Multiobjective bilevel optimization

Mathematical Programming

Volumn 123, Issue 2, 2010, Pages 419-449

  Eichfelder, Gabriele ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Bilevel optimization; Multicriteria optimization; Sensitivity; Two level optimization; Vector optimization

Indexed keywords

ADAPTIVE PARAMETERS; ARTIFICIAL PROBLEMS; BI-LEVEL OPTIMIZATION; BICRITERIA OPTIMIZATION; BILEVEL OPTIMIZATION PROBLEMS; EFFICIENT SETS; ITERATIVE PROCESS; MINIMAL SOLUTIONS; MULTI OBJECTIVE; MULTI-OBJECTIVE OPTIMIZATION PROBLEM; MULTICRITERIA OPTIMIZATION; OPTIMISTIC APPROACH; SCALARIZATION APPROACH; TWO-LEVEL OPTIMIZATION; VECTOR OPTIMIZATIONS;

MULTIOBJECTIVE OPTIMIZATION;

EID: 77949540007     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-008-0259-0     Document Type: Article

References (43)

1. M. Abo-Sinna 2001 A bi-level non-linear multi-objective decision making under fuzziness Opsearch 38 5 484 495 05230772 2220490
2. W. Alt 1991 Parametric optimization with applications to optimal control and sequential quadratic programming Bayreuther Math. Schr. 35 1 37 0734.90094 1104518
3. Bard, J.F.: Practical Bilevel Optimization. Algorithms and Applications. Nonconvex Optimization and Its Applications, vol. 30. Kluwer, Dordrecht (1998)
4. H. Bonnel J. Morgan 2006 Semivectorial bilevel optimization problem: Penalty approach J. Optim. Theory Appl. 131 3 365 382 05166365 10.1007/s10957-006-9150-4 2283538
5. I. Das J. Dennis 1997 A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems Struct. Optim. 14 63 69 10.1007/BF01197559
6. I. Das J. Dennis 1998 Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems SIAM J. Optim. 8 3 631 657 0911.90287 10.1137/S1052623496307510 1627156
7. Dempe S.: Foundations of Bilevel Programming. Nonconvex Optimization and Its Applications, vol. 61. Kluwer, Dordrecht (2002)
8. S. Dempe 2003 Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints Optimization 52 3 333 359 1140.90493 10.1080/0233193031000149894 1996321
9. Dempe, S.: Bilevel programming-a survey. Preprint 2003-11, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, Germany (2003)
10. Dinkelbach, W., Dürr, W.: Effizienzaussagen bei Ersatzprogrammen zum Vektormaximumproblem, iv. Oberwolfach-Tag. Operations Res 1971. Oper. Res. Verf. 12:69-77 (1972)
11. Ehrgott, M.: Multicriteria optimisation. Lect. Notes Econ. math. Syst, vol. 491. Springer, Berlin (2000)
12. Eichfelder, G.: Parametergesteuerte Lösung nichtlinearer multikriterieller Optimierungsprobleme. PhD Thesis, Univ. Erlangen- Nürnberg, Germany (2006)
13. Eichfelder, G.: Scalarizations for adaptively solving multi-objective optimization problems. Comput. Optim. Appl. (2007) doi: 10.1007/s10589-007-9155- 4
14. Eichfelder, G.: An adaptive scalarization method in multi-objective optimization. SIAM J. Optim. (to appear)
15. Fiacco, A.V.: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Mathematics in Science and Engineering, vol. 165. Academic Press, London (1983)
16. J. Fliege 2004 Gap-free computation of Pareto-points by quadratic scalarizations Math. Methods Oper. Res. 59 1 69 89 1131.90054 10.1007/s001860300316 2037450
17. J. Fliege LN Vicente 2006 Multicriteria approach to bilevel optimization J. Optim. Theory Appl. 131 2 209 225 1139.90417 10.1007/s10957-006-9136-2 2279595
18. Y. Haimes L. Lasdon D. Wismer 1971 On a bicriterion formulation of the problems of integrated system identification and system optimization IEEE Trans. Syst. Man Cybern. 1 296 297 0224.93016 10.1109/TSMC.1971.4308298 300411
19. C. Hillermeier J. Jahn 2005 Multiobjective optimization: Survey of methods and industrial applications Surv. Math. Ind. 11 1 42 1160.90651 10.1007/3-540-26949-5-1
20. Jahn J.: Vector Optimization: Theory, Applications and Extensions. Springer, Berlin (2004)
21. J. Jahn 2006 Multiobjective search algorithm with subdivision technique Comput. Optim. Appl. 35 161 175 1153.90533 10.1007/s10589-006-6450-4 2263915
22. J. Jahn A. Merkel 1992 Reference point approximation method for the solution of bicriterial nonlinear optimization problems J. Optim. Theory Appl. 74 1 87 103 0795.90056 10.1007/BF00939894 1168998
23. K. Jittorntrum 1984 Solution point differentiability without strict complementarity in nonlinear programming Math. Program. Study 21 127 138 0571.90080 751247
24. I. Kim O. de Weck 2005 Adaptive weighted sum method for bi-objective optimization Struct. Multidisciplinary Optim. 29 149 158 10.1007/s00158-004- 0465-1
25. J.G. Lin 2005 On min-norm and min-max methods of multi-objective optimization Math. Program. 103 1 1 33 10.1007/s10107-003-0462-y 2166532
26. P. Loridan 1984 ε-solutions in vector minimization problems J. Optim. Theory Appl. 43 265 276 0517.90074 10.1007/BF00936165 748600
27. Marglin S.: Public Investment Criteria. MIT Press, Cambridge (1967)
28. Miettinen K.M.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)
29. I. Nishizaki M. Sakawa 1999 Stackelberg solutions to multiobjective two-level linear programming problems J. Optim. Theory Appl. 103 1 161 182 0945.90057 10.1023/A:1021729618112 1714988
30. M. Osman M. Abo-Sinna A. Amer O. Emam 2004 A multi-level nonlinear multi-objective decision-making under fuzziness Appl. Math. Comput. 153 1 239 252 1049.90032 10.1016/S0096-3003(03)00628-3 2063158
31. A. Pascoletti P. Serafini 1984 Scalarizing vector optimization problems J. Optim. Theory Appl. 42 4 499 524 0505.90072 10.1007/BF00934564 739432
32. Prohaska, J.: Optimierung von Spulenkonfigurationen zur Bewegung magnetischer Sonden. Diplomarbeit, Univ. Erlangen-Nürnberg, Germany (2005)
33. S. Ruzika M. Wiecek 2005 Approximation methods in multiobjective programming J. Optim. Theory Appl. 126 3 473 501 1093.90057 10.1007/s10957-005- 5494-4 2164788
34. Sawaragi Y., Nakayama H., Tanino T.: Theory of Multiobjective Optimization. Number 176 in Mathematics in science and engineering. Academic Press, London (1985)
35. B. Schandl K. Klamroth M.M. Wiecek 2001 Norm-based approximation in bicriteria programming Comput. Optim. Appl. 20 1 23 42 0983.90081 10.1023/A:1011267305444 1849978
36. X. Shi H. Xia 1997 Interactive bilevel multi-objective decision making J. Oper. Res. Soc. 48 9 943 949 0892.90200
37. X. Shi H. Xia 2001 Model and interactive algorithm of bi-level multi-objective decision-making with multiple interconnected decision makers J. Multi-Criteria Decis. Anal. 10 27 34 0985.90054 10.1002/mcda.285
38. T. Staib 1988 On two generalizations of Pareto minimality J. Optim. Theory Appl. 59 2 289 306 0628.90076 974035
39. C.-X. Teng L. Li H.-B. Li 2000 A class of genetic algorithms on bilevel multi-objective decision making problem J. Syst. Sci. Syst. Eng. 9 3 290 296 1804255
40. H. Tuy A. Migdalas N. Hoai-Phuong 2007 A novel approach to bilevel nonlinear programming J. Global Optim. 38 4 527 554 1145.90083 10.1007/s10898-006-9093-1 2335310
41. L.N. Vicente P.H. Calamai 1994 Bilevel and multilevel programming: A bibliography review J. Glob. Optim. 5 3 291 306 0822.90127 10.1007/BF01096458 1299018
42. Y. Yin 2000 Multiobjective bilevel optimization for transportation planning and management problems J. Adv. Transp. 36 1 93 105
43. Younes, Y.: Studies on discrete vector optimization. Dissertation, University of Demiatta, Egypt (1993)