Uma Abordagem Alternativa para Otimizar Múltiplos Objetivos em Contexto Industrial
Uma Abordagem Alternativa para Otimizar Múltiplos Objetivos em Contexto Industrial
Índice
1. Introdução
2. Objectivo e metodologia utilizada
3. Revisão da Literatura
4. Abordagem Proposta
5. Exemplos
5. Discussão de resultados
5. Conclusões
Os processos e os produtos têm inerentes múltiplas características que devem ser otimizadas simultaneamente de modo a que seja possível encontrar a melhor solução de compromisso. Em contraste com a prática frequentemente usada mas fortemente desencorajada da otimização separada de cada uma das características que se pretendem otimizar, neste artigo sugere-se a utilização de um critério para a otimização simultânea de várias caraterísticas que é fácil de entender e de implementar, bem como métricas para avaliar a qualidade das soluções geradas. A utilização destas métricas permitirá ao decisor selecionar a solução com base no desvio cumulativo das respostas em relação aos respetivos valores alvo, na qualidade das previsões e/ou na robustez. Para avaliar e comparar o desempenho da abordagem proposta com a de outra frequentemente utilizada na resolução de problemas industriais, simularam-se condições adversas de operação em termos da variância nos processos de fabrico e analisaram-se quatro casos de estudo com diferentes tipos e número de respostas, regiões de operação e número de variáveis.
Nuno Costa é docente no Instituto Politécnico de Setúbal – Escola Superior de Tecnologia de Setúbal, no Departamento de Engenharia Mecânica, e é investigador no UNIDEMI-DEMI da FCT-UNL. Os seus trabalhos têm sido apresentados em eventos internacionais e publicados em revistas indexadas na SCI-Thomson Reuters®. Além de 4 dos seus trabalhos terem recebido prémios internacionais tem também 4 capítulos de livro publicados. Desenvolve atividade de investigação nas áreas da Gestão de Operações e da Qualidade, nomeadamente em Desenho de Experiências e Métodos de Taguchi, Controlo Estatístico do Processo e metodologia 6-Sigma.
João Lourenço é doutorado em Engenharia Electrotécnica e Computadores pelo Instituto Superior Técnico (IST) da Universidade Técnica de Lisboa. Atualmente é docente no IPS-ESTSetubal, no Departamento de Sistemas e Informática, e é investigador no INESC-ID. Tem vários trabalhos publicados em atas de congressos, em revistas indexadas na SCI-Thomson Reuters® e quatro capítulos de livro publicados. Dois dos seus trabalhos foram premiados internacionalmente. As suas áreas de pesquisa são a identificação de sistemas e previsões, o controlo preditivo, o controlo adaptativo baseado em modelos múltiplos, mecanismos de aprendizagem e a otimização de múltiplas respostas.
Nuno Ricardo Costa is a lecturer at the Instituto Politécnico de Setúbal – Escola Superior de Tecnologia de Setúbal (IPS-ESTSetubal) and is a researcher at UNIDEMI-DEMI of Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa. He has presented works in international events and has publications in journals indexed to SCIThomson Reuters®. His research interests include quality and operations management.
João Lourenço holds a Ph.D. degree in Electrothecnical and Computers Engineering from the Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal. Currently he is a Professor at the IPS-ESTSetubal, in the Department of Systems and Informatics and is invited Researcher at R&D Unit INESC-ID. His research interests are system identification and forecast, predictive and adaptive control, switched multiple model adaptive control, learning mechanisms, and multiresponse optimization.
Almeida, A., Almeida, J., Costa, A. Almeida-Filho, A. (2016). A new method for elicitation of criteria weights in additive models: Flexible and interactive trade off. European Journal of Operational Research, 250: 179-191.
Alves, M., Clímaco, J. (2007). A review of interactive methods for multiobjective integer and mixed- integer programming. European Journal of Operational Research, 180: 99-115.
Anderson, M., Whitcomb, P. (2005). RSM Simplified: Optimizing processes using response surface methods for design of experiments. Productivity Press, USA, Minneapolis, MN.
Antony J, Coleman S, Montgomery D, Anderson M, Silvestrini R. (2011). Design of Experiments for Non-Manufacturing Processes: Benefits, Challenges and Some Examples. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 225: 2078- 2087.
Ardakani, M., Wulff, S. (2013). An Overview of Optimization Formulations for Multiresponse Surface Problems. Quality and Reliability Engineering International, 29: 3-16.
Ayvaz, M., Kayhan, A., Ceylan, H., Gurarslan, G. (2009). Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems. Engineering Optimization, 41, 1119-1144.
Beasley, M. (2008). Seemingly unrelated regression models as a solution to path analytic models with correlated errors. Multiple Linear Regression Viewpoints, 34: 1-7.
Bergquist, B., Albing, M. (2006). Statistical methods – does anyone really use them? Total Quality Management & Business Excellence, 17: 961-972.
Box, G., Hunter, J., Hunter, W. (2005). Statistics for experimenters: design, innovation, and discovery (2nd Ed.), New Jersey: John Wiley & Sons.
Chapman, J., Lu, L., Anderson-Cook, C. (2014). Process Optimization for Multiple Responses Utilizing the Pareto Front Approach. Quality Engineering, 26: 253-268.
Chen, W., Wiecek, M., Zhang, J. (1999). Quality utility: a compromise programming approach to robust design. Journal of Mechanical Design, 121: 179-187
Cheng, S., Li, M. (2015). Robust optimization using hybrid differential evolution and sequential quadratic programming. Engineering Optimization, 47: 87-106.
Ch’ng, C., Quah, S., Low, H. (2005). A new approach for multiple-response optimization. Quality Engineering, 17: 621-626.
Costa, N. (2010a). Simultaneous optimization of mean and standard deviation. Quality Engineering, 22: 140-149.
Costa, N. (2010b). Multiple response optimization: methods and results. International Journal of Industrial and Systems Engineering, 5: 442-459.
Costa, N., Lourenço, J. (2014). A Comparative Study of Multiresponse Optimization Criteria Working Ability. Chemometrics and Intelligent Laboratory Systems, 138: 171-177.
Costa, N., Lourenço, J. (2015). On the generation and selection of solutions to multiple response problems. International Journal of Industrial and Systems Engineering, 20: 437-456.
Costa, N., Lourenço, J. (2016). Gaussian Process Model – An Exploratory Study in the Response Surface Methodology. Quality and Reliability Engineering International, in press, doi: 10.1002/qre.1940. Costa, N., Lourenço, J., Pereira, Z. (2011b). Desirability function approach: A review and performance evaluation in adverse conditions. Chemometrics and Intelligent Laboratory Systems, 107: 234-244.
Costa, N., Lourenço, J., Pereira, Z. (2011c). Multiresponse optimization and Pareto frontiers. Quality and Reliability Engineering International, 28: 701-712.
Costa, N., Lourenço, J., Pereira, Z. (2012). Responses Modeling and Optimization Criteria Impact on the Optimization of Multiple Quality Characteristics. Computers & Industrial Engineering, 62, 972-935.
Costa, N., Pereira, Z. (2010). Multiple response optimization: a global criterion-based method. Journal of Chemometrics, 24: 333-342
Costa, N., Pereira, Z., Tanco, M. (2010b). Optimization Measures for Assessing Compromise Solutions in Multiresponse Problems. World Congress on Engineering – ICMEEM 2010, pp. 2252-2257, London:UK.
Costa, N., Pereira, Z., Tanco, M. (2011a). Optimization measures for assessing compromise solutions in multiresponse problems. In: Lecture Notes in Electrical Engineering, Vol. 90: 445-457, ed. by Sio-Iong and G. Len, International Association of Engineers.
Costa, N., Pires, R., Ribeiro, C. (2006). Guidelines to help practitioners of design of experiments. Total Quality Management Magazine, 18: 386-399.
Das, P., Sengupta, S. (2010). Composite desirability index in cases of negative and zero desirability. Journal of Management Research, 10: 25-38.
Derringer, G., Suich, R. (1980). Simultaneous optimization of several response variables. Journal of Quality Technology, 12: 214-218.
Derringer, G. (1994). A balancing act: optimizing product’s properties. Quality Progress, June: 51-58.
Fan, S-K, Chang, J-M (2009). A parallel particle swarm optimization algorithm for multi-objective optimization problems. Engineering Optimization, 41: 673-697.
Figueira, J., Greco, S., Ehrgott, M. (eds.) (2005). Multiple criteria decision analysis: State of the art surveys. New York: Springer.
Freeman, L., Ryan, A., Kensler, J., Dickinson, R., Vining, G. (2013). A Tutorial on the Planning of Experiments. Quality Engineering, 25: 315-332.
Frey, D., Wang, H. (2006). Adaptive one-factor-at-a-time experimentation and expected value of improvement. Technometrics, 48: 418-431.
Gabrel, V., Murat, C., Thiele, A. (2014). Recent advances in robust optimization: An overview. European Journal of Operational Research, 235: 471-483.
Greene, W. (2008). Econometric analysis, (6th ed.). New Jersey: Pearson Prentice Hall.
Gupta, S., Kulahci, M., Montgomery, D., Borror, C. (2010). Analysis of Signal – Response Systems Using Generalized Linear Mixed Models. Quality and Reliability Engineering International, 26, 375-385.
Hwang-Dae, K., Robinson, T., Wulff, S., Parker, P. (2007). Comparison of Parametric, Nonparametric and Semiparametric Modeling of Wind Tunnel Data. Quality Engineering, 19, 179-190.
Ilzarbe, L., Alvarez, M., Viles, E., Tanco, M. (2008). Practical applications of design of experiments in the field of engineering: A bibliographical review. Quality and Reliability Engineering International, 24: 417-428.
Jeong, I., Kim, K. (2009). An interactive desirability function method to multiresponse optimization. European Journal of Operational Research, 195: 412-426.
Jeong, I., Kim, K., Chang, S. (2005). Optimal weighting of bias and variance in dual response surface optimization. Journal of Quality Technology, 37: 236-247.
Kazemzadeh, B., Bashiri, M., Atkinson, A., Noorossana, R. (2008). A general framework for multiresponse optimization problems based on goal programming. European Journal of Operational Research, 189: 421-429.
Khuri, A., Mukhopadhyay, S. (2010). Response surface methodology. Wiley Interdisciplinary Reviews: Computational Statistics, 2: 128-149.
Kim, K., Lin, D. (1998). Dual response surface optimization: a fuzzy modelling approach. Journal of Quality Technology, 30: 1-10.
Kim, K., Lin, D. (2000). Simultaneous optimization of multiple responses by maximining exponential desirability functions. Applied Statistics C, 49: 311-325.
Kim, K., Lin, D. (2006). Optimization of multiple responses considering both location and dispersion effects. European Journal of Operational Research, 169: 133-145.
Ko, Y., Kim, K., Jun, C. (2005). A new loss function-based method for multiresponse optimization. Journal of Quality Technology, 37: 50-59.
Lee, M., Kim, Y. (2007). Separate response surface modelling for multiple response optimization: multivariate loss function approach. International Journal of Industrial Engineering – Theory, Applications and Practice, 14: 227-235.
Lee, D., Jeong, I., Kim, K. (2010). A posterior preference articulation approach to dual response surface optimization. IIE Transactions, 42: 161-171.
Lee, D., Kim, K., Köksalan, M. (2011). A posterior preference articulation approach to multiresponse surface optimization. European Journal of Operational Research, 210: 301-309.
Lee, D., Kim, K., Köksalan, M. (2012). An interactive method to multiresponse surface optimization based on pairwise comparisons. IIE Transactions, 44: 13-26.
Lopes, I., Nunes, E., Sousa, S., Esteves, D. (2011). Quality Improvement Practices Adopted by Industrial Companies in Portugal. Proceedings of the World Congress on Engineering 2011, Vol. I, pp. 696-701, WCE 2011, July, London, U.K.
Marler, R., Arora, J. (2004). Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, 26: 369-395.
Marler, R., Arora, J. (2005). Function-transformation methods for multi-objective optimization. Engineering Optimization, 37: 551-570.
Marler, R., Arora, J. (2010). The weighted sum method for multi-objective optimization: some insights. Structural and Multidisciplinary Optimization, 41: 853-862.
Messac, A., Ismail-Yahaya, A. (2001). Required relationship between objective function and pareto frontier orders: practical implications. AIAA Journal, 39: 2168-2174.
Messac, A., Sundararaj, G., Tappeta, R., Renaud, J. (2000). Ability of objective functions to generate points on non-convex Pareto frontiers. AIAA Journal, 38: 1084-1091.
Myers, R., Montgomery, D. (1995). Response surface methodology: process and product optimization using designed experiments, New Jersey: Wiley.
Myers, R., Montgomery, D., Anderson-Cook, C. (2009). Response Surface Methodology: process and product optimization using designed experiments (3rd Ed.). New Jersey: John Wiley & Sons.
Murphy, T., Tsui, K., Allen, J. (2005). A review of robust design methods for multiple responses. Research in Engineering Design, 15: 201-215.
Ortiz, F., Simpson, J., Pignatielo, J., Heredia-Langner, A. (2004). A genetic algorithm approach to multiple-response optimization. Journal of Quality Technology, 36: 432-450.
Owen, M., Armitage, M., Chatfield, M. (2003). A scientist’s viewpoint on promoting effectiveness of experimental design: ten things a scientist wants to know about experimental design. Pharmaceutical Statistics, 2: 15-29.
Ozdemir, A., Cho, B. (2016). A Nonlinear Integer Programming Approach to Solving the Robust Parameter Design Optimization Problem. Quality and Reliability Engineering International, in press, DOI: 10.1002/qre.1970.
Pal, S., Gauri, S. (2010). Assessing effectiveness of the various performance metrics for multi-response optimization using multiple regression. Computers & Industrial Engineering, 59: 976-985.
Pignatiello, J. (1993). Strategies for robust multi-response quality engineering. IIE Transactions, 25: 5- 15.
Robinson, T., Wulff, S., Khuri, A., Montgomery, D. (2006). Robust parameter design using generalized linear mixed models. Journal of Quality Technology, 38: 65-75.
Salmasnia, A., Kazemzadeh, R., Seyyed-Esfahani, M., Hejazi, T. (2013). Multiple response surface optimization with correlated data. International Journal of Advanced Manufacturing Technology, 64, 841-855.
Saraiva, P. (2003). Manual Prático para a Certificação e Gestão da Qualidade com base nas Normas ISO9000: 2000. Unidade 3, capítulo 5, subcapítulo 2.1. Editora VERLAG.
Sörensen, K. (2013). Metaheuristics – the metaphor exposed. International Transactions in Operational Research, in press, DOI: 10.1111/itor.12001.
Saraiva, P., d’ Orey, J., Sampaio, P., Reis, M., Cardoso, C., Pinheiro, J., Tomé, L. (2010). O Futuro da Qualidade em Portugal. APQ.
Shah, H., Montgomery, D., Carlyle, W. (2004). Response surface modelling and optimization in multiresponse experiments using seemingly unrelated regressions. Quality Engineering, 16: 387- 397.
Shaibu, A., Cho, B. (2009). Another view of dual response surface modelling and optimization in robust parameter design. International Journal of Advanced Manufacturing Technology, 4: 631-641.
Shin, S., Cho, B. (2009). Studies on a bi-objective robust design optimization problem. IIE Transactions, 41: 957-968.
Sibalija, T., Majstorovic, V. (2012). An integrated simulated annealing-based method for robust multiresponse process optimization. International Journal of Advanced Manufacturing Technology, 59:1227-1244.
Sousa D., Aspinwall E., Sampaio A., Rodrigues A. (2005). Performance Measures and Quality Tools in Portuguese Small and Medium Enterprises: Survey Results. Total Quality Management, 16: 277- 307.
Tanco, M., Costa, N., Viles, E. (2009a). Experimental design selection: guidelines for practitioners. International Journal of Productivity and Quality Management, 4: 283-302.
Tanco, M., Viles, E., Ilzarbe, L., Alvarez, M. (2009b). Implementation of Design of Experiments projects in industry. Applied Stochastic Models in Business and Industry, 25: 478-505.
Tanco, M., Viles, E., Alvarez, M., Ilzarbe, L. (2010). Why is not design of experiments widely used by engineers in Europe? Journal of Applied Statistics, 37: 1961-1977.
Vining, G. (1998). A compromise approach to multiresponse optimization. Journal of Quality Technology, 30: 309-313.
Vining, G., Myers, R. (1990). Combining taguchi and response surface philosophies: A dual response approach. Journal of Quality Technology, 22: 38-45.
Wan, W., Birch, J. (2011). A semiparametric technique for the multi-response optimization problem. Quality and Reliability Engineering International, 27: 47-59.
Wu, F-C. (2005). Optimization of correlated multiple quality characteristics using desirability function. Quality Engineering, 17: 119-126.
Wu, F-C, Chyu, C. (2004). Optimization of robust design for multiple quality characteristics. International Journal of Production Research, 4: 337-354.
Xu, K., Lin, D., Tang, L., Xie, M. (2004). Multiresponse Systems optimization using a goal attainment approach. IIE Transactions, 36: 433-445.
Younis, A., Dong, Z. (2010). Trends, features, and tests of common and recently introduced global optimization methods. Engineering Optimization, 42: 691-718.
Zellner, A. (1962). An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias. Journal of American Statistical Association, 57: 348-368.
Zhou, X., Ma, Y., Tu, Y., Feng, Y. (2013). Ensemble of Surrogates for Dual Response Surface Modeling in Robust Parameter Design. Quality and Reliability Engineering International, 29, 173-197.
Otimização, Custo, Variância, Robustez.
