Stochastic Adaptive Search

  • Graham R. Wood
  • Zelda B. Zabinsky
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 62)


Large scale optimisation problems are often tackled using stochastic adaptive search algorithms, but the convergence of such methods to the global optimum is generally poorly understood. In recent years a variety of theoretical stochastic adaptive algorithms have been put forward and their favourable convergence properties confirmed analytically. Such research has two purposes: it offers some understanding of the convergence of stochastic adaptive methods while also providing motivation for the development of practical algorithms which approximate the ideal performance. This chapter summarises these developments.


Localisation Search Global Optimization Global Optimization Problem Termination Region Adaptive Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderssen, R.S. (1972). Global optimization. In Anderssen, R.S., Jennings, L.S., and Ryan, D.M., editors, Optimization,pages 1–15. University of Queensland Press.Google Scholar
  2. Baritompa, W.P., Mladineo, R.H., Wood, G.R., Zabinsky, Z.B., and Zhang, B. (1995). Towards pure adaptive search. Journal of Global Optimization, 7: 93–110.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Brooks, S.H. (1958). A discussion of random methods for seeking maxima. Operations Research, 6: 244–251.MathSciNetCrossRefGoogle Scholar
  4. Bulger, D.W., Baritompa, W.P., and Wood, G.R. (2000). Implementing pure adaptive search with Grover’s quantum algorithm. Scholar
  5. Bulger, D.W. and Wood, G.R. (1996). On the convergence of localisation search. In Floudas, C.A. and Pardalos, Panos M., editors, State of the Art in Global Optimization: Computational methods and applications,pages 227–233. Kluwer Academic Publishers.Google Scholar
  6. Bulger, D.W. and Wood, G.R. (1998). Hesitant adaptive search for global optimisation. Mathematical Programming, 81: 89–102.MathSciNetzbMATHGoogle Scholar
  7. Dixon, L.C.W. and Szegö, G.P., editors (1975). Towards Global Optimization. North-Holland, Amsterdam.Google Scholar
  8. Dixon, L.C.W. and Szegö, G.P., editors (1978). Towards Global Optimization 2. North-Holland, Amsterdam.Google Scholar
  9. Grover, L.K. (1996). A fast quantum mechanical algorithm for database search. In Proceedings of the 28th annual ACM symposium on theory of computing.Google Scholar
  10. Hendrix, E.M.T. and Klepper, O. (2000). On uniform covering, adaptive random search and raspberries. Journal of Global Optimization, 18: 143–163.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Johnson, N.L., Kotz, S., and Kemp, A.W. (1992). Univariate Discrete Distributions. John Wiley and Sons, New York.zbMATHGoogle Scholar
  12. Kristinsdottir, B.P., Zabinsky, Z.B., and Wood, G.R. (2001). Discrete backtracking adaptive search for global optimization. In Dzemyda, G., Saltenis, V., and Zilinskas, A., editors, Stochastic methods in global optimization, dedicated to the 70th anniversary of Professor J. Mockus. Kluwer Academic Publishers. To appear.Google Scholar
  13. Mladineo, R.H. (1986). An algorithm for finding the global maximum of a multimodal, multivariate function. Mathematical Programming, 34: 188–200.MathSciNetzbMATHCrossRefGoogle Scholar
  14. Patel, N.R., Smith, R.L., and Zabinsky, Z.B. (1988). Pure adaptive search in Monte Carlo optimization. Mathematical Programming, 43: 317–328.MathSciNetCrossRefGoogle Scholar
  15. Piyayskii, S.A. (1972). An algorithm for finding the absolute extremum of a function. USSR Comp. Math. and Math. Phys., 12: 57–67.CrossRefGoogle Scholar
  16. Reaume, D.J., Romeijn, H.E., and Smith, R.L. (2001). Implementing pure adaptive search for global optimization using 1VIarkov chain sampling. Journal of Global Optimization, 20: 33–47.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Romeijn, H.E. and Smith, R.L. (1994a). Simulated annealing and adaptive search in global optimization. Probability in the Engineering and Informational Sciences, 8: 571–590.CrossRefGoogle Scholar
  18. Romeijn, H.E. and Smith, R.L. (1994b). Simulated annealing for constrained global optimization. Journal of Global Optimization, 5: 101–126.MathSciNetzbMATHCrossRefGoogle Scholar
  19. Shubert, B.O. (1972). A sequential method seeking the global maximum of a function. SIAM J. Numer. Anal., 9: 379–388.MathSciNetzbMATHCrossRefGoogle Scholar
  20. Wood, G.R. (1992). The bisection method in higher dimensions. Mathematical Programming, 55: 319–337.MathSciNetzbMATHCrossRefGoogle Scholar
  21. Wood, G.R., Zabinsky, Z.B., and Kristinsdottir, B.P. (2001). Hesitant adaptive search: the distribution of the number of iterations to convergence. Mathematical Programming, 89: 479–486.MathSciNetzbMATHCrossRefGoogle Scholar
  22. Zabinsky, Z.B. and Smith, R.L. (1992). Pure adaptive search in global optimization. Mathematical Programming, 53: 323–338.Google Scholar
  23. 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
  24. Zabinsky, Z.B., Wood, G.R., Steel, M.A., and Baritompa, W.P. (1995). Pure adaptive search for finite global optimization. Mathematical Programming, 69: 443–448.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Graham R. Wood
    • 1
  • Zelda B. Zabinsky
    • 2
  1. 1.Institute of Information Sciences and TechnologyMassey UniversityPalmerston NorthNew Zealand
  2. 2.Industrial EngineeringUniversity of WashingtonSeattleUSA

Personalised recommendations