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The sine-cosine algorithm is concerned as a recent meta-heuristic method that takes benefit of orthogonal functions to scale its walking steps through the search space. The idea is utilized here in a different manner to develop a modified sine-cosine algorithm (MSCA). It is based on the controlled perturbation about current solutions by applying a novel combination of sine and cosine functions. The desired transition from exploration to exploitation phases mainly relies on such a term that provides continued fluctuations within a dynamic amplitude. Performance of the proposed algorithm is further evaluated on a set of thirteen test functions with unimodal and multimodal search spaces, as well as on engineering and structural problems in a variety of discrete, continuous and mixed discrete-continuous types. Numerical simulations show that MSCA can find the best literature results for such benchmarks problems. Additional fair comparisons, declare competitive performance of the proposed method with other meta-heuristic algorithms and its enhancement with respect to the standard sine-cosine algorithm.