Integrative Population Analysis for Better Solutions to Large-Scale Mathematical Programs

  • Fred Glover
  • John Mulvey
  • Dawei Bai
  • Michael T. Tapia
Part of the Applied Optimization book series (APOP, volume 16)

Abstract

Integrative Population Analysis unties the learning process called target analysis and a generalized form of sensitivity analysis to yield improved approaches for optimization, particularly where problems from a particular domain must be solved repeatedly. The resulting framework introduces an adaptive design for mapping problems to groups, as a basis for identifying processes that permit problems within a given group to be solved more effectively. We focus in this paper on processes embodied in parameter-based definitions of regionality,accompanied by decision rules that extract representative solutions from given regions in order to yield effective advanced starting points for our solution methods. Applied to several industrial areas, our approach generates regions and representations that give an order of magnitude improvement in the time required to solve new problems that enter the population and therefore makes the application of large scale optimization models practical in reality.

Keywords

Data Envelopment Analysis Model Artificial Agent Efficient Frontier Representative Agent Indifference Curve 
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.

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References

  1. [1]
    D. R. Carino, T. Kent, D.H. Myers, C. Stacy, M. Sylvanus, A. Turner, K. Watanabe, and W.T. Ziemba, 1994, The Russell—Yasuda Kasai Financial Planning Model, Interfaces, 24, 29–49.CrossRefGoogle Scholar
  2. [2]
    A. Brooke, D. Kendrick, and A. Meeraus, 1988, GAMS: A user’s guide, Scientific Press, Redwood City.Google Scholar
  3. [3]
    R. Fourer, D.M. Gay, and B.W. Kernighan, 1993, AMPL: A Modeling Language for Mathematical Programming, The Scientific Press, San Francisco.Google Scholar
  4. [4]
    M. R. Anderberg, 1973, Cluster Analysis for Applications, Academic Press, New York.Google Scholar
  5. [5]
    F. Glover and H.J. Greenberg, 1989, New approaches for heuristic search: A bilateral linkage with artificial intelligence, European Journal of Operations Research, 39, 119–130.CrossRefGoogle Scholar
  6. [6]
    F. Glover, 1986, Future paths for integer programming and links to artificial intelligence, Computers and Operations Research, 13, 533–549.CrossRefGoogle Scholar
  7. [7]
    M. Laguna and F. Glover, 1993, Integrating target analysis and tabu search for improved scheduling systems, Expert System with Applications, 6, 287297.Google Scholar
  8. [8]
    F. Glover, 1995, Tabu Search fundamentals and uses, University of Colorado, Boulder, CO 80309–0419, Technical report.Google Scholar
  9. [9]
    D. Kraay and P. Harker, 1995, Case Based Reasoning for Repetitive Combinatorial Optimization Problems, Part I: Framework and Part I I: Numerical, Purdue University and the Wharton School, Technical Report(s).Google Scholar
  10. [10]
    S. Andradottir, 1995, A Stochastic Approximation Algorithm with Varying Bounds, Operations Research, 13, 1037–1048.CrossRefGoogle Scholar
  11. [11]
    F. Glover, J. Kelly, and M. Laguna, 1995, Tabu Search and Hybrid Methods for Optimization, INFORMS Conference.Google Scholar
  12. [12]
    R. Barr and M. Durchholz, 1996, Parallel and Hierarchical Decomposition Approaches for Solving Large-Scale Data Envelopment Analysis Models, to appear, Annals of Operations Research. (Technical report available).Google Scholar
  13. [13]
    F. Glover, J. Mulvey and Dawei Bai, 1996, Improved Approaches To Optimization Via Integrative Population Analysis, Princeton University and University of Colorado, Technical Report SOR-95–25, 1996.Google Scholar
  14. [14]
    N. Ireland, 1987, Product Differentiation and Non-Price Competition, Basil Blackwell, New York.Google Scholar
  15. [15]
    S. Anderson, A. Palma and J. Thisse, 1992, Discrete Choice Theory of Product Differentiation, The MIT Press, Cambridge, Massachusetts.Google Scholar
  16. [16]
    D. Bai, T. Carpenter, and J. Mulvey, 1994, Stochastic programming to promote network survivability, Department of Civil Engineering and Operations Research, Princeton University, Technical Report SOR-94–14.Google Scholar
  17. [17]
    G. Infanger, 1994, Planning under uncertainty: solving large-scale stochastic linear programs,Boyd and Fraser Publishing Company.Google Scholar
  18. [18]
    L. A. Cox, W. E. Kuehner, S. H. Parrish, and Y. Qiu, 1993, Optimal Expansion of Fiber-Optic Telecommunication Networks in Metropolitan Areas, Interfaces, 23, 35–48.CrossRefGoogle Scholar
  19. [19]
    K. Lancaster, 1966, A new approach to consumer theory, Journal of Political Economy, 74, 132–57.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Fred Glover
    • 1
  • John Mulvey
    • 2
  • Dawei Bai
    • 2
  • Michael T. Tapia
    • 3
  1. 1.The University of Colorado at BoulderBoulderUSA
  2. 2.Department of Civil Engineering and Operations ResearchPrinceton UniversityPrincetonUSA
  3. 3.Department of Management Science and Information SystemsThe University of Texas at AustinAustinUSA

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