CULTURAL ALGORITHM PARAMETER CONTROL USING LÉVY FLIGHT

Constantin URSACHE, Florina ȘERDEAN, Lucian TUDOSE

Abstract


This paper presents a comparative study between a traditional evolutionary algorithm with the values of the parameters set before the algorithm runs and that remain fixed during runtime, and a cultural algorithm using parameter control powered by Lévy flight to dynamically update the values of the parameters during runtime. The two algorithms are benchmarked on a subset of test problems, using an open-source platform for comparing continuous optimizers in a black box setting. The results obtained are examined in order to demonstrate the improved performance of the cultural algorithm using parameter control, its superiority becoming more evident as the dimensions of the test problems increase.

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References


N. Dey, Ed., Applied Genetic Algorithm and Its Variants: Case Studies and New Developments, 1st ed. 2023 edition. Springer, 2023.

A. Kaveh, Advances in Metaheuristic Algorithms for Optimal Design of Structures, 3rd ed. 2021 edition. Springer, 2021.

C. Balaji, Thermal System Design and Optimization, 2nd ed. 2021 edition. Cham: Springer, 2021.

A. R. Parkinson, R. J. Balling, and J. D. Hedengren, Optimization Methods for Engineering Design. Applications and Theory. Brigham Young University, 2013.

O. Buiga and S. Haragâș, “A 2 stage coaxial helical speed reducer gearings optimal design with Genetic Algorithms,” Acta Technica Napocensis - Series: Applied Mathematics and Mechanics, and Engineering, vol. 55, no. 3, Sep. 2012, [Online]. Available: https://atna-mam.utcluj.ro/index.php/Acta/article/view/240

O. Buiga and S. Haragâș, “Optimal design with Evolutionary Algorithms of a gear coupling,” Acta Technica Napocensis - Series: Applied Mathematics and Mechanics, and Engineering, vol. 54, no. 2, Apr. 2011, [Online]. Available: https://atna-mam.utcluj.ro/index.php/Acta/article/view/309

T. Bäck, D. B. Fogel, and Z. Michalewicz, Eds., Handbook of Evolutionary Computation. Oxford University Press, 1997.

A. E. Eiben, Z. Michalewicz, M. Schoenauer, and J. E. Smith, “Parameter Control in Evolutionary Algorithms,” in Parameter Setting in Evolutionary Algorithms, F. G. Lobo, C. F. Lima, and Z. Michalewicz, Eds., in Studies in Computational Intelligence. Berlin, Heidelberg: Springer, 2007, pp. 19–46. doi: 10.1007/978-3-540-69432-8_2.

C. Huang, Y. Li, and X. Yao, “A Survey of Automatic Parameter Tuning Methods for Metaheuristics,” IEEE Transactions on Evolutionary Computation, vol. 24, no. 2, pp. 201–216, Apr. 2020, doi: 10.1109/TEVC.2019.2921598.

A. L. Tuson, “Adapting operator probabilities in genetic algorithms,” Master’s thesis, Department of Artificial Intelligence, University of Edinburgh, 1995.

A. Petrowski and S. Ben-Hamida, Evolutionary Algorithms. John Wiley & Sons, 2017.

A. Slowik and H. Kwasnicka, “Evolutionary algorithms and their applications to engineering problems,” Neural Comput & Applic, vol. 32, no. 16, pp. 12363–12379, Aug. 2020, doi: 10.1007/s00521-020-04832-8.

G. M. Viswanathan et al., “Lévy flights in random searches,” Physica A: Statistical Mechanics and its Applications, vol. 282, no. 1, pp. 1–12, Jul. 2000, doi: 10.1016/S0378-4371(00)00071-6.

A. M. Reynolds and C. J. Rhodes, “The Lévy flight paradigm: random search patterns and mechanisms,” Ecology, vol. 90, no. 4, pp. 877–887, 2009, doi: 10.1890/08-0153.1.

C.-Y. Lee and X. Yao, “Evolutionary programming using mutations based on the Lévy probability distribution,” IEEE Transactions on Evolutionary Computation, vol. 8, no. 1, pp. 1–13, Feb. 2004, doi: 10.1109/TEVC.2003.816583.

F. Rusu, “Optimizations under uncertainty with applications in rolling bearing industry,” PhD Thesis, 2014.

R. G. Reynolds, “An introduction to cultural algorithms,” in Proceedings of the 3rd annual conference on evolutionary programming, World Scientific Publishing, World Scientific, 1994, pp. 131–139.

R. G. Reynolds, “Cultural algorithms: Theory and applications,” in New ideas in optimization, 1999, pp. 367–378.

R. G. Reynolds, “Cultural Algorithm Framework,” in Culture on the Edge of Chaos: Cultural Algorithms and the Foundations of Social Intelligence, R. G. Reynolds, Ed., in SpringerBriefs in Computer Science. Cham: Springer International Publishing, 2018, pp. 13–25. doi: 10.1007/978-3-319-74171-0_2.

A. Maheri, S. Jalili, Y. Hosseinzadeh, R. Khani, and M. Miryahyavi, “A comprehensive survey on cultural algorithms,” Swarm and Evolutionary Computation, vol. 62, p. 100846, Apr. 2021, doi: 10.1016/j.swevo.2021.100846.

N. Hansen et al., “COmparing Continuous Optimizers: numbbo/COCO on Github.” Zenodo, Mar. 15, 2019. doi: 10.5281/zenodo.2594848.

N. Hansen, A. Auger, D. Brockhoff, and T. Tušar, “Anytime Performance Assessment in Blackbox Optimization Benchmarking,” IEEE Transactions on Evolutionary Computation, vol. 26, no. 6, pp. 1293–1305, Dec. 2022, doi: 10.1109/TEVC.2022.3210897.

N. Hansen, A. Auger, R. Ros, O. Mersmann, T. Tušar, and D. Brockhoff, “COCO: a platform for comparing continuous optimizers in a black-box setting,” Optimization Methods and Software, vol. 36, no. 1, pp. 114–144, Jan. 2021, doi: 10.1080/10556788.2020.1808977.

N. Hansen, A. Auger, D. Brockhoff, D. Tušar, and T. Tušar, “COCO: Performance Assessment.” arXiv, May 11, 2016. doi: 10.48550/arXiv.1605.03560.

N. Hansen, S. Finck, R. Ros, and A. Auger, “Real-Parameter Black-Box Optimization Benchmarking 2009: Noisy Functions Definitions,” Jan. 2009.


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