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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.

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Sound Energy Optimizer (SEO) is a recent metaheuristic algorithm inspired by the propagation and reception of sound waves in physical environments. While conventional metaheuristics that rely on random number generators with certain distributions, SEO can utilize various real-world or simulated sound signals as the source of stochasticity to guide its search process. Concerning structural design by SEO, the effect of natural sound signals is compared with the artificial signals generated from uniform or normal distributions. In this regard, a 244-bar power transmission tower and a 1016-bar double-layer grid are simultaneously optimized with continuous geometry as well as discrete sizing variables to evaluate the impact of input signals on convergence behavior, solution quality and robustness of the algorithm. A sensitivity analysis is conducted to calibrate key control parameters of SEO. The results declare that the nature of the input sound signal can significantly affect the algorithm’s exploration-exploitation balance. In this study, the "Knocking sound" signal yields the best performance, while the synthetic random signals revealed less stable optimization trajectories.