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A hybrid optimization approach based on clustering and chaotic sequences

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Abstract

Evolutionary computation algorithms represent a class of stochastic methods that can be applied to a wide set of different complex optimization problems. Recently, the combination of approaches extracted from different computation techniques represents one of the most successful trends in evolutionary optimization. With this integration, the idea is to overcome the limitations of each single method and to reach a synergetic effect through their integration. In this paper, a hybrid optimization algorithm for solving optimization problems is introduced. The approach, called cluster–chaotic-optimization, combines the classification characteristics of a clustering method with the randomness of chaotic sequences to conduct its search strategy. Under the proposed method, at each generation, the population is divided into different clusters according to its space distribution. Then, individuals are modified considering two kinds of operators: intra-cluster and extra-cluster. In the intra-cluster operation, individuals of the same cluster are locally adjusted considering the position of the best element of the cluster in terms of its fitness value. On the other hand, in the extra-cluster operation, the best individual of each cluster is globally attracted to the best element of the complete population. In both operations, the adjustment on each individual position is produced by using deterministic rules and chaotic sequences. With such mechanisms, the proposed method efficiently examines the search space based on the spatial associations produced by the individuals during the optimization process. To exhibit the performance and robustness of the proposed method, different comparisons to other well-known evolutionary methods and hybrid approaches are conducted. The comparison considers several standard benchmark functions and real-world engineering problems which are typically found in the literature of evolutionary algorithms. The results suggest a high performance of the proposed methodology.

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  1. Departamento de Electrónica, Universidad de Guadalajara, CUCEI, Av. Revolución, 1500, Guadalajara, Jal, Mexico

    Jorge Gálvez, Erik Cuevas, Héctor Becerra & Omar Avalos

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  1. Jorge Gálvez
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  2. Erik Cuevas
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  3. Héctor Becerra
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  4. Omar Avalos
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Correspondence to Erik Cuevas.

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Appendices

Appendix 1: List of benchmark functions

See Tables 25, 26 and 27

Table 25 Unimodal benchmark functions used in the experimental study
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Table 26 Multimodal benchmark functions used in the experimental study
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Table 27 Hybrid benchmark functions used in the experimental study
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Appendix 2: Engineering design problems

See Tables 28, 29, 30 and 31.

Table 28 Three-bar truss design description used in the experimental study
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Table 29 Pressure vessel design description used in the experimental study
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Table 30 Tension/compression spring design description used in the experimental study
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Table 31 Welded beam design description used in the experimental study
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Gálvez, J., Cuevas, E., Becerra, H. et al. A hybrid optimization approach based on clustering and chaotic sequences. Int. J. Mach. Learn. & Cyber. 11, 359–401 (2020). https://doi.org/10.1007/s13042-019-00979-6

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