Março 2021 vol. 7 num. 1 - XI Encontro Científico de Física Aplicada

Artigo completo - Open Access.

Idioma principal | Segundo idioma

A comparative study of gradient-based and meta-heuristic optimization methods using Griewank benchmark function

A comparative study of gradient-based and meta-heuristic optimization methods using Griewank benchmark function

Dalla, C. E. R; da Silva, W. B.; Dutra, J. C. S.; Colaço, J. M.; , ;

Artigo completo:

Optimization methods are frequently applied to solve real-world problems such, engineering design, computer science, and computational chemistry. This paper aims to compare gradient-based algorithms and the meta-heuristic particle swarm optimization to minimize the multidimensional benchmark Griewank function, a multimodal function with widespread local minima. Several approaches of gradient-based methods such as steepest descent, conjugate gradient with Fletcher-Reeves and Polak- Ribiere formulations, and quasi-Newton Davidon-Fletcher-Powell approach were compared. The results presented showed that the meta-heuristic method is recommended for function with this behavior because is no needed prior information of the search space. The performance comparison includes computation time and convergence of global and local optimum.

Artigo completo:

Optimization methods are frequently applied to solve real-world problems such, engineering design, computer science, and computational chemistry. This paper aims to compare gradient-based algorithms and the meta-heuristic particle swarm optimization to minimize the multidimensional benchmark Griewank function, a multimodal function with widespread local minima. Several approaches of gradient-based methods such as steepest descent, conjugate gradient with Fletcher-Reeves and Polak- Ribiere formulations, and quasi-Newton Davidon-Fletcher-Powell approach were compared. The results presented showed that the meta-heuristic method is recommended for function with this behavior because is no needed prior information of the search space. The performance comparison includes computation time and convergence of global and local optimum.

Palavras-chave: ,

Palavras-chave: ,

DOI: 10.5151/xiecfa-Dalla

Referências bibliográficas
  • [1] Antoniou Andreas and Lu Wu-Sheng. Applications
  • [2] of Unconstrained Optimization, pages 231–
  • [3] 26 Springer US, Boston, MA, 2007.
  • [4] [2] M. Locatelli. Journal of Global Optimization,
  • [5] 25(2):169–174, 2003.
  • [6] [3] Yan Huang, Jian ping Li, and Peng Wang. Unusual
  • [7] phenomenon of optimizing the griewank
  • [8] function with the increase of dimension. Frontiers
  • [9] of Information Technology & Electronic Engineering,
  • [10] 20(10):1344–1360, October 2019.
  • [11] [4] Jasbir S. Arora. Numerical methods for unconstrained
  • [12] optimum design. In Introduction to Optimum
  • [13] Design, pages 411–441. Elsevier, 2012.
  • [14] [5] Xin-She Yang. Optimization algorithms. In Introduction
  • [15] to Algorithms for Data Mining and Machine
  • [16] Learning, pages 45–65. Elsevier, 2019.
  • [17] [6] M.R. Hestenes and E. Stiefel. Methods of conjugate
  • [18] gradients for solving linear systems. Journal
  • [19] of Research of the National Bureau of Standards,
  • [20] 49(6):409, December 1952.
  • [21] [7] Lukas Exl, Johann Fischbacher, Alexander Kovacs,
  • [22] Harald Oezelt, Markus Gusenbauer, and
  • [23] Thomas Schrefl. Preconditioned nonlinear conjugate
  • [24] gradient method for micromagnetic energy
  • [25] minimization. Computer Physics Communications,
  • [26] 235:179–186, February 2019.
  • [27] [8] R. Fletcher. Function minimization by conjugate
  • [28] gradients. The Computer Journal, 7(2):149–154,
  • [29] February 1964.
  • [30] [9] E. Polak and G. Ribiere. Note sur la convergence
  • [31] de méthodes de directions conjuguées. Revue
  • [32] française d'informatique et de recherche opérationnelle.
  • [33] Série rouge, 3(16):35–43, 1969.
  • [34] [10] R. E. Ricketts. Practical optimization. International
  • [35] Journal for Numerical Methods in Engineering,
  • [36] 18(6):954–954, June 1982.
  • [37] [11] Saptarshi Sengupta, Sanchita Basak, and Richard
  • [38] Peters. Particle swarm optimization: A survey
  • [39] of historical and recent developments with
  • [40] hybridization perspectives. Machine Learning
  • [41] and Knowledge Extraction, 1(1):157–191, October
  • [42] 2018.
  • [43] 5
Como citar:

Dalla, C. E. R; da Silva, W. B.; Dutra, J. C. S.; Colaço, J. M.; , ; "A comparative study of gradient-based and meta-heuristic optimization methods using Griewank benchmark function", p. 156-160 . In: Anais do XI Encontro Científico de Física Aplicada. São Paulo: Blucher, 2021.
ISSN 2358-2359, DOI 10.5151/xiecfa-Dalla

últimos 30 dias | último ano | desde a publicação


downloads


visualizações


indexações