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Cuckoo Search Algorithm for Parametric Data Fitting of Characteristic Curves of the Van der Waals Equation of State

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Applications of Cuckoo Search Algorithm and its Variants

Part of the book series: Springer Tracts in Nature-Inspired Computing ((STNIC))

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Abstract

The Van der Waals (VdW) equation is an equation of state that generalizes the ideal gas law by taking into account molecular size and molecular interaction forces. This equation is widely used to analyze the interplay and transitions between the liquid and gas phases. To this purpose, two characteristic curves, called binodal and spinodal curves, are to be computed. They are usually reconstructed through polynomial fitting from a collection of 2D points in the pressure–volume plane by using standard numerical procedures. However, the resulting fitting models are strongly limited in several ways and can be further improved. In this paper, we address this issue through least-squares approximation of the set of 2D points by using free-form Bézier curves. This new approach requires to perform a proper data parameterization in addition to computing the poles of the curves. This is achieved through a powerful swarm intelligence method inspired in nature for continuous optimization: the cuckoo search algorithm. To test the performance of this new approach, it has been applied to real data, in this case for a gas. Our experimental results prove that this method can reconstruct these characteristic curves with a significant accuracy. Furthermore, we carried out a comparative analysis between this method and four alternative techniques present in the literature, including two of the latest methods in the field (polynomial curve fitting and the multilayer perceptron neural network) and two popular nature-inspired metaheuristic methods (firefly algorithm and bat algorithm). Such comparative analysis shows that our approach outperforms these four methods for at least two orders of magnitude for the studied example. We conclude, not only that the mentioned approach is certainly promising, but also that is it ready for being successfully applied to real, practical instances of chemical components and mixtures.

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Acknowledgements

The authors acknowledge the financial support from the project PDE-GIR of the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 778035, and from the Spanish Ministry of Science, Innovation and Universities (Computer Science National Program) under grant #TIN2017-89275-R of the Agencia Estatal de Investigación and European Funds EFRD (AEI/FEDER, UE).

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Authors and Affiliations

  1. School of Chemical, Biological and Environmental Engineering (CBEE), College of Engineering, Oregon State University, Corvallis, OR, USA

    Almudena Campuzano

  2. School of Industrial Engineering, University of Cantabria, Santander, Spain

    Almudena Campuzano

  3. Department of Information Science, Faculty of Sciences, Toho University, Funabashi, Japan

    Andrés Iglesias & Akemi Gálvez

  4. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Santander, Spain

    Andrés Iglesias & Akemi Gálvez

Authors
  1. Almudena Campuzano
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  2. Andrés Iglesias
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  3. Akemi Gálvez
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Corresponding author

Correspondence to Andrés Iglesias .

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Editors and Affiliations

  1. Department of Information Technology, Techno International New Town, Kolkata, West Bengal, India

    Nilanjan Dey

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Campuzano, A., Iglesias, A., Gálvez, A. (2021). Cuckoo Search Algorithm for Parametric Data Fitting of Characteristic Curves of the Van der Waals Equation of State. In: Dey, N. (eds) Applications of Cuckoo Search Algorithm and its Variants. Springer Tracts in Nature-Inspired Computing. Springer, Singapore. https://doi.org/10.1007/978-981-15-5163-5_2

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