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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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This paper presents the chaotic variants of the particle swarm optimization-statistical regeneration mechanism (PSO-SRM). The nine chaotic maps named Chebyshev, Circle, Iterative, Logistic, Piecewise, Sine, Singer, Sinusoidal, and Tent are used to increase the performance of the PSO-SRM. These maps are utilized instead of the random number, which defines the solution generation method. The robustness and performance of these methods are tested in the three steel frame design problems, including the 1-bay 10-story steel frame, 3-bay 15-story steel frame, and 3-bay 24-story steel frame. The optimization results reveal that the applied chaotic maps improve the performance of the PSO-SRM.