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Solving Systems of Nonlinear Equations Using Jaya and Jaya-Based Algorithms: A Computational Comparison

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Proceedings of International Conference on Paradigms of Communication, Computing and Data Analytics (PCCDA 2023)

Part of the book series: Algorithms for Intelligent Systems ((AIS))

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Abstract

Solving systems of nonlinear equations is a very challenging problem, particularly as the size of the systems increases, and there is no general numerical method that is both efficient and robust enough to tackle it. On the other hand, metaheuristic algorithms are a broad class of high-level techniques or heuristics for addressing hard and challenging problems. Some of these algorithms are known to produce high-quality approximate solutions for optimization problems, albeit without ensuring optimality. Jaya is a simple and parameter-less metaheuristic algorithm that was found to be effective in solving a variety of real-world problems. However, its effectiveness in solving nonlinear equation systems, perhaps the hardest class of numerical problems to solve, needs to be assessed and verified. This study examines Jaya and a few of its variants with respect to the problem of solving a set of difficult scalable nonlinear equation systems. The results showed that the so-called enhanced Jaya algorithm produced the best results overall, while the modified Jaya algorithm had the worst outcomes, thereby not being suitable for solving the important class of numerical problems considered.

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References

  1. Pérez R, Lopes V (2004) Recent applications and numerical implementation of quasi-Newton methods for solving nonlinear systems of equations. Numer Alg 35(2):261–285

    Article  MathSciNet  MATH  Google Scholar 

  2. Kelley C (2003) Solving nonlinear equations with Newton’s method. SIAM, Philadelphia, PA

    Book  MATH  Google Scholar 

  3. Karr C, Weck B, Freeman L (1998) Solutions to systems of nonlinear equations via genetic algorithms. Eng Appl Artif Intell 11(3):369–375

    Article  Google Scholar 

  4. Grau-Sánchez M (2009) Improving order and efficiency: composition with a modified Newton’s method. J Comput Appl Math 231(2):592–597

    Article  MathSciNet  MATH  Google Scholar 

  5. Choi H, Kim S, Shin BC (2022) Choice of an initial guess for Newton’s method to solve nonlinear differential equations. Comput Math Appl 117:69–73

    MathSciNet  MATH  Google Scholar 

  6. Dokeroglu T, Sevinc E, Kucukyilmaz T, Cosar A (2019) A survey on new generation metaheuristic algorithms. Comput Ind Eng 137:106040

    Article  Google Scholar 

  7. Lin MH, Tsai JF, Yu CS (2012) A review of deterministic optimization methods in engineering and management. Math Probl Eng 2012:756023

    Article  MathSciNet  MATH  Google Scholar 

  8. Sihwail R, Solaiman O, Omar K, Ariffin K, Alswaitti M, Hashim I (2021) A hybrid approach for solving systems of nonlinear equations using Harris hawks optimization and Newton’s method. IEEE Access 9:95791–95807

    Article  Google Scholar 

  9. Kumar N (2022) An alternative computational optimization technique to solve linear and nonlinear Diophantine equations using discrete WQPSO algorithm. Soft Comput 26(22):12531–12544

    Article  Google Scholar 

  10. Pan L, Zhao Y, Li L (2022) Neighborhood-based particle swarm optimization with discrete crossover for nonlinear equation systems. Swarm Evol Comput 69:101019

    Article  Google Scholar 

  11. Verma P, Parouha R (2022) Solving systems of nonlinear equations using an innovative hybrid algorithm. Iran J Sci Technol Trans Electr Eng 46(4):1005–1027

    Google Scholar 

  12. Jui J, Ahmad M (2021) A hybrid metaheuristic algorithm for identification of continuous-time Hammerstein systems. Appl Math Model 95:339–360

    Article  MathSciNet  MATH  Google Scholar 

  13. Suid M, Ahmad M (2023) A novel hybrid of nonlinear sine cosine algorithm and safe experimentation dynamics for model order reduction. Automatika 64(1):34–50

    Article  Google Scholar 

  14. Rao R (2016) Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7:19–34

    Google Scholar 

  15. Degertekin S, Lamberti L, Ugur I (2018) Sizing, layout and topology design optimization of truss structures using the Jaya algorithm. Appl Soft Comput 70:903–928

    Article  Google Scholar 

  16. Rao R (2019) Jaya: an advanced optimization algorithm and its engineering applications. Springer, Cham, Switzerland

    MATH  Google Scholar 

  17. Elattar EE, ElSayed SK (2019) Modified JAYA algorithm for optimal power flow incorporating renewable energy sources considering the cost, emission, power loss and voltage profile improvement. Energy 178:598–609

    Article  Google Scholar 

  18. Zhang Y, Chi A, Mirjalili S (2021) Enhanced Jaya algorithm: a simple but efficient optimization method for constrained engineering design problems. Knowl Based Syst 233:107555

    Article  Google Scholar 

  19. Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219(15):8121–8144

    MathSciNet  MATH  Google Scholar 

  20. Rao R, Saroj A (2017) A self-adaptive multi-population based Jaya algorithm for engineering optimization. Swarm Evol Comput 37:1–26

    Article  Google Scholar 

  21. Yu J, Kim C, Rhee SB (2019) Oppositional Jaya algorithm with distance-adaptive coefficient in solving directional over current relays coordination problem. IEEE Access 7:150729–150742

    Article  Google Scholar 

  22. Liang J, Qu B, Suganthan P, Hernández-Díaz A (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Technical Report 201212, computational intelligence laboratory. Zhengzhou University, Zhengzhou, China

    Google Scholar 

  23. Bodon E, Del Popolo A, Lukšan L, Spedicato E (2001) Numerical performance of ABS codes for systems of nonlinear equations. Technical Report DMSIA 01/2001, Universitá degli Studi di Bergamo, Bergamo, Italy

    Google Scholar 

  24. Friedlander A, Gomes-Ruggiero M, Kozakevich D, Martínez J, Santos S (1997) Solving nonlinear systems of equations by means of quasi-Newton methods with a nonmonotone strategy. Optim Methods Softw 8(1):25–51

    Article  MathSciNet  MATH  Google Scholar 

  25. van Hentenryck P, McAllester D, Kapur D (1997) Solving polynomial systems using a branch and prune approach. SIAM J Numer Anal 34(2):797–827

    Article  MathSciNet  MATH  Google Scholar 

  26. Kelley C, Qi L, Tong X, Yin H (2011) Finding a stable solution of a system of nonlinear equations. J Ind Manag Optim 7(2):497–521

    Article  MathSciNet  MATH  Google Scholar 

  27. Moré J, Garbow B, Hillstrom K (1981) Testing unconstrained optimization software. ACM Trans Math Softw 7(1):17–41

    Article  MathSciNet  MATH  Google Scholar 

  28. Yamamura K, Kawata H, Tokue A (1998) Interval solution of nonlinear equations using linear programming. BIT Numer Math 38(1):186–199

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate Program in Informatics Engineering, University of Madeira, Funchal, Madeira Is., Portugal

    Sérgio Ribeiro

  2. Doctoral Program in Informatics Engineering, University of Madeira, Funchal, Portugal

    Bruno Silva

  3. Regional Secretariat for Education, Science and Technology, Regional Government of Madeira, Funchal, Portugal

    Bruno Silva

  4. Faculty of Exact Sciences and Engineering, University of Madeira, 9020–105, Funchal, Madeira Is., Portugal

    Luiz Guerreiro Lopes

Authors
  1. Sérgio Ribeiro
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  2. Bruno Silva
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  3. Luiz Guerreiro Lopes
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Corresponding author

Correspondence to Luiz Guerreiro Lopes .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Dr. B. R. Ambedkar National Institute Technology, Jalandhar, India

    Anupam Yadav

  2. Department of Electronics and Communication Engineering, Malaviya National Institute of Technology Jaipur, Jaipur, India

    Satyasai Jagannath Nanda

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Meng-Hiot Lim

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© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Ribeiro, S., Silva, B., Lopes, L.G. (2023). Solving Systems of Nonlinear Equations Using Jaya and Jaya-Based Algorithms: A Computational Comparison. In: Yadav, A., Nanda, S.J., Lim, MH. (eds) Proceedings of International Conference on Paradigms of Communication, Computing and Data Analytics. PCCDA 2023. Algorithms for Intelligent Systems. Springer, Singapore. https://doi.org/10.1007/978-981-99-4626-6_10

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