SciELO - Scientific Electronic Library Online

 
vol.23 número1A new method for the analysis of signals: the square wave transform (SWT)Controlled condensation in k-NN and its application for real time color identification índice de autoresíndice de assuntospesquisa de artigos
Home Pagelista alfabética de periódicos  

Serviços Personalizados

Journal

Artigo

Indicadores

Links relacionados

  • Não possue artigos similaresSimilares em SciELO

Compartilhar


Revista de Matemática Teoría y Aplicaciones

versão impressa ISSN 1409-2433

Rev. Mat vol.23 no.1 San José Jan./Jun. 2016

 

Artículos

SC: a novel fuzzy criterion for solving engineering and constrained optimization problems

SC: un nuevo criterio difuso para resolver problemas de ingeniería y de optimización con restricciones

Sergio G. De-Los-Cobos-Silva1 

Miguel A. Gutiérrez-Andrade2 

Eric A. Rincón-García3 

Pedro Lara-Velázquez4 

Roman A. Mora-Gutiérrez5 

Antonin S. Ponsich6 

1Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería Eléctrica, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, México D.F., C.P. 09340, México. EMail: cobos@xanum.uam.mx

2Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería Eléctrica, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, México D.F., C.P. 09340, México. EMail: gamma@xanum.uam.mx

3Universidad Autónoma Metropolitana-Azcapotzalco, Departamento de Sistemas, Av. San Pablo 180, Colonia Reynosa Tamaulipas, México D.F., C.P. 02200, México. E-Mail: rigaeral@correo.azc.uam.mx

4Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería Eléctrica, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, México D.F., C.P. 09340, México. EMail:plara@xanum.uam.mx

5Universidad Autónoma Metropolitana-Azcapotzalco, Departamento de Sistemas, Av. San Pablo 180, Colonia Reynosa Tamaulipas, México D.F., C.P. 02200, México. E-Mail:mgra@correo.azc.uam.mx

6Universidad Autónoma Metropolitana-Azcapotzalco, Departamento de Sistemas, Av. San Pablo 180, Colonia Reynosa Tamaulipas, México D.F., C.P. 02200, México. E-Mail:aspo@correo@correo.azc.uam.mx

Abstract

In this paper a novel fuzzy convergence system (SC) and its fundamentals are presented. The model was implemented on a monoobjetive PSO algorithm with three phases: 1) Stabilization, 2) generation and breadthfirst search, and 3) generation and depth-first. The system SC-PSO-3P was tested with several benchmark engineering problems and with several CEC2006 problems. The computing experience and comparison with previously reported results is presented. In some cases the results reported in the literature are improved.

Keywords: particle swarm optimization (PSO); optimization

Resumen

En este trabajo se presenta un novedoso sistema de convergencia (SC), sus fundamentos y la experiencia computacional. Se implementó en un algoritmo PSO monoobjetivo de tres fases: Estabilización, generación y búsqueda en amplitud, generación y búsqueda a profundidad, el cual se probó con diversos problemas benchmark tanto de ingeniería como de la serie CEC2006. La experiencia computacional y la comparación con resultados previamente reportados se presenta. En algunos casos, se mejoran los resultados de la literatura.

Palabras clave: optimización por enjambres de partículas; optimización

Ver contenido en pdf.

Acknowledgements

The authors wish to thank the three anonymous referees since their comments helped to considerably improve the present work.

S.G. de C. would also like to thank D.Sto. and to P.V.Gpe. for their inspiration, and to Ma, Ser, Mon, Chema, and to his Flaquita for all their support

REFERENCES

Aragon, V.S.; Coello, C.A.C. (2010) "A modified version of a t-cell algorithm for constrained optimization problems", Int. J. Numer. Methods Eng84(3): 351-378. [ Links ]

Belegundu, A.D. (1982) A Study of Mathematical Programming Methods for Structural Optimization. Ph.D. Thesis, Department of Civil Environmental Engineering, University of Iowa, Iowa City. [ Links ]

Coello, C.A.C. (2000) "Use of a self-adaptive penalty approach for engineering optimization problems", Comput. Ind41(2): 113-127. [ Links ]

Deb, K.(1991) "Optimal design of a welded beam via genetic algorithms", AIAA J29(11): 2013-2015. [ Links ]

de-los-Cobos-Silva, S.G.(2015) "SC: system of convergence. Theory and fundaments", Revista de Matemática: Teoría y Aplicaciones22(2): 341- 367. [ Links ]

Dubois, D.; Prade, H. (1978) "Operations on fuzzy numbers", International Journal of Systems Science 9(6): 613-626. [ Links ]

Elsayed, S.M.; Sarker, R.A.; Essam, D.L.(2012) "On an evolutionary approach for constrained optimization problem solving", Applied Soft Computing 12(10): 3208-3227. [ Links ]

Gavana, A.(2007?) "Global optimization benchmarks and AMPGO. Test functions", in: http://infinity77.net/global_optimization/Links ]

Glover, F.(1989) "Tabu search, Part I", ORSA Journal on Computing 1(3): 190-206. [ Links ]

Glover, F.(1998) "A template for scatter search and path relink", in: J.K.Hao, E.Lutton, E.Ronald, M.Schoenauer&D.Snyers (Eds.) Artificial Evolution, Lecture Notes on Computer Science 1363, Springer, Berlin: 1- 51. [ Links ]

He, Q.; Wang, L.(2007a) "An effective co-evolutionary particle swarm optimization for constrained engineering design problems", Eng. Appl. Artif. Intell20(1): 89-99. [ Links ]

He, Q.; Wang, L.(2007b) "A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization", Appl. Math. Comput186(2): 1407-1422. [ Links ]

Hedar, A.R.(2007?) "Global optimization test problems", in: http:// www-optima.amp.i.kyoto-u.ac.jp/member/student/ hedar/Hedar_files/go.htmLinks ]

Hibbeler, R.C.(2000) Mechanics of Materials, 8th ed. Prentice Hall, NewJersey. [ Links ]

Holland, J.H. (1975) Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor MI. [ Links ]

Imran, M.; Hashima, R.; Khalid, N.E.A. (2013) "An overview of particle swarm optimization variants", Procedia Engineering 53: 491-496. [ Links ]

Kalami Heris, S.M.(s.f.) "S. Mostapha Kalami Heris' homepage", http://www.kalami.irLinks ]

Kannan, B.K.; Kramer, S.N. (1994) "An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design", J. Mech. Des116(2): 405-411. [ Links ]

Kennedy, J.; Eberhart, R.(1995) "Particle swarm optimization", in: Proc. of the IEEE International Conference on Neural Networks, vol. 4: 1942- 1948. [ Links ]

Kennedy, J.; Eberhart, R.C.; Shi, Y.(2001) Swarm Intelligence. Morgan Kaufmann, San Francisco. [ Links ]

Kirkpatrick, S.; Gelatt, C.; Vecchi, M. (1983) "Optimization by simulated annealing", Science 220: 671-680. [ Links ]

Liang, J.J.; Runarsson, T.P.; Mezura-Montes, E.; Clerc, M.; Suganthan, P.N.; Coello Coello, C.A.; Deb, K. (2006) "Problem definitions and evaluation criteria for the CEC 2006, special session on constrained realparameter optimization", Technical Report, IEEE Congress on Evolutionary Computation, 24 pp. [ Links ]

Liou, T.S.; Wang, M.J.J. (1992) "Ranking fuzzy numbers with integral value", Fuzzy Sets and Systems50(3): 247-255. [ Links ]

Liu, C.A.(2007) "New multiobjective PSO algorithm for nonlinear constrained programming problems", in: R.Wang, E. ShenE. &F.Gu(Eds.) Advances in Cognitive Neurodynamics ICCN: 955-962. [ Links ]

Liu, H.; Cai, Z.; Wang, Y.(2010) "Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization", Appl. Soft Comput10(2): 629-640. [ Links ]

Lu, H.; Chen, W.(2008) "Self-adaptive velocity particle swarm optimization for solving constrained optimization problems", J. Glob. Opt.41(3): 427-445. [ Links ]

Mazhoud, I.; Hadj-Hamou, K.; BigeonJ.; JoyeuxP.(2013) "Particle swarm optimization for solving engineering problems: a new constraint-handling mechanism", Eng. Appl. of Art. Intel26(4): 1263-1273. [ Links ]

Mezura-Montes, E.; Velázquez-Reyes, J.V.; Coello-Coello, C.A. (2006) "Modified differential evolution for constrained optimization", in: IEEE Congress on Evolutionary Computation: 25-32. [ Links ]

Mezura-Montes, E.; Miranda-Varela, M.E.; Gómez-Ramón, R.C.(2010) "Differential evolution in constrained numerical optimization: An empirical study", Inf. Sci.180(22): 4223-4262. [ Links ]

Rao, S.S.(1996) Engineering Optimization: Theory and Practice. Wiley, New York. [ Links ]

Sedighizadeh, D.; Masehian, E. (2009) "Particle swarm optimization methods, taxonomy and applications", Int. Journal of Computer Theory and Engineering 1(5): 486-502. [ Links ]

Tessema, B.; Yen, G.G. (2009) "An adaptive penalty formulation for constrained evolutionary optimization", IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans39(3): 565-578. [ Links ]

Toscano-Pulido, G.; Coello, C.A.C. (2004) "A constraint-handling mechanism for particle swarm optimization", in: IEEE Congress on Evolutionary Computation, vol. 2, IEEE Press: 1396-1403. [ Links ]

Zitzler, E.; Deb, K.; Thiele, L.(2000) "Comparison of multiobjective evolutionary algorithm: empirical results", Evolutionary Computation8(2): 173-195 [ Links ]

Wang, Y.; Cai, Z.; Zhou, Y.(2009) "Accelerating adaptive trade-off model using shrinking space technique for constrained evolutionary optimization", Int. J. Numer. Methods Eng77(11): 1501-1534. [ Links ]

Received: October 02, 2014; Revised: October 05, 2015; Accepted: October 06, 2015

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License