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Optimization and Engineering

, Volume 2, Issue 2, pp 139–157 | Cite as

Algorithms for Noisy Problems in Gas Transmission Pipeline Optimization

  • R.G. Carter
  • J.M. Gablonsky
  • A. Patrick
  • C.T. Kelley
  • O.J. Eslinger
Article

Abstract

In this paper we describe some algorithms for noisy optimization in the context of problems from the gas transmission industry. The algorithms are implicit filtering, DIRECT, and a new hybrid of these methods, which uses DIRECT to find an intitial iterate for implicit filtering. We report on numerical results that illustrate the performance of the methods.

noisy optimization implicit filtering DIRECT gas transmission pipeline 

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References

  1. D. M. Bortz and C. T. Kelley, “The simplex gradient and noisy optimization problems,” in Computational Methods in Optimal Design and Control, vol. 24: Progress in Systems and Control Theory, J. T. Borggaard, J. Burns, E. Cliff, and S. Schreck, eds., 1998, pp. 77–90.Google Scholar
  2. C. G. Broyden, “Quasi-Newton methods and their application to function minimization,” Math. Comp. vol. 21, pp. 368–381, 1967.Google Scholar
  3. C. G. Broyden, “A new double-rank minimization algorithm,” AMS Notices vol. 16, p. 670, 1969.Google Scholar
  4. R. G. Carter, “Compressor station optimization—computational accuracy and speed,” in Proceedings of the Pipeline Simulation Interest Group, Twenty-Eighth Annual Meeting, San Francisco CA, 1996, Paper number PSIG-9605.Google Scholar
  5. R. G. Carter, “Pipeline optimization: dynamic programming after 30 years,” in Proceedings of the Pipeline Simulation Interest Group, Denver Colorado, 1998, Paper number PSIG-9803.Google Scholar
  6. R. G. Carter, “Nonsequential dynamic programming for optimizing pipelines,” in The 1999 SIAM Conference on Optimization, 1999.Google Scholar
  7. R. G. Carter, W. W. Schroeder, and T. D. Harbick, “Some causes and effect of discontinuities in modeling and optimizing gas transmission networks,” in Proceedings of the Pipeline Simulation Interest Group, Pittsburg PA, 1993, Paper number PSIG-9308.Google Scholar
  8. T. D. Choi, “Bound constrained optimization,” Ph.D. Thesis, North Carolina State University, Raleigh, North Carolina, 1999.Google Scholar
  9. T. D. Choi, O. J. Eslinger, P. Gilmore, A. Patrick, C. T. Kelley, and J. M. Gablonsky, “IFFCO: implicit filtering for constrained optimization, version 2,” Technical Report CRSC-TR99-23, North Carolina State University, Center for Research in Scientific Computation, 1999.Google Scholar
  10. T. D. Choi, O. J. Eslinger, C. T. Kelley, J. W. David, and M. Etheridge, “Optimization of automotive valve train components with implicit filtering,” Optimization and Engineering vol. 1, pp. 9–28, 2000.Google Scholar
  11. T. D. Choi and C. T. Kelley, “Superlinear convergence and implicit filtering,” SIAM J. Optim. vol. 10, pp. 1149–1162, 2000.Google Scholar
  12. A. R. Conn, K. Scheinberg, and P. Toint, “Derivative free optimization algorithms for constrained problems,” in The 1999 SIAM Conference on Optimization, 1999.Google Scholar
  13. A. R. Conn, K. Scheinberg, and P. L. Toint, “On the convergence of derivative-free methods for unconstrained optimization,” in Approximation Theory and Optimization: Tributes to M. J. D. Powell, A. Iserles and M. Buhmann, eds., Cambridge: U.K., 1997a, pp. 83–108.Google Scholar
  14. A. R. Conn, K. Scheinberg, and P. L. Toint, “Recent progress in unconstrained optimization without derivatives,” Math. Prog. Ser. B vol. 79, pp. 397–414, 1997b.Google Scholar
  15. A. R. Conn, K. Scheinberg, and P. L. Toint, “A derivative free optimization algorithm in practice,” in Proceeedings of 7-th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St Louis, MO. Sep. 2–4, 1998.Google Scholar
  16. A. R. Conn and P. L. Toint, “An algorithm using quadratic interpolation for unconstrained derivative-free optimization,” Facultès Universitaires de Namur, Technical Report 95/6, 1995.Google Scholar
  17. J. W. David, C. Y. Cheng, T. D. Choi, C. T. Kelley, and J. Gablonsky, “Optimal design of high speed mechanical systems,” North Carolina State University, Center for Research in Scientific Computation, Technical Report CRSC-TR97-18, 1997, Mathematical Modeling and Scientific Computing, to appear.Google Scholar
  18. J. E. Dennis and V. Torczon, “Direct search methods on parallel machines,” SIAM J. Optim. vol. 1, pp. 448–474, 1991.Google Scholar
  19. L. Dixon and G. Szeg, “The global optimisation problem: An introduction,” in Towards Global Optimization 2 vol. 2,L. Dixon and G. Szeg, eds., North-Holland: Amsterdam, pp. 1–15.Google Scholar
  20. M. Etheridge “Preliminary performance of carbon-carbon valves in high speed pushrod type valve trains,” Master's Thesis, North Carolina State University, Raleigh, North Carolina, 1998.Google Scholar
  21. A. V. Fiacco and G. P. McCormick, Nonlinear Programming, no. 4: Classics in Applied Mathematics. SIAM: Philadelphia, 1990.Google Scholar
  22. R. Fletcher, “A new approach to variable metric methods,” Comput. J. vol. 13, pp. 317–322, 1970.Google Scholar
  23. S. J. Fortune, D. M. Gay, B. W. Kernighan, O. Landron, R. A. Valenzuela, and M. H. Wright, “WISE design of indoor wireless systems,” IEEE Computational Science and Engineering vol. 2, pp. 58–68, 1995.Google Scholar
  24. J. M. Gablonsky, “DIRECT version 2.0 user guide,” Center for Research in Scientific Computation, North Carolina State University, Technical Report CRSC-TR01-08, 2001a.Google Scholar
  25. J. M. Gablonsky, “Modifications of the DIRECT algorithm,” Ph.D. Thesis, North Carolina State University, Raleigh, North Carolina, 2001b.Google Scholar
  26. J. M. Gablonsky and C. T. Kelley, “A locally-biased form of the DIRECT algorithm,” North Carolina State University, Center for Research in Scientific Computation, Technical Report CRSC-TR00-31, 2000, Journal of Global Optimization vol. 21, pp. 27–37, 2001.Google Scholar
  27. P. Gilmore, “An algorithm for optimizing functions with multiple minima,” Ph.D. Thesis, North Carolina State University, Raleigh, North Carolina, 1993a.Google Scholar
  28. P. Gilmore, “IFFCO: implicit filtering for constrained optimization,” Center for Research in Scientific Computation, North Carolina State University, Technical Report CRSC-TR93-7, 1993b. Available by anonymous ftp from ftp.math.ncsu.edu in FTP/kelley/iffco/ug.psGoogle Scholar
  29. P. Gilmore and C. T. Kelley, “An implicit filtering algorithm for optimization of functions with many local minima,” SIAM J. Optim. vol. 5, pp. 269–285, 1995.Google Scholar
  30. P. Gilmore, P. Pernambuco-Wise, and Y. Eyssa, “An optimization code for pulse magnets,” National High Magnetic Field Laboratory, Florida State University, Technical Report, 1994.Google Scholar
  31. P. A. Gilmore, S. S. Berger, R. F. Burr, and J. A. Burns, “Automated optimization techniques for phase change piezoelectric ink jet performance enhancement,” in 1997 International Conference on Digital Printing Technologies, pp. 716–721, November, 1997.Google Scholar
  32. D. Goldfarb, “A family of variable metric methods derived by variational means,” Math. Comp. vol. 24, pp. 23–26, 1970.Google Scholar
  33. R. Hooke and T. A. Jeeves, “Direct search' solution of numerical and statistical problems,” Journal of the Association for Computing Machinery vol. 8, pp. 212–229, 1961.Google Scholar
  34. W. Huyer and A. Neumaier, “Global optimization by multilevel coordinate search,” J. Global Optim. vol. 14, no. 4, pp. 331–355, 1999.Google Scholar
  35. E. Janka, “Vergleich stochastischer verfahren zur globalen optimierung,” Diplomarbeit, Universität Wien, 1999.Google Scholar
  36. D. R. Jones, “The DIRECT global optimization algorithm,” To appear in the Encylopedia of Optimization, 1999.Google Scholar
  37. D. R. Jones, C. C. Perttunen, and B. E. Stuckman, “Lipschitzian optimization without the lipschitz constant,” J. Optim. Theory Appl. vol. 79, pp. 157–181, 1993.Google Scholar
  38. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, no. 16: Frontiers in Applied Mathematics. SIAM: Philadelphia, 1995.Google Scholar
  39. C. T. Kelley, Iterative Methods for Optimization, no. 18: Frontiers in Applied Mathematics. SIAM: Philadelphia, 1999.Google Scholar
  40. J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. vol. 7, pp. 308–313, 1965.Google Scholar
  41. D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comp. vol. 24, pp. 647–657, 1970.Google Scholar
  42. D. Stoneking, G. Bilbro, R. Trew, P. Gilmore, and C. T. Kelley, “Yield optimization using a GaAs process simulator coupled to a physical device model,” IEEE Transactions on Microwave Theory and Techniques vol. 40, pp. 1353–1363, 1992.Google Scholar
  43. V. Torczon, “On the convergence of the multidimensional direct search,” SIAM J. Optim. vol. 1, pp. 123–145, 1991.Google Scholar
  44. V. Torczon, “On the convergence of pattern search algorithms,” SIAM J. Optim. vol. 7, pp. 1–25, 1997.Google Scholar
  45. Y. Yao, “Dynamic tunneling algorithm for global optimization,” IEEE Transactions on Systems, Man, and Cybernetics vol. 19, no. 5, pp. 1222–1230, 1989.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • R.G. Carter
    • 1
  • J.M. Gablonsky
    • 2
  • A. Patrick
    • 2
  • C.T. Kelley
    • 2
  • O.J. Eslinger
    • 3
  1. 1.Stoner Associates, IncHoustonUSA
  2. 2.Center for Research in Scientific Computation and Department of MathematicsNorth Carolina State UniversityRaleighUSA
  3. 3.TICAM, 3SWo1B ACEAustinUSA

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