379
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Nonconvex optimization of desirability functions

, &

References

  • Akteke-Öztürk, B. 2010. New approaches to desirability functions by nonsmooth and nonlinear optimization, Ph.D. Thesis, Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey.
  • Akteke-Öztürk, B., G.W. Weber, and G. Köksal. 2015. Desirability functions in multiresponse optimization. Optimization in the natural sciences. Communications in Computer and Information Science 499:129–146.
  • BARON 2010. www.gams.com/solver, v. 8.1.5.
  • Bartels, S. G., L. Kuntz, and S. Scholtes. 1995. Continuous selections of linear functions and nonsmooth critical point theory. Nonlinear Analysis, Theory, Methods and Applications, 24(3):385–407.
  • Bazaraa, M. S., H. D. Sherali, and C. M. Shetty. 2006. Nonlinear programming theory and algorithms. 3rd ed. John Wiley and Sons, Inc.
  • Bellucci, J. P., and K. W. Bauer, Jr. 2017. The use of nested desirability functions and quality indices for multi-response robust parameter design problems. Quality Engineering, DOI:10.1080/08982112.2017.1288914.
  • Box, G. E. P., and D. W. Behnken. 1960. Some new three-level designs for the study of quantitative variables. Technometrics 2:455–475.
  • Boyd, S., S. J. Kim, L. Vandenberghe, and A. Hassibi. 2007. A tutorial on geometric programming. Optimization and Engineering 8:67–127.
  • Burachik, R. S., R. N. Gasimov, N. A. Ismayilova, and C. Y. Kaya. 2006. On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian. Journal of Global Optimization 34(1):55–78.
  • Chen, H-W., W. K. Wong, and X. Hongquan. 2012. An augmented approach to the desirability function. Journal of Applied Statistics 39(3):599–613.
  • Ch’ng, C. K., S. H. Quah, and H. C. Low. 2005. A new approach for multiple-response optimization. Quality Engineering 17:621–626.
  • Cho, Y. H., and S. H. Park. 2006. Optimization in multiple response model with modified desirability function. Asian Journal on Quality 7(3):46–57.
  • Clarke, F. 1983. Optimization and nonsmooth analysis. SIAM's Classics in Applied Mathematics Series.
  • Conn, A. R., K. Scheinberg, and L. N. Vicente. 2009. Introduction to Derivative-Free Optimization, MPS-SIAM Book Series on Optimization. Philadelphia: SIAM.
  • Costa, N. R., J. Lourenço, and Z. L. Pereira. 2011. Desirability function approach: a review and performance evaluation in adverse conditions. Chemometrics and Intelligent Laboratory Systems 107:234–244.
  • CONOPT. 2010. www.gams.com/solver, v. 3.14S.
  • Del Castillo, E., D. C. Montgomery, and D. R. McCarville. 1996. Modified desirability functions for multiple response optimization. Journal of Quality Technology 28(3):337–345.
  • Das, P. 2010. Hybridization of artificial neural network using desirability functions for process optimization. International Journal for Quality Research 4(1):37–50.
  • Das, P., and S. Sengupta. 2010. Composite desirability index in cases of negative and zero desirability. Journal of Management Research 10(1):25–38.
  • Demyanov, V. F., and A. M. Rubinov. 1986. Quasidifferentiable calculus, Optimization Software, New York: Publications Division.
  • Derringer, G., and R. Suich. 1980. Simultaneous optimization of several response variables. Journal of Quality Technology 12:214–219.
  • Derringer, G. 1994. A balancing act, Optimizing a products properties. Quality Progress, 27:51–57.
  • DESIGN-EXPERT. 2016. Stat-Ease, v. 10.0.0.3.
  • DICOPT. 2010. www.gams.com/solver, v. 2x-C.
  • Drud, A. S. 1995. CONOPT: A system for large scale nonlinear optimization, Tutorial for CONOPT Subroutine Library. 16p, ARKI Consulting and Development A/S, Bagsvaerd, Denmark.
  • Dutta, J. 2005. Generalized derivatives and nonsmooth optimization, a finite dimensional tour. TOP 13(2):185–314.
  • Ehrgott, M. 2005. Multicriteria optimization. Berlin: Springer.
  • Floudas, C. A. 1995. Nonlinear and mixed-integer optimization: fundamentals and applications. Topics in Chemical Engineering, Oxford University Press.
  • Fuller, D., and W. Scherer. 1998. The desirability function: Underlying assumptions and application implications, Paper Presented at the Systems, Man, and Cybernetics, IEEE International Conference, San Diego, CA.
  • GAMS. 2010. www.gams.com, v. 23.0.2.
  • Gasimov, R.N. 2002. Augmented Lagrangian duality and nondifferentiable optimization methods in nonconvex programming. Journal of Global Optimization 24:187–203.
  • Gasimov, R. N., and A. M. Rubinov. 2004. On augmented Lagrangians for optimization problems with a single constraint. Journal of Global Optimization 28:153–173.
  • Gasimov, R. N., and O. Ustun. 2007. Solving the quadratic assignment problem using F-MSG algorithm. Journal of Industrial and Management Optimization 3(2):173–191.
  • Harrington, E. C. Jr. 1965. The desirability function. Industrial Quality Control 21:494–498.
  • He, Z., and P. F. Zhu. 2009. A hybrid genetic algorithm for multi-response parameter optimization within desirability function framework. 16th International Conference on Industrial Engineering and Engineering Management, IE&EM’09, pp. 612–617.
  • He, Z., P. F. Zhu, and S. H. Park. 2012. A robust desirability function method for multi-response surface optimization considering model uncertainty. IEEE 221(1):241–247.
  • Hooke, R., and T. A. Jeeves. 1960. Direct search solution of numerical and statistical problems. Journal of Association for Computing Machinery 8:212–229.
  • Jeong, I. J., and K. J. Kim. 2008. An interactive desirability function method to multiresponse optimization. European Journal of Operational Research 195(2):412–426.
  • Jeong, I. J., and K. J. Kim. 2005. D-STEM: a modified step method with desirability function concept. Computers and Operations Research 32:3175–3190.
  • Khuri, A. I. 1996. Multiresponse surface methodology. In Handbook of Statistics: Design and Analysis of Experiments, eds. A. Ghosh and C. R. Rao. 13:377–406.
  • Kim, K., and D. Lin. 2000. Simultaneous optimization of multiple responses by maximizing exponential desirability functions. Applied Statistics 49(C):311–325.
  • Ko, Y. H., K. J. Kim, and C. H. Jun. 2005. A new loss function-based method for multiresponse optimization. Journal of Quality Technology 37(1):50–59.
  • Köksoy, O. 2006. Multiresponse robust design: Mean Square Error (MSE) criterion. Applied Mathematics and Computation 175(2):1716–1729.
  • Köksoy, O. 2005. Dual response optimization: The desirability approach. International Journal of Industrial Engineering 12(4):335–342.
  • Kuntz, L., and S. Scholtes. 1995. Qualitative aspects of the local approximation of a piecewise smooth function. Nonlinear Analysis: Theory, Methods and Applications 25:197–215.
  • Kushwaha, S., S. Sikdar, I. Mukherjee, and P. K. Ray. 2013. A modified desirability function approach for mean-variance optimization of multiple responses. International Journal of Software Science and Computational Intelligence 5(3):7–21.
  • Lasdon, L. S., A. D. Waren, A. Jain, and M. Ratner. 1978. Design and testing of a generalized reduced gradient code for nonlinear programming. ACM Transactions on Mathematical Software 4(1):34–50.
  • Lee, D. H., K. J. Kim, and M. Köksalan. 2011. A posterior preference articulation approach to multiresponse surface optimization. European Journal of Operational Research 210:301–309.
  • Lee, D. H., K. J. Kim, and M. Köksalan. 2012. An interactive method to multiresponse surface optimization based on pairwise comparisons. IIE Transactions 44(1):13–26.
  • Lemarechal, C. 1978. Bundle-methods in nonsmooth optimization. In Nonsmooth Optimization, eds. C. Lemarechal and R. Mifflin. Oxford: Pergamon Press.
  • Logothetis, N., and H. P. Wynn. 1989. Quality through design. Oxford Science Publications, Oxford: Clarendon Press.
  • Lundell, A., and T. Westerlund. 2012. Global optimization of mixed-integer signomial programming problems. In Mixed Integer Nonlinear Programming, eds. J. Lee, S. Leyffer, vol. 154 of The IMA Volumes in Mathematics and its Applications, 349–369. New York: Springer.
  • Miettinen, K. 1999. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers.
  • MINITAB. 2016. https://www.minitab.com/en-us/, v. 17.2.1.
  • MATLAB. 2016. MATLAB and statistics toolbox release 2014b. Natick, MA: The MathWorks, Inc.
  • Montgomery, D. C. 2009. Design and analysis of experiments. 7th ed. New York: John Wiley and Sons.
  • Murphy, T., K-L. Tsui, and J. K. Allen. 2005. A review of robust design methods for multiple responses. Research in Engineering Design 16:118–132.
  • Özdaglar, A., and P. Tseng. 2006. Existence of global minima for constrained optimization. Journal of Optimization Theory and Applications 128:523–546.
  • Pardalos, P. M., and H. E. Romeijn, eds. 2002. Handbook of global optimization, vol. 2. Dordrecht: Kluwer Academic.
  • Park, K. S., and K. J. Kim. 2005. Optimizing multi-response surface problems: How to use multi-objective optimization techniques. IIE Transactions 37(6):523–532.
  • Pörn, R., K. M. Björk, and T. Westerlund. 2008. Global solution of optimization problems with signomial parts. Discrete Optimization 5:108–120.
  • Park, S. H., and J. O. Park. 1998. Simultaneous optimization of multiple responses using a weighted desirability function. Quality Improvement Through Statistical Methods, Statistics for Industry and Technology, part 3:299–311.
  • Pasandideh, S. H. R., and S. T. A. Niaki. 2006. Multi-response simulation optimization using genetic algorithm within desirability function framework. Applied Mathematics and Computation, 175:366–382.
  • Ribardo, C., and T. Allen. 2003. An alternative desirability function for achieving Six Sigma quality. Quality and Reliability Engineering International 19(3):227–240.
  • Rijckaert, M. J., and X. M. Martens. 1978. Comparison of generalized geometric programming algorithms. Journal of Optimization Theory and Applications 26(2):205–242.
  • Ryoo, H. S., and N. V. Sahinidis. 1996. A branch-and-reduce approach to global optimization. Journal of Global Optimization 8(2):107–138.
  • Sahinidis, N. BARON Software, archimedes.cheme.cmu.edu/?q =baron.
  • Steuer, D. 1999. Multi-criteria-optimisation and desirability indices; Technical Report 20/99, University of Dortmund, Statistics Department.
  • Trautmann, H., and C. Weihs. 2004. Pareto-optimality and desirability indices. Technical Report, SFB 475, 63.
  • Tawarmalani, M., and N. V. Sahinidis. 2005. A polyhedral branch-and-cut approach to global optimization. Mathematical Programming 103(2):225–249.
  • Sahinidis, N. V. 2014. BARON 14.4.0: global optimization of mixed-integer nonlinear programs, User's manual.
  • Wan, W., and J. B. Birch. 2011. Using a modified genetic algorithm to find feasible regions of a desirability function. Quality and Reliatibility Engineering 27(8):1173–1182.
  • Wu, C. F. J., and M. Hamada. 2000. Experiments: planning, analysis, and parameter design optimization. New York: Wiley-Interscience.
  • Wu, F.-C. 2004. Optimization of correlated multiple quality characteristics using desirability function. Quality Engineering 17(1):119–126.
  • Wu, F.-C. 2009. Robust design of nonlinear multiple dynamic quality characteristics. Computers and Industrial Engineering 56:1328–1332.
  • Yadav, O. P., G. Thambidorai, B. Nepal, and L. Monplaisir. 2014. A robust framework for multi-response surface optimization methodology. Quality Reliability Engineering International 30:301–311.
  • Zeybek, M., and O. Köksoy. 2016. Optimization of correlated multiresponse quality engineering by the upside-down normal loss function. Engineering Optimization 48(8):1419–1431.
  • Zowe, J. 1985. Nondifferentiable optimization: A motivation and a short introduction into the subgradient and the bundle concept. In NATO SAI Series, 15, Computational Mathematical Programming, ed. K. Schittkowski, 323–356. New York: Springer-Verlag.
  • Zong, Z., Z. He, and X. Kong. 2006. A new desirability function based method for multi-response robust parameter design, Paper Presented at the International Technology and Innovation Conference, Tianjin/China, November 6–7.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.