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Enhanced golden jackal optimizer-based shape optimization of complex CSGC-Ball surfaces

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Abstract

The geometric design and shape optimization of complex surfaces are pivotal and knotty techniques in computer aided geometric design (CAGD), and widely used in many complex product manufacturing fields involving surfaces modeling, e.g., for ships, aircraft wing, automobiles, etc. In this paper, an enhanced golden jackal optimization (GJO) algorithm is used to optimize the shape of complex composite shape-adjustable generalized cubic Ball (CSGC-Ball, for short) surfaces. Firstly, the shape design of CSGC-Ball surfaces is mathematically an optimization problem that can be efficiently dealt with by meta-heuristic algorithms. In this regard, an enhanced GJO (EGJO), combined with opposition-based learning, spring vibration-based adaptive mutation and binomial-based cross-evolution strategy, is developed to improve the convergence speed and calculation accuracy of the original GJO. The performance of EGJO is assessed on 23 benchmark test functions, IEEE CEC-2019 and 4 actual engineering optimization problems, and the competition and practicability of EGJO algorithm are confirmed. Secondly, the CSGC-Ball surfaces with global and local shape parameters is constructed based on a class of cubic generalized Ball basis functions, and then the conditions of G1 and G2 continuity for the surfaces are derived. The shapes of CSGC-Ball surfaces can be adjusted and optimized expediently by utilizing their shape parameters. Finally, the minimum energy-based shape optimization models of CSGC-Ball surfaces with 1th-order and 2th-order geometric continuity are established, respectively. Furthermore, the proposed EGJO is utilized to solve the established optimization models, and the CSGC-Ball surfaces with minimum energy are obtained. Four representative examples are given to demonstrate the excellence and effectiveness of EGJO in solving the shape optimization problems of complex CSGC-Ball surfaces.

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Data availability

All data generated or analysed during this study are included in this published article.

Code availability

The Matlab source code of the EGJO related to this article can be found online at https://www.researchgate.net/publication/371902375_EGJO_Code.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 51875454).

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Authors and Affiliations

  1. Department of Applied Mathematics, Xi’an University of Technology, Xi’an, 710054, People’s Republic of China

    Gang Hu & Liuxin Chen

  2. School of Computer Science and Engineering, Xi’an University of Technology, Xi’an, 710048, People’s Republic of China

    Gang Hu

  3. University of North Carolina at Pembroke, Pembroke, NC, 28372, USA

    Guo Wei

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  1. Gang Hu
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GH, LC and GW wrote the main manuscript text and LC prepared all figures. All authors reviewed the manuscript.

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Correspondence to Gang Hu.

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Hu, G., Chen, L. & Wei, G. Enhanced golden jackal optimizer-based shape optimization of complex CSGC-Ball surfaces. Artif Intell Rev 56 (Suppl 2), 2407–2475 (2023). https://doi.org/10.1007/s10462-023-10581-6

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