Skip to main content

An Interactive Multiobjective Complex Search for Stochastic Problems

  • Chapter
Models & Methods for Project Selection

Abstract

In Chapter 8 we described a sampling based procedure for stochastic multiobjective mathematical programming problems. In this chapter we will present a procedure which also uses sampling but in a more structured approach. The method presented here is an interactive procedure based on Box’s complex search. It requires the decision maker to provide progressive articulation of preferences. This method has an advantage over the interactive methods described in Chapter 8 in that the decision maker’s underlying value function need not be explicitly specified. Also, the problem may have nonlinear objective functions and nonlinear constraints as well as objective function coefficients that are random variables.

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

Access this chapter

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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Benayoun, R., de Montgolfier, J., Tergny, J. and Larichev, O. (1971) Linear programming with multiple objective functions: Step method (STEM). Mathematical Programming 1(3), 366–375.

    Article  Google Scholar 

  • Biles, W.E. & Swain, J.J. (1979). Mathematical programming and the optimization of computer simulation. Mathematica/Programming Study 11, 189–207.

    Article  Google Scholar 

  • Box, M.J., (1965). A new method of constrained optimization and a comparison with other methods. Computer Journal 8(42), 42–52.

    Article  Google Scholar 

  • Dyer, J.S. (1972). Interactive goal programming. Management science 19(1), 62–70.

    Article  Google Scholar 

  • Fichefet, J (1976). GpSTEM: an interactive multiobjective optimization method. In: A. Prekopa (Ed..), Progress in Operations Research. Vol. 1, (pp. 317–332). Amsterdam, North-Holland.

    Google Scholar 

  • Frank, M. & Wolfe, P. (1956) An algorithm for quadratic programming. Naval Research Logistics Quarterly 3(1), 95–110.

    Article  Google Scholar 

  • Geoffrion, A.M., Dyer, J.S. & Feinberg, A. (1972). An interactive approach for multi-criterion optimization, With an application to the operation of an academic department. Management Science 19(4), 357–368.

    Article  Google Scholar 

  • Guin, J.A., (1968) Modification of the complex method of constrained optimization. Computer Journal 10, 416–417.

    Article  Google Scholar 

  • Haimes, Y.Y. & Hall, W.A. (1974). Multiobjectives in water resources systems analysis: the surrogate worth trade-off method. Water Resources Research 10(4), 615–623.

    Article  Google Scholar 

  • Keeney, R.L. (1972). An illustrated procedure for assessing multiattributed utility functions. Sloan Management Review 14, 31–50.

    Google Scholar 

  • Kryzsztofowicz, R., Castano, E. & Fike, R. (1977). Comment on ‘A review and evaluation of multi-objective programming techniques’ by J.L. Cohon and D.H. Marks, Water Resources Research 13(3) 690–692.

    Article  Google Scholar 

  • Kuester, J.L. & Mize, J.H. (1973). Optimization techniques with FORTRAN. New York, McGraw Hill.

    Google Scholar 

  • Monarchi, D.E., Kisiel, C.C. & Duckstein, L. (1973). Interactive multi-objective programming in water resources: a case study. Water Resources Research 9(4), 837–850.

    Article  Google Scholar 

  • Nelder, J.A. & Mead, R. (1964). A simplex method for function minimization. Computer Journal 7, 308–313.

    Article  Google Scholar 

  • Ringuest, J.L. & Gulledge, Jr., T.R. (1985). Interactive multi-objective complex search. European Journal of Operational Rresearch 19, 362–371.

    Article  Google Scholar 

  • Rosenbrock, H.H. (1960). An automatic method for finding the greatest or least value of a function. Computer Journal 3, 175–184.

    Article  Google Scholar 

  • Spendley, W., Hext, G.R. and Himsworth, F.R. (1962). Sequential applications of simplex designs in optimization and evolutionary operation. Technometrics 4, 441–461.

    Article  Google Scholar 

  • Steuer, R.E. & Schuler, A.T. (1978). An interactive multiple objective linear programming approach to a problem in forest management. Operations Research 26(2), 254–269.

    Article  Google Scholar 

  • Zeleny, M. (1974). A concept of compromise solutions and the method of the displaced ideal. Computers and Operations Research 1(4), 479–496

    Article  Google Scholar 

  • Zionts, S. & Wallenius, J. (1983). An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions. Management Science 29(5), 519–529.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media New York

About this chapter

Cite this chapter

Graves, S.B., Ringuest, J.L., Medaglia, A.L. (2003). An Interactive Multiobjective Complex Search for Stochastic Problems. In: Models & Methods for Project Selection. International Series in Operations Research & Management Science, vol 58. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0280-7_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-0280-7_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5001-9

  • Online ISBN: 978-1-4615-0280-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics