Skip to main content
SpringerLink
Log in

Enhancing Sine–Cosine mutation strategy with Lorentz distribution for solving engineering design problems

  • ORIGINAL ARTICLE
  • Published:
International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

To solve global optimization, this paper proposes an improved sine–cosine algorithm to address the limitation of the basic sine cosine algorithm problems such as low solution precision and sluggish convergent speed. To overcome this weakness and to increase its search capabilities, two strategies were involved. Firstly, exponential decreasing conversion parameter which is used to balance the global exploration and local search ability of the algorithm. Secondly the Lorentz search strategy to generate new candidate individual and the capacity to avoid early convergence to effectively explore the search space. Sine Cosine Algorithm is developed to solve difficult problems, implying it has a higher accuracy and convergence rate based on the position updating equations incorporation of the objective function component and the trigonometric function term. Sometimes the search path does not search towards the global best and the result obtained is only a local optimum when solving multi-parameter optimization and highly ill-conditioned problems. Therefore, in the present study new method called Lorentz-SCA is introduced, which tries to alleviate all these problems. The suggested proposed algorithm has been put to the test against a standard set of 23 well-known benchmark functions and 12 highly non -linear engineering design problems to test the effectiveness of the design algorithm. The experimental results show that the proposed algorithm can effectively avoid falling into the local optimum, and it has faster convergence speed and higher optimization accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data availability

Authors can confirm that all relevant data are included in the article.

References

  • Arora S, Singh S (2018) Butterfly Optimization algorithm: a novel approach for global optimization. Soft Comput 23:715–734

    Article  Google Scholar 

  • Banerjee M & Garg V,(2022a) Solving Structural and Reliability Optimization problem by investing efficient mutation strategies embedded in Sine-Cosine Algorithm, Integ J Syst Assure Eng Manage.

  • Banerjee M, GargV, (2022b) A state-of-the-art of stock market prediction using neural network in recent years proceedings of the international conference on computational intelligence and sustainable technologies. Algor Intell Syst 148:385–394

    Google Scholar 

  • Eiben AE, Schippers CA (1998) On evolutionary exploration and exploitation. Fundam Inform 35:35–50

    Article  Google Scholar 

  • Elaziz MA (2017) Oliva D & Xiong S. An improved opposition-based sine cosine algorithm for global optimization, Expert Syst Appl

    Google Scholar 

  • Fan Y, Wang P, Heidari AA, Wang M, Zhao X, Chen H, Li C (2020) Rationalized fruit fly optimization with sine cosine algorithm: a comprehensive analysis. Expert Syst Appl 157:113486

    Article  Google Scholar 

  • Fleury C, Braibant V (1986) Structural optimization: a new dual method using mixed variables. Int J Num Method Eng 23:409–428

    Article  MathSciNet  Google Scholar 

  • Gandomi AH, Yang X-S, Alavi AH (2011) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35

    Article  Google Scholar 

  • Gandomi AH, Yang XS, Alavi AH, & Talatahari S, (2013) Metaheuristic algorithm in modelling and optimization, Metaheuristic Appl Struct Infrastruct, 1–24.

  • Garg V, Deep K (2015) A state-of-the-art review of biogeography-based optimization. Adv Vol- 336:533–549

    Google Scholar 

  • Garg V, Deep K (2016) Performance of Laplacian biogeography-based optimization algorithm on CEC 2014 continuous optimization benchmarks and camera calibration problem. Swarm Evolution Comput 27:132–144

    Article  Google Scholar 

  • Garg V, Deep K (2016a) Efficient mutation strategies embedded in Laplacian-biogeography-based optimization algorithm for unconstrained function minimization. Int J Appl Swarm Intell 7:12–44

    Google Scholar 

  • Garg V, Deep K (2019) Portfolio optimization using Laplacian biogeography-based optimization. Springer 56:1117–1141

    MathSciNet  Google Scholar 

  • Garg V, Deep K (2022) Constrained Laplacian biogeography based optimization for economic load dispatch problems. Process Integrat Opt Sustain 6:483–496

    Article  Google Scholar 

  • Gold S, & Krishnamurty S, (1997) Trade-offs in Robust Engineering Design, Proceedings of the 1997 ASME Design Engineering Technical Conference, California, 80449: V002T29A035

  • Guo JJ, Chen Y & Lai G, et.al (2021) Neural networks-based adaptive control of uncertain nonlinear systems with unknown input constraints, J Ambient Int Human Comput

  • Gupta S, Deep K (2019) A hybrid self-adaptive sine cosine algorithm with opposition- based learning. Expert Syst Appl 119:210–230

    Article  Google Scholar 

  • Gupta V, Mittal M (2018) ECG Signals Interpretation using Chaos Theory. J Adv Res Dyna & Cont Syst 9:2392–2397

    Google Scholar 

  • Gupta V, Mittal M (2019) QRS complex detection using STFT chaos analysis, and PCA in standard and real-time ECG database. J Instit Eng India (series b) 100:489–497

    Article  Google Scholar 

  • Gupta V, Mittal M, Mittal V (2019) R-peak detection using chaos analysis in standard and real time ECG databases. IRBM 40:341–354

    Article  Google Scholar 

  • Gupta V, Mittal M, Mittal V (2020) Chaos theory: an emerging tool for Arrhythmia detection. Sens Imag. 21:1–22

    Google Scholar 

  • Gupta V, Mittal M, Mittal V (2021b) Chaos theory and ARTFA: emerging tools for interpreting ECG Signals to diagnose cardiac arrhythmis. Wireless Personal Commun 118:3615–3646

    Article  Google Scholar 

  • Gupta V, Chaturvedi Y, & Kumar P ,et.al (2021a) Attractor Plot as an Emerging Tool in ECG Signal Processing foe Improved Health Informatics, 920: 359–367.

  • Hafez AI, Zawbaa MH, Emary E (2016) & Hassanien AE. A sine cosine algorithm for feature selection, IEEE

    Google Scholar 

  • Issa M, Hassanien AE, Oliva D (2018) ASCA-PSO: Adaptive sine cosine optimization algorithm integrated with particle swarm for pairwise local sequence alignment. Expert Syst Appl 99:56–70

    Article  Google Scholar 

  • Jiang B (2013) Head\Tail Breaks: a new classification scheme for data with a heavy-tailed distribution. Prof Geograp 65:482–494

    Article  Google Scholar 

  • Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) Algorithm. J Global Opt 39:459–464

    Article  MathSciNet  Google Scholar 

  • Kaveh A, Bakshpoori T (2016) A new metaheuristic for continuous structural optimization: water exploration optimization structural multidiscipline optrimization. Struct Multidisciplin Opt 54:23–43

    Article  Google Scholar 

  • Li N, Wang L (2020) Bare-bones based sine cosine algorithm for global optimization. J Comput Sci 47:1–27

    Article  MathSciNet  Google Scholar 

  • Li JP, Balazs ME, Parks GT (2007a) Engineering design optimization using species-conserving genetic algorithms. Eng Opt 39:147–161

    Article  Google Scholar 

  • Li J-P, Balazs ME, Parks GT (2007b) Engineering design optimization using species-conserving genetic algorithms. Eng Opt 39:147–216

    Article  Google Scholar 

  • Majid KI (1974) Optimum design of structures. Newnes-Butter worths, London

    Google Scholar 

  • Mirajalili S (2016) A sine cosine algorithm for solving optimization problems. Knowl Based Syst 96:120–133

    Article  Google Scholar 

  • Mirjalili S, Lewis A (2016) The whale optimization algorithm. Advances Eng Softw 95:51–67

    Article  Google Scholar 

  • Nenavath H, Kumar Jatoth RK, Das S (2018) A synergy of the sine-cosine algorithm and particle swarm optimizer for improved global optimization and object tracking. Swarm Evolution Comput 43:1–30

    Article  Google Scholar 

  • Nowacki H, (1973) Optimization in pre-contract ship design, Comput Appl Automat Shipyard Operat Ship Design

  • Peng ZW, Yu WX, Wang JN et al (2020) Dynamic analysis of seven -dimensional fractional-order chaotic system and its applications in encrypted communication. J Ambient Int Human Comput 11:5399–5417

    Article  Google Scholar 

  • Pham DT, Karaboga D (2000) Intelligent optimisation techniques. Springer Sci Business Media 34:330–331

    Google Scholar 

  • Rao SS (1996) Engineering optimization: theory and practice, 3rd edn. John Wiley & Sons, Chichester

    Google Scholar 

  • Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Opt 33:735–748

    Article  Google Scholar 

  • Rigatos G, Siano P, Zervos N, (2012) An approach to fault diagnosis of nonlinear system networks with invariance to Fourier transform, 4: 621 639

  • Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. J Mech Design 112:223–229

    Article  Google Scholar 

  • Sindhu R, Ngadiran R, Yacob YM (2017) Sine–cosine algorithm for feature selection with elitism strategy and new updating mechanism. Neural Comput Appl 28:2947–2958

    Article  Google Scholar 

  • Yong LIU, Liang MA (2017) Sine cosine algorithm with nonlinear decreasing conversion parameter. Comput Eng Appl 53:1–5

    Google Scholar 

Download references

Funding

There was no funding obtained for this study.

Author information

Authors and Affiliations

  1. Galgotias University, Greater Noida, Uttar Pradesh, 203201, India

    Mousumi Banerjee & Vanita Garg

  2. Indian Institute of Technology, Roorkee, Roorkee, Uttarakhand, 247667, India

    Kusum Deep

  3. School of Engineering and Technology, Sunway University, Petaling Jaya, Selangor Darul Ehsan, Malaysia

    Muhammed Basheer Jasser

  4. Department of Electrical Engineering, Aswan University, Aswan, Egypt

    Salah Kamel

  5. Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Cairo, Egypt

    Ali Wagdy Mohamed

  6. Egypt Applied Science Research Center, Applied Science Private University, Amman, Jordan

    Ali Wagdy Mohamed

Authors
  1. Mousumi Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vanita Garg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kusum Deep
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammed Basheer Jasser
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Salah Kamel
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ali Wagdy Mohamed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vanita Garg.

Ethics declarations

Conflict of interest

All the authors have no conflict of interest.

Consent to participate

NA.

Consent for publication

All the authors agreed for publication.

Ethics approval

NA.

Informed Consent

Informed Consent is obtained from all the authors.

Research involving human participate and/or animal

NA

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Banerjee, M., Garg, V., Deep, K. et al. Enhancing Sine–Cosine mutation strategy with Lorentz distribution for solving engineering design problems. Int J Syst Assur Eng Manag 15, 1536–1567 (2024). https://doi.org/10.1007/s13198-023-02008-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13198-023-02008-w

Keywords

Search

Navigation