Skip to main content
SpringerLink
Log in

Stochastic Methods for Practical Global Optimization

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

Engineering design problems often involve global optimization of functions that are supplied as ‘black box’ functions. These functions may be nonconvex, nondifferentiable and even discontinuous. In addition, the decision variables may be a combination of discrete and continuous variables. The functions are usually computationally expensive, and may involve finite element methods. An engineering example of this type of problem is to minimize the weight of a structure, while limiting strain to be below a certain threshold. This type of global optimization problem is very difficult to solve, yet design engineers must find some solution to their problem – even if it is a suboptimal one. Sometimes the most difficult part of the problem is finding any feasible solution. Stochastic methods, including sequential random search and simulated annealing, are finding many applications to this type of practical global optimization problem. Improving Hit-and-Run (IHR) is a sequential random search method that has been successfully used in several engineering design applications, such as the optimal design of composite structures. A motivation to IHR is discussed as well as several enhancements. The enhancements include allowing both continuous and discrete variables in the problem formulation. This has many practical advantages, because design variables often involve a mixture of continuous and discrete values. IHR and several variations have been applied to the composites design problem. Some of this practical experience is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bulger, D. W. and Wood, G. R. (1998), Hesitant adaptive search for global optimisation, Mathematical Programming 81(1): 89–102.

    Google Scholar 

  2. Dekkers, A. and Aarts, E. (1991), Global optimization and simulated annealing, Mathematical Programming 50: 367–393.

    Google Scholar 

  3. Graesser, D. L., Zabinsky, Z. B., Tuttle, M. E. and Kim, G. I. (1991), Designing laminated composites using random search techniques, Composite Structures 18: 311–325.

    Google Scholar 

  4. Graesser, D. L., Zabinsky, Z. B., Tuttle, M. E. and Kim, G. I. (1993), Optimal design of composite structures, Composite Structures 24: 273–281.

    Google Scholar 

  5. Haftka, R. T. and Gürdal, Z. (1992), Elements of Structural Optimization, Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  6. Horst, R. and Pardalos, P. M. (1995), Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  7. Jones, R. M. (1975), Mechanics of Composite Materials, Scripta Book, Washington, D. C.

    Google Scholar 

  8. Kirkpatrick, S., Gelatt, C. D. Jr. and Vecchi, M. P. (1983), Optimization by simulated annealing, Science 220(4598): 671–679.

    Google Scholar 

  9. Kristinsdottir, B. P. (1997), Analysis and Development of Random Search Algorithms, Ph. D. Dissertation, University of Washington, Seattle.

    Google Scholar 

  10. Lawrence, J. P. III and Steiglitz, K. (1972), Randomized pattern search, IEEE Transactions on Computers C-21: 382–385.

    Google Scholar 

  11. Locatelli, M. (1996), Convergence properties of simulated annealing for continuous global optimization, Journal of Applied Probability 33: 1127–1140.

    Google Scholar 

  12. Mabson, G. E., Flynn, B. W., Ilcewicz, L. B. and Graesser, D. L. (1994), The use of COSTADE in developing composite commercial aircraft fuselage structures, Proceedings of the 35th AIAA/ASME/ASCE/AHS/ASC Structure, Structural Dynamics, and Materials Conference, Hilton Head, SC.

    Google Scholar 

  13. Mabson, G. E., Fredrikson, H. G., Graesser, D. L., Metschan, S. L., Proctor, M. R., Stogin, D. C., Tervo, D. K., Zabinsky, Z. B., Tuttle, M. E. and Gutowski, T. G. (1995), Cost optimization software for transport aircraft design evaluation, Proceedings of the 6th NASA/DOD/ARPA Advanced Composite Technology Conference.

  14. Metschan, S. L., Graesser, D. L., Mabson, G. E., Proctor, M. R., Tervo, D. K. and Ilcewicz, L. B. (1994), Manufacturing data for costade analysis of composite fuselage panels, Proceedings of the 5th NASA ACT Conference.

  15. Mutseniyeks, V. A. and Rastrigin, L. A. (1964), Extremal control of continuous multi-parameter systems by the method of random search, Engineering Cybernetics 1: 82–90.

    Google Scholar 

  16. Neogi, S. (1997), Design of Large Composite Structures using Global Optimization and Finite Element Analysis, Ph. D. Dissertation, University of Washington, Seattle.

    Google Scholar 

  17. Neogi, S., Zabinsky, Z. B. and Tuttle, M. E. (1994), Optimal design of composites using mixed discrete and continuous variables, Proceedings of the ASME Winter Annual Meeting, Symposium on Processing, Design and Performance of Composite Materials, MD-Vol. 52, pp. 91–107.

    Google Scholar 

  18. Neogi, S., Zabinsky, Z. B., Tuttle, M. E. and Kristinsdottir, B. P. (1995), Load redistribution issues in optimal design of composites airplane structures, Proceedings of the ICCE/2 Conference, New Orleans.

  19. Patel, N. R., Smith, R. L. and Zabinsky, Z. B. (1988), Pure adaptive search in Monte Carlo optimization, Mathematical Programming 4: 317–328.

    Google Scholar 

  20. Rastrigin, L. A. (1960), Extremal control by the method of random scanning, Automation and Remote Control 21: 891–896.

    Google Scholar 

  21. Rastrigin, L. A. (1963), The convergence of the random search method in the extremal control of a many-parameter system, Automation and Remote Control 24: 1337–1342.

    Google Scholar 

  22. Romeijn, H. E. and Smith, R. L. (1994), Simulated annealing for constrained global optimization, Journal of Global Optimization 5: 101–126.

    Google Scholar 

  23. Romeijn, H. E., Zabinsky, Z. B., Graesser, D. L. and Neogi, S. (1995), Simulated annealing for mixed integer/continuous global optimization, technical report Erasmus University. Forthcoming in Journal of Optimization: Theory and Applications 101(1) (April 1999).

  24. Schrack, G. and Borowski, N. (1972), An experimental comparison of three random searches, in F. Lootsma (ed.), Numerical Methods for Nonlinear Optimization, pp. 137–147, Academic Press, London.

    Google Scholar 

  25. Schrack, G. and Choit, M. (1976), Optimized relative step size random searches, Mathematical Programming 10: 230–244.

    Google Scholar 

  26. Schumer, M. A. and Steiglitz, K. (1968), Adaptive step size random search, IEEE Transactions on Automatic Control AC-13: 270–276.

    Google Scholar 

  27. Seifer, J. D. (1995) Incorporating realistic engineering considerations into the optimal design of composite structures, Master's Thesis, University of Washington, Seattle.

    Google Scholar 

  28. Smith, R. L. (1984), Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions, Operations Research 32: 1296–1308.

    Google Scholar 

  29. Solis, F. J. and Wets, R. J.-B. (1981), Minimization by random search techniques, Mathematics of Operations Research 6: 19–30.

    Google Scholar 

  30. Swanson, G. D., Ilcewicz, L. B., Walker, T., Graesser, D. L., Tuttle, M. E. and Zabinsky, Z. B. (1991), Local design optimization for transport fuselage crown panels, Proceedings of the 9th DoD/NASA/FAA Conference on Fibrous Composites in Structural Design, Lake Tahoe, Nevada.

    Google Scholar 

  31. Vanderplaats, G. N. (1993) Thirty years of modern structural optimization, Advances in Engineering Software 16: 81–88.

    Google Scholar 

  32. Wood, G. R., Zabinsky, Z. B. and Kristinsdottir, B. P. (1997), Hesitant adaptive search: the distribution of the number of iterations to convergence, technical report, Central Queensland University.

  33. Zabinsky, Z. B. (1994), Global optimization for composite structural design, Proceedings of the 35th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material Conference, Hilton Head, SC.

    Google Scholar 

  34. Zabinsky, Z. B., Graesser, D. L., Tuttle, M. E. and Kim, G. I. (1992), Global optimization of composite laminate using Improving Hit and Run, in C. A. Floudas and P. M. Pardalos (eds.), Recent Advances in Global Optimization, pp. 343–365, Princeton University Press, Princeton.

    Google Scholar 

  35. Zabinsky, Z. B., Seifer, J. D., Tuttle, M. E., Kristinsdottir, B. P. and Neogi, N. (1995), Optimal design of composite panels with varying loads, Proceedings of the ICCE/2 Conference, New Orleans.

  36. Zabinsky, Z. B. and Smith, R. L. (1992), Pure adaptive search in global optimization, Mathematical Programming 53: 323–338.

    Google Scholar 

  37. Zabinsky, Z. B., Smith, R. L., McDonald, J. F., Romeijn, H. E. and Kaufman, D. E. (1993), Improving Hit and Run for global optimization, Journal of Global Optimization 3: 171–192.

    Google Scholar 

  38. Zabinsky, Z. B., Wood, G. R., Steel, M. A. and Baritompa, W. P. (1995), Finite pure adaptive search, Mathematical Programming 69: 443–448.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Industrial Engineering, University of Washington, Seattle, Washington, USA

    Zelda B. Zabinsky

Authors
  1. Zelda B. Zabinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zabinsky, Z.B. Stochastic Methods for Practical Global Optimization. Journal of Global Optimization 13, 433–444 (1998). https://doi.org/10.1023/A:1008350230239

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008350230239

Search

Navigation