Integration of two multiobjective optimization methods for nonlinear problems

Optimization Methods and Software

Volumn 18, Issue 1, 2003, Pages 63-80

  Miettinen, Kaisa ^a   Lotov, Alexander V ^b   Kamenev, George K ^b   Berezkin, Vadim E ^b  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

^b RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

Classification; Decision support; Feasible goals method; Multiobjective optimization; NIMBUS method; WWW NIMBUS

Indexed keywords

DECISION MAKING; DECISION SUPPORT SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING; VECTORS;

FEASIBLE GOAL METHOD; MULTIOBJECTIVE OPTIMIZATION;

OPTIMIZATION;

EID: 0038359362     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/1055678031000116538     Document Type: Article

References (28)

1. V. Berezkin, G. Kamenev and A. Lotov (2000). Implementation of the Feasible Goals Method for Non-Linear Models in MS Excel. Computer Center of RAS, Moscow (in Russian).
2. A. Charnes and W.W. Cooper (1961). Management Models and Industrial Applications of Linear Programming, Vol. 1, John Wiley & Sons, New York.
3. J. Climaco and C.H. Antunes (1991). Flexible method bases and man-machine interfaces as key features in interactive MOLP approaches. In: P. Korhonen, A. Lewandowski and Wallenius (Eds.), Multiple Criteria Decision Support, pp. 209-216. Springer-Verlag, Berlin.
4. J. Cohon (1978). Multiobjective Programming and Planning. Academic Press, New York.
5. L.R. Gardiner and R.E. Steuer (1994). Unified interactive multiple objective programming. European J. Oper. Res., 74(3), 391-406.
6. A.M. Geoffrion, J.S. Dyer and A. Feinberg (1972). An interactive approach for multi-criterion optimization, with an application to the operation of an academic department. Management Science, 19(4), 357-368.
7. J.P. Hämäläinen, K. Miettinen, P. Tarvainen and J. Toivanen (2003). Interactive solution approach to a multiobjective optimization problem in paper machine headbox design. J. Optim. Theory Appl., 116(2), 265-281.
8. A. Jaszkiewicz and R. Slowinski (1999). The 'Light Beam Search' approach - an overview of methodology and applications. European J. Oper. Res., 113(2), 300-314.
9. G.K. Kamenev and D.L. Kondtrat'ev (1992). Method for the exploration of non-closed nonlinear models. Mat. Model., 4(3), 105-118 (in Russian).
10. G.K. Kamenev (2001). Approximation of completely bounded sets by the method of deep holes. Comput. Math. Math. Phys., 41(11), 1667-1675.
11. R.L. Keeney and H. Raiffa (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs. John Wiley & Sons, New York.
12. P. Korhonen and J. Wallenius (1990). A multiple objective linear programming decision support system. Decision Support Systems, 6(3), 243-251.
13. O. Larichev (1992). Cognitive validity in design of decision aiding techniques. Journal of Multi-Criteria Decision Analysis, 1(3), 127-138.
14. A. Lotov (1996). Comment to the Paper by D.J. White "A characterization of the feasible set of objective function vectors in linear multiple objective problems". European J. Oper. Res., 89(1), 215-220.
15. A. Lotov, V. Bushenkov and O. Chernykh (1997). Multi-criteria DSS for river water quality planning. Microcomputers in Civil Engineering, 12(1), 57-67.
16. A. V. Lotov, V.A. Bushenkov and G.K. Kamenev (1999). Feasible Goals Method. Edwin Mellen Press, Lewiston, New York (in Russian).
17. A. V. Lotov, V.A. Bushenkov and G.K. Kamenev (2001). Feasible Goals Method. Search for Smart Decisions. Computing Center of RAS, Moscow.
18. A. V. Lotov, V.A. Bushenkov, O.L. Chernykh, H. Wallenius and J. Wallenius (1998). Interactive decisions map, with an example illustrating ocean waste management decisions. In: T.J. Stewart and R.C. van den Honert (Eds.), Trends in Multicriteria Decision Making, pp. 313-323, Springer-Verlag, Berlin.
19. K.M. Miettinen (1999). Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston.
20. K. Miettinen and M.M. Mäkelä (1995). Interactive bundle-based method for nondifferentiable multiobjective optimization: NIMBUS. Optimization, 34(3), 231-246.
21. K. Miettinen and M.M. Mäkelä (1999). Comparative evaluation of some interactive reference point-based methods for multi-objective optimisation. Journal of the Operational Research Society, 50(9), 949-959.
22. K. Miettinen and M.M. Mäkelä (2000). Interactive multiobjective optimization system WWW-NIMBUS on the Internet. Comput. Oper. Res., 27(7-8), 709-723.
23. K. Miettinen and M.M. Mäkelä (2002). On scalarizing functions in multiobjective optimization. OR Spectrum, 24(2), 193-213.
24. K. Miettinen, M.M. Mäkelä and T. Männikkö (1998). Optimal control of continuous casting by nondifferentiable multiobjective optimization. Comput. Optim. Appl., 11(2), 177-194.
25. G.R. Reeves and J.J. Gonzales (1989). A comparison of two interactive MCDM procedures. European J. Oper. Res., 41(2), 203-209.
26. C. Romero (1991). Handbook of Critical Issues in Goal Programming. Pergamon Press.
27. R.E. Steuer (1986). Multiple Criteria Optimization: Theory, Computation, and Application. John Wiley & Sons, New York.
28. M. Tamiz, D. Jones and C. Romero (1998). Goal programming for decision making: an overview of the current state-of-the-art. European J. Oper. Res., 111(3), 569-581.