Evolutionary Algorithms (EAs) are well-known terms in many science fields. EAs usually interfere with science problems when common mathematical methods are unable to provide a good solution or finding the exact solution requires an unreasonable amount of time. Nowadays, many EA methods have been proposed and developed. Most of them imitate natural behavior, such as swarm animal movement. In this paper, inspired by the natural phenomenon of growth, a new metaheuristic algorithm is presented that uses a mathematic concept called the fractal. Using the diffusion property which is seen regularly in random fractals, the particles in the new algorithm explore the search space more efficiently. To verify the performance of our approach, both the constrained and unconstrained standard benchmark functions are employed. Some classic functions including unimodal and multimodal functions, as well as some modern hard functions, are employed as unconstrained benchmark functions; On the other hand, some well-known engineering design optimization problems commonly used in the literature are considered as constrained benchmark functions. Numerical results and comparisons with other state of the art stochastic algorithms are also provided. Considering both convergence and accuracy simultaneously, experimental results prove that the proposed method performs significantly better than other previous well-known metaheuristic algorithms in terms of avoiding getting stuck in local minimums, and finding the global minimum.
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