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This article presents a comprehensive review of chaos embedded meta-heuristic optimization algorithms and describes the evolution of this algorithms along with some improvements, their combination with various methods as well as their applications. The reported results indicate that chaos embedded algorithms may handle engineering design problems efficiently in terms of precision and convergence and, in most cases they outperform the results presented in the previous works. The main goal of this paper is to providing useful references to fundamental concepts accessible to the broad community of optimization practitioners.

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The big bang-big crunch (BB-BC) algorithm is a popular metaheuristic optimization technique proposed based on one of the theories for the evolution of the universe. The algorithm utilizes a two-phase search mechanism: big-bang phase and big-crunch phase. In the big-bang phase the concept of energy dissipation is considered to produce disorder and randomness in the candidate population while in the big-crunch phase the randomly created solutions are shrunk into a single point in the design space. In recent years, numerous studies have been conducted on application of the BB-BC algorithm in solving structural design optimization instances. The objective of this review study is to identify and summarize the latest promising applications of the BB-BC algorithm in optimal structural design. Different variants of the algorithm as well as attempts to reduce the total computational effort of the technique in structural optimization problems are covered and discussed. Furthermore, an empirical comparison is performed between the runtimes of three different variants of the algorithm. It is worth mentioning that the scope of this review is limited to the main applications of the BB-BC algorithm and does not cover the entire literature.

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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.