Skip to main content
SpringerLink
Log in

A Reference Direction Interactive Algorithm of the Multiple Objective Nonlinear Integer Programming

  • Conference paper
Multiple Criteria Decision Making

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 448))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Britton, J.K. “Integer Solution of Systems of Quadratic Equations”, Mathematical Proceedings of the Cambridge Philosophical Society, 86, No 3, (1979) pp. 385–389.

    Article  Google Scholar 

  2. Evans G., “An Overview of Techniques for Solving Multiobjective Mathematical Programs”, Management Science, 30, No 11, (1984), pp. 1268–1282.

    Article  Google Scholar 

  3. Garey M. R. and Johnson D. S. Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, San Francisco 1979.

    Google Scholar 

  4. Gouljashki V., “An Exact Search Procedure for Solving Single Objective Convex Integer Problems and its Implementation in Multiobjective Programming”, In: S. M. Markov (eds.): Scientific Computation and Mathematical Modelling, Proceedings of the International Conference on Mathematical Modelling and Scientific Computation (MMSC93), September 14–18. 1993, Sozopol, BULGARIA, 1993, pp. 117–120.

    Google Scholar 

  5. Gouljashki V., “Methods, Combining an Exact Search Procedure with the Methaheuristic Tabu Search for Solving the Convex Integer Programming Problem”, In: A. Popov, R. Romanski (eds.): Automated Systems —Design and Applications, Proceedings of the 7-th International Conference “Systems for Automation of Engineering and Research”, (SAER’93), vol.1, October, 01.-03.1993, St. Konstantin — Varna, BULGARIA, 1993, pp. 255–259.

    Google Scholar 

  6. Gouljashki V. and V. Vassilev, “Two Nonlinear Integer Optimization Algorithms — Comparative Analysis of Test Results”, Problems of Engineering Cybernetics and Robotics, 43, (1995), 15–23.

    Google Scholar 

  7. Glover F. and McMillan C. “The General Employee Scheduling Problem: An Integration of MS and AI”, Computers and Operations Research 13, 5, (1986), pp. 563–573.

    Article  Google Scholar 

  8. Glover F. “Future Paths for Integer Programming and Links to Artificial Intelligence”, Computers and Operations Research 13, 5, (1986), pp. 533–549.

    Article  Google Scholar 

  9. Gupta O. K. and Ravindran A., “Branch and Bound Experiments in Convex Nonlinear Integer Programming”, Man. Sci. 31,12, (1985), pp. 1533–1546.

    Article  Google Scholar 

  10. Hachijan, L. G., “Convexity and Algorithmic Complexity of the Polynomial Programming Problems”, Izvestija AS-USSR. Technicheskaja Kibernetika, 6, (1982), pp. 45–56 (in Russian).

    Google Scholar 

  11. Jeroslaw, R. G., “There Cannot be Any Algorithm for Integer Programming with Quadratic Constraints”, Operations Research, 21, (1973), 221–224.

    Article  Google Scholar 

  12. Korhonen P. and J. Laakso, “A Visual Interactive Method for Solving the Multiple Criteria Problem”, European Journal of Operational Research, vol. 24, (1986) pp. 277–287.

    Article  Google Scholar 

  13. Korhonen P. and J. Wallenius “A Multiple Objective Linear Programming Decision Support System”, Decision Support Systems, vol. 6, (1990), pp. 243–251.

    Article  Google Scholar 

  14. Narula S., Kirilov L., Vassilev V., “Reference Direction Approach for Solving Multiple Objective Nonlinear Problems”, IEEE Transaction on System, Man, and Cybernetics, 24, No 5, (1994), pp. 804–806.

    Article  Google Scholar 

  15. Narula S., Vassilev V. “An Interactive Algorithm for Solving Multiple Objective Integer Linear Programming Problems”, European Journal of Operational Research, 74, (1994), pp. 170–178.

    Article  Google Scholar 

  16. Nemhauser G.L. and Wolsey L.A. Integer and Combinatorial Optimization, Wiley, New York, 1988.

    Google Scholar 

  17. Papadimitriou, C. H. and Steiglitz, K. Combinatorial Optimization: Algorithms and Complexity, Prentice Hall, Englewood Cliffs, N. J. 1982.

    Google Scholar 

  18. Ramesh R., S. Zionts, M. H. Karwan, “A Class of Practical Interactive Branch and Bound Algorithms for Multicriteria Integer Programming”, European Journal of Operational Research, 26, (1986), pp. 83–95.

    Article  Google Scholar 

  19. Steuer R., Multiple Criteria Optimization Tlteory, Computation and Application, John Wiley & Sons, New York, 1986.

    Google Scholar 

  20. Teghem, J., P.L. Kunsh, “Interactive Methods for Multiobjective Integer Linear Programming”, In: G. Fandel, M. Graur, A. Karzanski, and A. P. Wierzbicki, (eds.) Large Scale Modelling and Interactive Decision Analysis., Springer Verlag, Berlin, 1985, pp. 75–87.

    Google Scholar 

  21. Vassilev V., Narula S., “A Reference Direction Algorithm for Solving Multiple Objective Integer Linear Programming Problems”, Journal of the Operational Research Society, 44, No 12, (1993) 1201–1209.

    Google Scholar 

  22. Werra D. and A. Hertz, “Tabu Search Techniques: A Tutorial and an Application to Neural Networks”, OR Spectrum, (1989) pp. 131–141.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Information Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 29A, Sofia, 1113, Bulgaria

    Vassil G. Gouljashki, Leonid M. Kirilov & Vassil S. Vassilev

  2. School of Business, Virginia Commonwealth University, Richmond, VA, 23284-4000, USA

    Subhash C. Narula

Authors
  1. Vassil G. Gouljashki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leonid M. Kirilov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Subhash C. Narula
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vassil S. Vassilev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fernuniversität Hagen, Fachbereich Wirtschaftswissenschaft, Feithstrasse l40/AVZ II, D-58097, Hagen, Germany

    Günter Fandel

  2. Thomas Hanne Fernuniversität Hagen Fachbereich Wirtschaftswissenschaft, Fach Operations Research und Wirtschaftsmathematik, Lütkenheider Strasse 2, D-58084, Hagen, Germany

    Tomas Gal

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gouljashki, V.G., Kirilov, L.M., Narula, S.C., Vassilev, V.S. (1997). A Reference Direction Interactive Algorithm of the Multiple Objective Nonlinear Integer Programming. In: Fandel, G., Gal, T. (eds) Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59132-7_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59132-7_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62097-6

  • Online ISBN: 978-3-642-59132-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation