An ensemble method is introduced to solve optimization problems efficiently. The method is mainly based on using the gradient directions along which, the function is reduced at most. Large step sizes are employed for exploration in the first phase. The use of smaller step sizes in subsequence phases will allow for more accurate exploration. To increase the efficiency of the gradient techniques, some enhancements such as mutation, crossover and fly-back operations are introduced to explore the entire design space. The efficiency and the reliability of the multi-phase gradient approach are examined by solving 29 complicated multimodal functions introduced in CEC 2017 and a structural shape optimization problem under frequency constraints. The results are compared with several well-known population-based algorithms.

Keywords: multi-phase gradient, multimodal problems, global optimization, CEC 2017

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