to overcome this issue. Thus, it aims to overcome this issue with the employment of the NM method. The SCANM algorithm was firstly compared with the SCA algorithm through 23 well-known test functions. The statistical assessment confirmed the better performance of the proposed algorithm. The comparative convergence profiles further demonstrated the significant performance improvement of the proposed SCANM algorithm. Besides, a non-parametric test was performed, and the results that showed the ability of the proposed approach were not by coincidence. A popular and well-performed metaheuristic algorithm known as grey wolf optimization was also used along with the recent and promising two other algorithms (Archimedes optimization and Harris hawks optimization) to comparatively demonstrate the performance of the SCANM algorithm against well-known classical benchmark functions and CEC 2017 test suite. The comparative assessment showed that the SCANM algorithm has promising performance for optimization problems. The non-parametric test further verified the better capability of the proposed SCANM algorithm for optimization problems.