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A comprehensive investigation into the performance, robustness, scalability and convergence of chaos-enhanced evolutionary algorithms with boundary constraints

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Abstract

The purpose of this research is to investigate the effects of different chaotic maps on the exploration/exploitation capabilities of evolutionary algorithms (EAs). To do so, some well-known chaotic maps are embedded into a self-organizing version of EAs. This combination is implemented through using chaotic sequences instead of random parameters of optimization algorithm. However, using a chaos system may result in exceeding of the optimization variables beyond their practical boundaries. In order to cope with such a deficiency, the evolutionary method is equipped with a recent spotlighted technique, known as the boundary constraint handling method, which controls the movements of chromosomes within the feasible solution domain. Such a technique aids the heuristic agents towards the feasible solutions, and thus, abates the undesired effects of the chaotic diversification. In this study, 9 different variants of chaotic maps are considered to precisely investigate different aspects of coupling the chaos phenomenon with the baseline EA, i.e. the convergence, scalability, robustness, performance and complexity. The simulation results reveal that some of the maps (chaotic number generators) are more successful than the others, and thus, can be used to enhance the performance of the standard EA.

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Ahmad Mozaffari

  2. Babol University of Technology, Babol, Mazandaran, Iran

    Mahdi Emami & Alireza Fathi

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  1. Ahmad Mozaffari
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  2. Mahdi Emami
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  3. Alireza Fathi
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Correspondence to Ahmad Mozaffari.

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Supplementary file

The detailed mathematical implementation of the objective function of Damavand power plant is given in the supplementary file which is available online. (docx. 176 KB)

Appendix A: Benchmark problems

Appendix A: Benchmark problems

See Table 20.

Table 20 Characteristics of the benchmark problems
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Mozaffari, A., Emami, M. & Fathi, A. A comprehensive investigation into the performance, robustness, scalability and convergence of chaos-enhanced evolutionary algorithms with boundary constraints. Artif Intell Rev 52, 2319–2380 (2019). https://doi.org/10.1007/s10462-018-9616-4

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