LX-BBSCA: Laplacian biogeography-based sine cosine algorithm for structural engineering design optimization

Vanita Garg; Kusum Deep; Khalid Abdulaziz Alnowibet; Ali Wagdy Mohamed; Mohammad Shokouhifar; Frank Werner; Vanita Garg; Kusum Deep; Khalid Abdulaziz Alnowibet; Ali Wagdy Mohamed; Mohammad Shokouhifar; Frank Werner

doi:10.3934/math.20231565

AIMS Mathematics

2023, Volume 8, Issue 12: 30610-30638. doi: 10.3934/math.20231565

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LX-BBSCA: Laplacian biogeography-based sine cosine algorithm for structural engineering design optimization

1.
School of Basic and Applied Sciences, Galgotias University, Greater Noida 201306, India
2.
Department of Mathematics, Indian Institute of Technology, Roorkee, Uttarakhand 247667, India
3.
Statistics and Operations Research Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
4.
Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
5.
Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan
6.
Department of Electrical & Computer Engineering, Shahid Beheshti University, Tehran 1983969411, Iran
7.
Faculty of Mathematics, Otto-von-Guericke University, Magdeburg 39016, Germany

Received: 08 October 2023 Revised: 02 November 2023 Accepted: 07 November 2023 Published: 13 November 2023
MSC : 90C59

In this paper, an ensemble metaheuristic algorithm (denoted as LX-BBSCA) is introduced. It combines the strengths of Laplacian biogeography-based optimization (LX-BBO) and the sine cosine algorithm (SCA) to address structural engineering design optimization problems. Our primary objective is to mitigate the risk of getting stuck in local minima and accelerate the algorithm's convergence rate. We evaluate the proposed LX-BBSCA algorithm on a set of 23 benchmark functions, including both unimodal and multimodal problems of varying complexity and dimensions. Additionally, we apply LX-BBSCA to tackle five real-world structural engineering design problems, comparing the results with those obtained using other metaheuristics in terms of objective function values and convergence behavior. To ensure the statistical validity of our findings, we employ rigorous tests such as the t-test and the Wilcoxon rank test. The experimental outcomes consistently demonstrate that the ensemble LX-BBSCA algorithm outperforms not only the basic versions of BBO, SCA and LX-BBO but also other state-of-the-art metaheuristic algorithms.
- nature inspired algorithms,
- optimization,
- biogeography-based optimization (BBO),
- sine cosine algorithm (SCA),
- mutation operator,
- Laplacian migration operator
Citation: Vanita Garg, Kusum Deep, Khalid Abdulaziz Alnowibet, Ali Wagdy Mohamed, Mohammad Shokouhifar, Frank Werner. LX-BBSCA: Laplacian biogeography-based sine cosine algorithm for structural engineering design optimization[J]. AIMS Mathematics, 2023, 8(12): 30610-30638. doi: 10.3934/math.20231565

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Abstract

In this paper, an ensemble metaheuristic algorithm (denoted as LX-BBSCA) is introduced. It combines the strengths of Laplacian biogeography-based optimization (LX-BBO) and the sine cosine algorithm (SCA) to address structural engineering design optimization problems. Our primary objective is to mitigate the risk of getting stuck in local minima and accelerate the algorithm's convergence rate. We evaluate the proposed LX-BBSCA algorithm on a set of 23 benchmark functions, including both unimodal and multimodal problems of varying complexity and dimensions. Additionally, we apply LX-BBSCA to tackle five real-world structural engineering design problems, comparing the results with those obtained using other metaheuristics in terms of objective function values and convergence behavior. To ensure the statistical validity of our findings, we employ rigorous tests such as the t-test and the Wilcoxon rank test. The experimental outcomes consistently demonstrate that the ensemble LX-BBSCA algorithm outperforms not only the basic versions of BBO, SCA and LX-BBO but also other state-of-the-art metaheuristic algorithms.

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