Abstract
The main goal of this paper is to study the performance of two metaheuristics, that are classified as belonging to Swarm Intelligence, when dealing with complex optimization problems. In this case, the Algorithms are the Grey Wolf Optimizer (GWO) algorithm and Firefly Algorithm (FA). In this case study, we are presenting in this paper the Mathematical Benchmark Functions that were given in the IEEE Congress on Evolutionary Computation 2015 (CEC’ 15) competition, in order to compare these popular algorithms.
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References
H.R. Maier, Z. Kapelan, Evolutionary algorithms and other metaheuritics in water resources: Current status, research challenges and future directions. Environ. Model Softw. 62, 271–299 (2014)
U. Can, B. Alatas, Physics based Metaheuristic algorithms for global optimization. Am. J. Inf. Sci. Comput. Eng. 1, 94–106 (2015)
X. Yang, M. Karamanoglu, Swarm Intelligence and Bio-Inspired Computation: An Overview, Swarm Intelligence and Bio-Inspired Computation, pp. 3–23. Elsevier (2013)
D.H. Wolpert, W.G. Macready, No free lunch theorems for optimization. Evolut. Comput. IEEE Trans. 1, 67–82 (1997)
S. Mirjalili, M. Mirjalili, A. Lewis, Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)
C. Muro, R. Escobedo, L. Spector, R. Coppinger, Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations. Behav. Process. 88, 192–197 (2011)
L. Rodriguez, O. Castillo, J. Soria, P. Melin, F. Valdez, C. Gonzalez, G. Martinez, J. Soto, A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl. Soft Comput. 57, 315–328 (2017)
X.S. Yang, Firefly Algorithm, Lévy Flights and Global Optimization (2010). arXiv:1003.1464v1
X.S. Yang, Firefly Algorithm: Recent Advances and Applications (2013). arXiv:1308.3898v1
J. Digalakis, K. Margaritis, On benchmarking functions for genetic algorithms. Int. J. Comput. Math. 77, 481–506 (2001)
M. Molga, C. Smutnicki, Test Functions for Optimization Needs (2005)
X.S. Yang, Test Problems in Optimization (2010). arXiv:1008.0549
W. Guohua, R. Mallipeddi, P.N. Suganthan, Problem Definitions and Evaluation Criteria for the CEC 2017 Competition on Constrained Real-Parameter Optimization (2017)
L. Rodriguez, O. Castillo, M. Garcia, J. Soria, F. Valdez, P. Melin, Dynamic Simultaneous Adaptation of Parameters in the Grey Wolf Optimizer Using Fuzzy Logic, FUZZ-IEEE. Naples Italy (2017)
M. Lagunes, O. Castillo, J. Soria, Optimization of Membership Functions Parameters for Fuzzy Controller of an Autonomous Mobile Robot Using the Firefly Algorithm, Fuzzy Logic Augmentation of Neural and Optimization Algorithms, pp. 199–206 (2018)
R. Larson, B. Farber, Elementary Statistics Picturing the World, pp. 428–433. Pearson Education Inc. (2003)
B. Gonzalez, P. Melin, F. Valdez, G. Prado-Arechiga, Ensemble Neural Network Optimization Using a Gravitational Search Algorithm with Interval Type-1 and Type-2 Fuzzy Parameter Adaptation in Pattern Recognition Applications, Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications, pp. 17–27. Springer (2018)
E. Bernal, O. Castillo, J. Soria, Imperialist Competitive Algorithm with Dynamic Parameter Adaptation Applied to the Optimization of Mathematical Functions, Nature-Inspired Design of Hybrid Intelligent Systems, pp. 329–341 Springer (2017)
J. Barraza, P. Melin, F. Valdez, C.I. Gonzalez, Fuzzy fireworks algorithm based on a sparks dispersion measure. Algorithms 10 (2017)
J. Barraza, P. Melin, F. Valdez, C. Gonzalez, Fuzzy FWA with Dynamic Adaptation of Parameters, pp. 4053–4060. IEEE CEC 2016, Vancouver, Canada (2016)
L. Rodríguez, O. Castillo, M. García, J. Soria, A Comparative Study of Dynamic Adaptation of Parameters in the GWO Algorithm Using Type-1 and Interval Type-2 Fuzzy Logic, Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications, pp. 3–16. Springer (2018)
C. Caraveo, A. Fevrier, O. Castillo, optimization mathematical functions for multiple variables using the algorithm of self-defense of the plants. Nature-Inspired Design of Hybrid Intelligent Systems, pp. 631–640. Springer (2017)
M. Guerrero, O. Castillo, M. Garcia, Cuckoo search algorithm via Lévy flight with dynamic adaptation of parameter using fuzzy logic for benchmark mathematical functions. Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Studies in Computational Intelligence, pp. 555–571. Springer (2016)
C. Leal Ramírez, O. Castillo, P. Melin, A. Rodríguez Díaz, Simulation of the bird age-structured population growth based on an interval type-2 fuzzy cellular structure. Inf. Sci. 181(3), 519–535 (2011)
N.R. Cázarez-Castro, L.T. Aguilar, O. Castillo, Designing type-1 and type-2 fuzzy logic controllers via fuzzy lyapunov synthesis for nonsmooth mechanical systems. Eng. Appl. of AI 25(5), 971–979 (2012)
E. Rubio, O. Castillo, F. Valdez, P. Melin, C. I. González, G. Martinez: an extension of the fuzzy possibilistic clustering algorithm using type-2 fuzzy logic techniques. Adv. Fuzzy Syst. 7094046:1–7094046:23 (2017)
O. Castillo, P. Melin, Intelligent systems with interval type-2 fuzzy logic. Int. J. Innov. Comput. Inf. Control 4(4), 771–783 (2008)
G.M. Mendez, O. Castillo, in The 14th IEEE International Conference on Type-2 TSK fuzzy logic systems using hybrid learning algorithm, Fuzzy Systems, FUZZ’05, pp. 230–235 (2005). https://scholar.google.com.mx/citations?view_op=view_citation&hl=en&user=1C8gb8IAAAAJ&cstart=40&citation_for_view=1C8gb8IAAAAJ:qxL8FJ1GzNcCInterval
P. Melin, C.I. González, J.R. Castro, O. Mendoza, O. Castillo, Edge-detection method for image processing based on generalized type-2 fuzzy logic. IEEE Trans. Fuzzy Syst. 22(6), 1515–1525 (2014)
C.I. González, P. Melin, J.R. Castro, Oscar Castillo, Olivia Mendoza: Optimization of interval type-2 fuzzy systems for image edge detection. Appl. Soft Comput. 47, 631–643 (2016)
C.I. González, P. Melin, J.R. Castro, Olivia Mendoza, Oscar Castillo: An improved Sobel edge detection method based on generalized type-2 fuzzy logic. Soft. Comput. 20(2), 773–784 (2016)
E. Ontiveros, P. Melin, O. Castillo, High order α-planes integration: a new approach to computational cost reduction of general type-2 fuzzy systems. Eng. Appl. of AI 74, 186–197 (2018)
P. Melin, O. Castillo, Intelligent control of complex electrochemical systems with a neuro-fuzzy-genetic approach. IEEE Trans. Ind. Electron. 48(5), 951–955
L. Aguilar, P. Melin, O. Castillo, Intelligent control of a stepping motor drive using a hybrid neuro-fuzzy ANFIS approach. Appl. Soft Comput. 3(3), 209–219 (2003)
P. Melin, O. Castillo, Adaptive intelligent control of aircraft systems with a hybrid approach combining neural networks, fuzzy logic and fractal theory. Appl. Soft Comput. 3(4), 353–362 (2003)
P. Melin, J. Amezcua, F. Valdez, O. Castillo, A new neural network model based on the LVQ algorithm for multi-class classification of arrhythmias. Inf. Sci. 279, 483–497 (2014)
P. Melin, O. Castillo, Modelling, simulation and control of non-linear dynamical systems: an intelligent approach using soft computing and fractal theory (CRC Press, USA and Canada, 2002)
P. Melin, D. Sánchez, O. Castillo, Genetic optimization of modular neural networks with fuzzy response integration for human recognition. Inf. Sci. 197, 1–19 (2012)
M.A. Sanchez, O. Castillo, J.R. Castro, P. Melin, Fuzzy granular gravitational clustering algorithm for multivariate data. Inf. Sci. 279, 498–511 (2014)
D. Sanchez, P. Melin, Optimization of modular granular neural networks using hierarchical genetic algorithms for human recognition using the ear biometric measure. Eng. Appl. Artif. Intell. 27, 41–56 (2014)
O. Castillo, Type-2 Fuzzy Logic in Intelligent Control Applications. Springer (2012)
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Rodríguez, L., Castillo, O., García, M., Soria, J. (2021). A Comparative Study of the Grey Wolf Optimizer and Firefly Algorithm in Mathematical Benchmark Functions of the CEC 15 Competition. In: Melin, P., Castillo, O., Kacprzyk, J. (eds) Recent Advances of Hybrid Intelligent Systems Based on Soft Computing. Studies in Computational Intelligence, vol 915. Springer, Cham. https://doi.org/10.1007/978-3-030-58728-4_9
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