Comparative study between the generalized reduced gradient and genetic algorithm in multiple response optimization
DOI:
https://doi.org/10.14488/1676-1901.v17i2.2566Keywords:
Optimization. Multiple Response. Genetic Algorithm. GRG.Abstract
In this paper we present a comparative study between the Generalized Reduced Gradient (GRG) and Genetic Algorithm (GA) methods to optimize multiple-response processes. Results from experiment design were used to compose the objective function to be minimized. The case studies in this work were selected from literature. A Microsoft Excel spreadsheet was used for parameters optimization using GRG, and the Scilab software was used to GA. Ten replicates were performed and the mean of the results was obtained. To assess the methods was used performance measures based on the mean percentage error. From the performance measures used, the AG showed better results compared to the GRG, indicating that the AG can generate better responses than GRG.
Downloads
References
ABADIE, J.; CARPENTIER, J. Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints. In: Optimization, ed. R. Fletcher, Londres: Academic Press, 1969.
AVILA, S. L., Otimização multiobjetivo e análise de sensibilidade para concepção de dispositivos. 2006. 148 f. Tese (Doutorado em Engenharia Elétrica) - Universidade Federal de Santa Catarina. Florianópolis, 2006.
BAZGAN, C.; JAMAIN, F.; VANDERPOOTEN, D. Approximate Pareto sets of minimal size for multi-objective optimization problems. Operations Research Letters, v. 43, n. 1, p. 1-6, 2015. http://dx.doi.org/10.1016/j.orl.2014.10.003
CASTILLO, E.; MONTGOMERY, D.; McCARVILLE, D. Modified desirability functions for multiple response optimization. Journal of Quality Technology, v. 28, p. 337-345, 1996.
CHENG, C. B.; CHENG, C. J.; LEE, E. S. Neuro-fuzzy and genetic algorithm in multiple response optimization, Computer and Mathematics with Applications, v. 44, n. 12, p. 1503-1514, 2002. http://dx.doi.org/10.1016/S0898-1221(02)00274-2
DERRINGER, G.; SUICH, R. Simultaneous optimization of several response variables. Journal of Quality Technology, v. 12, n. 4, p. 214-219, 1980.
DEHURI, S.; CHO, S.B. Multi-criterion Pareto based particle swarm optimized polynomial neural network for classification: A review and state-of-the-art. Computer Science Review, v.3, p. 19-40, 2009. http://dx.doi.org/10.1016/j.cosrev.2008.11.002
DÍAS-GARCÍA, J.A.; BASHIRI, M. Multiple response optimization: An approach from multiobjective stochastic programming. Applied Mathematical Modelling, v. 38, n. 7-8, p. 2015–2027, 2014. http://dx.doi.org/10.1016/j.apm.2013.10.010
FAGHIHI, V.; REINSCHMIDT, K.F.; KANG, J.H., Construction scheduling using genetic algorithm based on building information model, Expert Systems with Applications, v. 41, n. 16, p. 7565-7578, 2014.
http://dx.doi.org/10.1016/j.eswa.2014.05.047
FOGEL, L. J.; OWENS, A. J.; WALSH, M. J. Artificial intelligence through simulated evolution. New York: John Wiley, 1966.
GOLDBERG, D. E. Genetic algorithms, In Search: optimization and machine learning. Berkeley: Addison-Wesley, 1989.
GOMES, F.M. ; PEREIRA, F.M. ; SILVA, M.B. ; MARINS, F.A S. . Aplicação da Meta-heuristica Algoritmo Genético na Otimização de Problemas com Múltiplas Respostas. In: Encontro Nacional de Engenharia de Produção ENEGEP, 2015, Fortaleza. Anais do Encontro Nacional de Engenharia de Produção ENEGEP e ICIEOM, 2015.
HARIDY, S., GOUDA, S. A., WU, Z. An integrated framework of statistical process control and design of experiments for optimizing wire electrochemical turning process. International Journal of Advanced Manufacturing Technology, v.53, p. 191-207, 2011. http://dx.doi.org/10.1007/s00170-010-2828-7
HAMMOUCHE, K.; DIAF, M.; SIARRY, P. A Comparative study of various meta-heuristic techniques applied to the multilevel thresholding problem. Engineering Applications of Artificial Intelligence, v. 23, p. 676-688, 2010. http://dx.doi.org/10.1016/j.engappai.2009.09.011
HOLLAND, J. H. Adaptation in natural and artificial systems. Michigan: University of Michigan Press, 1975.
IGNÍZIO, J.P., CAVALIER, T.M. Linear Programming. Englewood Cliffs: Prentice Hall, 1994.
KHURI A.; CONLON M. Simultaneous optimization of multiple responses represented by polynomial regression functions. Technometrics, v. 23, n. 4, p. 363-375, 1981. http://dx.doi.org/10.2307/1268226
KHURI, A.I.; CORNELL, J.A. Response Surfaces: Designs and Analyses. New York: Marcel Dekker Inc., 1987.
KIM, K.J.; LIN, D.K.J. Optimization of multiple responses considering both location and dispersion effects. European Journal of Operational Research, v. 169, p. 133–145, 2006. http://dx.doi.org/10.1016/j.ejor.2004.06.020
KÖKSOY, O.; YALCINOZ, T. Mean square error criteria to multiresponse process optimization by a new genetic algorithm. Applied Mathematics and Computation, v. 175, n. 2, p. 1657-1674, 2006. http://dx.doi.org/10.1016/j.amc.2005.09.011
LASDON, L. S.; WAREN, A. D.; RATNER, M. W. GRG2 Users’s Guide University ofTexas at Austin, 1980.
MELO, A.; CATEN, C.S.T.; SANT’ANNA, A.M.O. Otimização dos parâmetros de usinagem na manufatura do ferro fundido. Revista Produção Online, v.13, n. 1, p. 375-388, 2013. http://dx.doi.org/10.14488/1676-1901.v13i1.1200.
MENDES, J. M. A comparative study of crossover operators for genetic algorithms to solve the job shop scheduling problem. Wseas Transactions on Computers, v. 12, n. 4, p. 164-173, 2013.
MONTGOMERY, C.D.; RUNGER, G.C. Estatística aplicada e probabilidade para engenheiros, 5 Ed., LTC, 2012.
PAULING; L. The Nature of the Chemical Bond. Ithaca: Cornell University Press, 1960.
RECHENBERG, I. Evolutionsstrategie: Optimierung technischer systeme nach prinzipien der biologischen evolution, Stuttgart: Frommann-Holzboog, 1973.
REEVES, C. Genetic algorithms. In: Handbook of Metaheuristics. New York: Springer, 2003.
ROSEN, J. B. The gradient projection method for nonlinear programming. Part I: Linear constraints. Journal of the Society for Industrial and Applied Mathematics, v. 8, n. 1, p. 181-217, 1960.
SUDENG, S.; WATTANAPONGSAKORN, N. Post Pareto-optimal pruning algorithm for multiple objective optimization using specific extended angle dominance. Engineering Applications of Artificial Intelligence, v. 38, p. 221-236, 2015.
http://dx.doi.org/10.1016/j.engappai.2014.10.020
TORRES JÚNIOR, N.; QUININO, R. C. O jogo da catapulta para compreender o planejamento e análise de experimentos: proposta de uma abordagem lúdica de ensino. Revista Produção Online, v. 14, n. 3, p. 939-971, 2014.
http://dx.doi.org/10.14488/1676-1901.v14i3.1576
TSAI, C.; TONG, L.; WANG, C. Optimization of Multiple Responses Using Data Envelopment Analysis and Response Surface Methodology. Tamkang Journal of Science and Engineering, v. 13, n. 2, p. 197-203, 2010.
VELDHUIZEN, D.A.V.; LAMONT, G.B. Multiobjective evolutionary algorithms: analyzing the state-of-the-Art. In: Evolutionary Computation, Cambridge: MIT Press, v. 8, n. 2, p. 125-147, 2000.
VINING G. A compromise approach to multiresponse optimization. Journal of Quality Technology, v. 30, n. 4, p. 309-313, 1998.
WAREN, A. D.; LASDON, L. S. The status of nonlinear programming software. Operations Research, v. 27, n. 3, p. 431-56, 1979.
WEISE, T., Global Optimization Algorithms – Theory and Application, 2ª ed, (2009). Disponível em: http://www.it-weise.de/projects/book.pdf=> acessado em 18 mar. 2015.
WOLFE, P. The Reduced Gradient Method. In: Recent Advances in Mathematical Programming. New York: R. L. Graves and P. Wolfe, 1963.
Published
How to Cite
Issue
Section
License
The Journal reserves the right to make spelling and grammatical changes, aiming to keep a default language, respecting, however, the style of the authors.
The published work is responsibility of the (s) author (s), while the Revista Produção Online is only responsible for the evaluation of the paper. The Revista Produção Online is not responsible for any violations of Law No. 9.610 / 1998, the Copyright Act.
The journal allows the authors to keep the copyright of accepted articles, without restrictions
This work is licensed under a Creative Commons License .