Modified Arithmetic Algorithm Based New Conjugate Gradient Method
DOI:
https://doi.org/10.54153/sjpas.2025.v7i2.1082Keywords:
Optimization, Arithmetic Optimization Algorithm, Conjugate Gradient Methods and Meta-Heuristic AlgorithmsAbstract
In this paper, a new hybrid algorithm is proposed, combining the Arithmetic Optimization Algorithm (AOA), which is a meta-heuristic algorithm that utilizes the distribution behaviour of basic arithmetic operations in mathematics, such as multiplication (M), division (D), subtraction (S), and addition (A), with the classical Conjugate Gradient Algorithm (CGA). The characteristics of CGA are used to enhance the primary population, which is randomly generated as the initial population for the AOA algorithm. The results of the hybrid algorithm are significantly better than those of the original algorithm. Through this hybrid approach, optimal solutions are achieved for most of the functions, with minimum values obtained for these functions. A comparison between the original and hybrid algorithms demonstrates that the hybrid algorithm outperforms the original. Six functions were used, with comparisons made at 500 and 1000 iterations.
References
1. W. I. Zangwill (1967). Non-linear programming via penalty functions. Management science, 13(5), 344-358, 1967.
2. X.-S. Yang (2010). Engineering optimization: an introduction with metaheuristic applications. John Wiley & Sons, USA.
3. T. E. Bruns & D. A. Tortorelli (2001). Topology optimization of non-linear elastic structures and compliant mechanisms, Computer methods in applied mechanics and engineering, 190(26-27), 3443-3459.
4. N.Kokash (2005). An introdaction to heuristic algorithms, Dep.Informatics Telecommun.
5. E.-G. Tallbi (2009). Metaheuristics: from design to implementation, John Wiley & Sons.
6. M. O. Okwu & L. K. Tartibu (2020). Metaheuristic Optimization: Nature-Inspired Algorithms Swarm and Computational Intelligence Theory and Applications, Springer Nature.
7. Abualigah, L., Diabat, A., Mirjalili, S., Abd Elaziz, M. & Gandomi, A.H. (2021). The arithmetic optimization algorithm. Computer methods in applied mechanics and engineering, 376, 113609.
8. M. J. D. (1976). Powell, Some convergence properties of the conjugate gradient method, Mathematical Programming, 11(1), 42-49.
9. J. Nocedal & S. J. (2006). Wright, Conjugate gradient methods, Numerical optimization. Springer.
10. B. T. Polyak (1969). The conjugate gradient method in extremal problems, USSR Computational Mathematics and Mathematical Physics, 9(4), 94-112.
11. Antoniou, A. & Lu, W., (2007). Practical Optimization, algorithms and engineering application. Springer Science& Business Media, LLC. USA.
12. Beale, E.M.L. (1988). Introduction to Optimization. Wiley-Interscience. Wiley–Blackwell. USA.
13. Laylani, Y.A., Hassan, B.A. & Khudhur, H.M. (2023). Enhanced spectral conjugate gradient methods for unconstrained optimization. Computer Science, 18(2), 163-172.
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