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Exploring Pareto Frontiers in the Response Surface Methodology

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Abstract

Multiple response optimization problems have many optimal solutions that impact differently on process or product. Some of these solutions lead to operation conditions more hazardous, more costly or more difficult to implement and control. Therefore, it is useful for the decision-maker to use methods capable of capturing solutions evenly distributed along the Pareto frontier. Three examples were used to evaluate the ability of three methods built on different approaches for depicting the Pareto frontier. Limitations of a desirability-based method are illustrated whereas the consistent performance of an easy-to-use global criterion gives confidence to use it in real-life problems developed under the Response Surface Methodology framework, as alternative to the sophisticated physical programming method.

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References

  1. Myers, R., Montgomery, D., Anderson-Cook, C.: Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd edn. Wiley, Hoboken (2009)

    MATH  Google Scholar 

  2. Costa, N., Lourenço, J., Pereira, Z.: Desirability function approach: a review and performance evaluation in adverse conditions. Chemom. Intell. Lab. Syst. 107, 234–244 (2011)

    Article  Google Scholar 

  3. Derringer, G., Suich, R.: Simultaneous optimization of several response variables. J. Qual. Technol. 12, 214–218 (1980)

    Google Scholar 

  4. Derringer, G.: A balancing act: optimizing a product’s properties. Qual. Prog. 27, 51–58 (1994)

    Google Scholar 

  5. Das, P., Sengupta, S.: Composite desirability index in cases of negative and zero desirability. J. Manag. Resour. 10, 25–38 (2010)

    Google Scholar 

  6. Murphy, T., Tsui, K., Allen, J.: A review of robust design methods for multiple responses. Res. Eng. Des. 15, 201–215 (2005)

    Article  Google Scholar 

  7. Ko, Y., Kim, K., Jun, C.: A new loss function-based method for multiresponse optimization. J. Qual. Technol. 37, 50–59 (2005)

    Google Scholar 

  8. Pignatiello, J.: Strategies for robust multi-response quality engineering. IIE Trans. 25, 5–15 (1993)

    Article  Google Scholar 

  9. Vining, G.: A compromise approach to multiresponse optimization. J. Qual. Technol. 30, 309–313 (1998)

    Google Scholar 

  10. Köksoy, O.: A nonlinear programming solution to robust multi-response quality problem. Appl. Math. Comput. 196, 603–612 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Pal, S., Gauri, S.: Assessing effectiveness of the various performance metrics for multi-response optimization using multiple regression. Comput. Ind. Eng. 59, 976–985 (2010)

    Article  Google Scholar 

  12. Tong, L.-I., Wang, C.-H.: Multi-response optimisation using principal component analysis and grey relational analysis. Int. J. Ind. Eng. 9, 343–350 (2002)

    Google Scholar 

  13. Liao, H.-C.: Multi-response optimization using weighted principal component. Int. J. Adv. Manuf. Technol. 27, 720–725 (2006)

    Article  Google Scholar 

  14. Awad, M., Kovach, J.: Multiresponse optimization using multivariate process capability index. Qual. Reliab. Eng. Int. 27, 465–477 (2011)

    Article  Google Scholar 

  15. Kwak, D.-S., Kim, K.-J., Lee, M.-S.: Multistage PRIM: patient rule induction method for optimisation of a multistage manufacturing process. Int. J. Prod. Res. 48, 3461–3473 (2010)

    Article  MATH  Google Scholar 

  16. Al-Refaie, A.: Optimizing performance with multiple responses using cross-evaluation and aggressive formulation in data envelopment analysis. IIE Trans. 44, 262–276 (2012)

    Article  Google Scholar 

  17. Govindaluri, S., Cho, B.: Robust design modeling with correlated quality characteristics using a multicriteria decision framework. Int. J. Adv. Manuf. Technol. 32, 423–433 (2007)

    Article  Google Scholar 

  18. Kazemzadeh, B., Bashiri, M., Atkinson, A., Noorossana, R.: A general framework for multiresponse optimization problems based on goal programming. Eur. J. Oper. Res. 189, 421–429 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Messac, A.: Physical programming: effective optimization for computational design. AIAA J. 34, 149–158 (1996)

    Article  MATH  Google Scholar 

  20. Chen, W., Sahai, A., Messac, A., Sundararaj, G.: Exploring the effectiveness of physical programming in robust design. J. Mech. Des. 122, 155–163 (2000)

    Article  Google Scholar 

  21. Peterson, J., Miró-Quesada, G., Del Castillo, E.: A bayesian reliability approach to multiple response optimization with seemingly unrelated regression models. Qual. Technol. Quant. Manag. 6, 353–369 (2009)

    Google Scholar 

  22. Dächert, K., Gorski, J., Klamroth, K.: An augmented weighted Tchebycheff method with adaptively chosen parameters for discrete bicriteria optimization problems. Comput. Oper. Res. 39, 2929–2943 (2012)

    Article  MathSciNet  Google Scholar 

  23. Lee, D., Jeong, I., Kim, K.: A posterior preference articulation approach to dual response surface optimization. IIE Trans. 42, 161–171 (2010)

    Article  Google Scholar 

  24. Lee, D., Kim, K., Köksalan, M.: An interactive method to multiresponse surface optimization based on pairwise comparisons. IIE Trans. 44, 13–26 (2012)

    Article  Google Scholar 

  25. Ardakani, M., Wulff, S.: An overview of optimization formulations for multiresponse surface problems. Qual. Reliab. Eng. Int. 29, 3–16 (2013)

    Article  Google Scholar 

  26. Costa, N., Lourenço, J.: Optimization criteria ability to depict Pareto frontiers. Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2014, WCE 2014, pp. 958–961. London, UK (2014)

    Google Scholar 

  27. Costa, N., Lourenço, J., Pereira, Z.: Multiresponse optimization and Pareto frontiers. Qual. Reliab. Eng. Int. 28, 701–712 (2011)

    Article  Google Scholar 

  28. Köksoy, O., Doganaksoy, N.: Joint optimization of mean and standard deviation using response surface methods. J. Qual. Technol. 35, 239–252 (2003)

    Google Scholar 

  29. Ch’ng, C., Quah, S., Low, H.: A new approach for multiple-response optimization. Qual. Eng. 17, 621–626 (2005)

    Article  Google Scholar 

  30. Costa, N., Pereira, Z.: Multiple response optimization: a global criterion-based method. J. Chemometr. 24, 333–342 (2010)

    Article  Google Scholar 

  31. Messac, A., Mattson, C.: Generating well-distributed sets of Pareto points for engineering design using physical programming. Optim. Eng. 3, 431–450 (2002)

    Article  MATH  Google Scholar 

  32. Lin, K.-P., Luo, Y.-Z., Tang, G.-J.: Multi-objective optimization of space station logistics strategies using physical programming. Eng Optim. (2014). doi:10.1080/0305215X.2014.954568

  33. Messac, A., Melachrinoudis, E., Sukam, C.: Mathematical and pragmatic perspectives of physical programming. AIAA J. 39, 885–893 (2001)

    Article  Google Scholar 

  34. Yuan, Y., Ling, Z., Gao, C., Cao, J.: Formulation and application of weight-function-based physical programming. Eng. Optim. 46, 1628–1650 (2014)

    Article  Google Scholar 

  35. Martínez, M., Sanchis, J., Blasco, X.: Integrated multiobjective optimization and a priori preferences using genetic algorithms. Inform. Sci. 178, 931–951 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. Martínez, M., Sanchis, J., Blasco, X.: Multi-objective engineering design using preferences. Eng. Optim. 40, 253–269 (2008)

    Article  Google Scholar 

  37. Sanchis, J., Martínez, M., Blasco, X., Reynoso-Meza, G.: Modelling preferences in multi-objective engineering design. Eng. Appl. Artif. Intel. 23, 1255–1264 (2010)

    Article  Google Scholar 

  38. Utyuzhnikov, S., Fantini, P., Guenov, M.: A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization. J. Comput. Appl. Math. 223, 820–841 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. Chen, W., Wiecek, M., Zhang, J.: Quality utility: a compromise programming approach to robust design. J. Mech. Des. 121, 179–187 (1999)

    Article  Google Scholar 

  40. Das, I., Dennis, J.: A closer look at drawbacks of minimizing weighted-sums of objectives for Pareto set generation in multicriteria optimization problems. Struct. Optim. 14, 63–69 (1997)

    Article  Google Scholar 

  41. Marler, R., Arora, J.: The weighted sum method for multi-objective optimization: some insights. Struct. Multidiscip. Optim. 41, 853–862 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  42. Athan, T., Papalambros, P.: A note on weighted criteria methods for compromise solutions in multi-objective optimization. Eng. Optim. 27, 155–176 (1996)

    Article  Google Scholar 

  43. Messac, A., Sundararaj, G., Tappeta, R., Renaud, J.: Ability of objective functions to generate points on non-convex Pareto frontiers. AIAA J. 38, 1084–1091 (2000)

    Article  Google Scholar 

  44. Marler, R., Arora, J.: Survey of multi-objective optimization methods for engineering. Struct. Multidiscip. Optim. 26, 369–395 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  45. Sanchis, J., Martínez, M., Blasco, X.: Multi-objective engineering design using preferences. Eng. Optim. 40, 253–269 (2008)

    Article  Google Scholar 

  46. Martínez, M., Sanchis, J., Blasco, X.: Multiobjective controller design handling human preferences. Eng. Appl. Artif. Intel. 19, 927–938 (2006)

    Article  Google Scholar 

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Acknowledgement

The authors are grateful to Instituto Politécnico de Setúbal for its finantial support to this publication.

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Correspondence to Nuno Ricardo Costa .

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Costa, N.R., Lourenço, J.A. (2015). Exploring Pareto Frontiers in the Response Surface Methodology. In: Yang, GC., Ao, SI., Gelman, L. (eds) Transactions on Engineering Technologies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9804-4_27

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  • DOI: https://doi.org/10.1007/978-94-017-9804-4_27

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-9803-7

  • Online ISBN: 978-94-017-9804-4

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