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Volumn 44, Issue 2, 2009, Pages 249-273

Scalarizations for adaptively solving multi-objective optimization problems

Author keywords

Adaptive parameter control; Approximation; Multi objective optimization; Scalarization; Sensitivity

Indexed keywords

ADAPTIVE PARAMETER CONTROL; APPROXIMATION; EFFICIENT SETS; HIGH QUALITY; MULTI-OBJECTIVE OPTIMIZATION PROBLEM; NORMAL BOUNDARY INTERSECTIONS; SCALARIZATION; SCALARIZATION APPROACH; SENSITIVITY; THEORETICAL RESULT;

EID: 70449523371     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-007-9155-4     Document Type: Article
Times cited : (65)

References (33)
  • 1
    • 0039267812 scopus 로고
    • A criterion for efficiency and some applications
    • B. Brosowski E. Martensen (eds). Peter Lang Frankfurt am Main
    • Brosowski, B.: A criterion for efficiency and some applications. In: Brosowski, B., Martensen, E. (eds.) Optimization in Mathematical Physics. Methoden und Verfahren der Mathematischen Physik, vol. 34, pp. 37-59. Peter Lang, Frankfurt am Main (1987)
    • (1987) Optimization in Mathematical Physics Methoden und Verfahren der Mathematischen Physik , vol.34 , pp. 37-59
    • Brosowski, B.1
  • 3
    • 0032348480 scopus 로고    scopus 로고
    • Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems
    • 0911.90287 10.1137/S1052623496307510 1627156
    • I. Das J.E. 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
    • (1998) SIAM J. Optim. , vol.8 , Issue.3 , pp. 631-657
    • Das, I.1    Dennis, J.E.2
  • 4
    • 0000898246 scopus 로고    scopus 로고
    • An improved technique for choosing parameters for Pareto surface generation using normal-boundary intersection
    • C.L. Bloebaum K.E. Lewis (eds) et al. University at Buffalo Buffalo
    • Das, I.: An improved technique for choosing parameters for Pareto surface generation using normal-boundary intersection. In: Bloebaum, C.L., Lewis, K.E., et al. (eds.) Proceedings of the Third World Congress of Structural and Multidisciplinary Optimization (WCSMO-3), vol. 2, pp. 411-413. University at Buffalo, Buffalo (1999)
    • (1999) Proceedings of the Third World Congress of Structural and Multidisciplinary Optimization (WCSMO-3) , vol.2 , pp. 411-413
    • Das, I.1
  • 5
    • 0442304861 scopus 로고
    • Effizienzaussagen bei Ersatzprogrammen zum Vektormaximumproblem
    • W. Dinkelbach W. Dürr 1972 Effizienzaussagen bei Ersatzprogrammen zum Vektormaximumproblem Oper.-Res.-Verfahren. 12 69 77
    • (1972) Oper.-Res.-Verfahren. , vol.12 , pp. 69-77
    • Dinkelbach, W.1    Dürr, W.2
  • 8
    • 70449533497 scopus 로고    scopus 로고
    • Preprint-Series of the Institute of Applied Mathematics, no. 308, University of Erlangen-Nürnberg, Germany
    • Eichfelder, G.: An adaptive scalarization method in multi-objective optimization. Preprint-Series of the Institute of Applied Mathematics, no. 308, University of Erlangen-Nürnberg, Germany (2006)
    • (2006) An Adaptive Scalarization Method in Multi-objective Optimization
    • Eichfelder, G.1
  • 10
    • 0001442712 scopus 로고
    • Approach to performance and sensitivity multiobjective optimization: The goal attainment method
    • 10.1109/TAC.1975.1101105
    • F.W. Gembicki Y.Y. Haimes 1975 Approach to performance and sensitivity multiobjective optimization: The goal attainment method IEEE Trans. Automat. Contr. 6 769 771 10.1109/TAC.1975.1101105
    • (1975) IEEE Trans. Automat. Contr. , vol.6 , pp. 769-771
    • Gembicki, F.W.1    Haimes, Y.Y.2
  • 11
    • 49949131515 scopus 로고
    • Proper efficiency and the theory of vector maximization
    • 0181.22806 10.1016/0022-247X(68)90201-1 229453
    • A.M. Geoffrion 1968 Proper efficiency and the theory of vector maximization J. Math. Anal. Appl. 22 618 630 0181.22806 10.1016/0022-247X(68) 90201-1 229453
    • (1968) J. Math. Anal. Appl. , vol.22 , pp. 618-630
    • Geoffrion, A.M.1
  • 12
    • 0041117307 scopus 로고
    • Nichtkonvexe Dualität in der Vektoroptimierung
    • 0548.90081 737738
    • C. Gerstewitz 1983 Nichtkonvexe Dualität in der Vektoroptimierung Wissenschaftl. Z. Tech. Hochsch. Leuna-Merseburg 25 3 357 364 0548.90081 737738
    • (1983) Wissenschaftl. Z. Tech. Hochsch. Leuna-Merseburg , vol.25 , Issue.3 , pp. 357-364
    • Gerstewitz, C.1
  • 14
    • 0015094608 scopus 로고
    • On a bicriterion formulation of the problems of integrated system identification and system optimization
    • 0224.93016 10.1109/TSMC.1971.4308298 300411
    • Y.Y. Haimes L.S. Lasdon D.A. 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
    • (1971) IEEE Trans. Syst. Man Cybern. , vol.1 , pp. 296-297
    • Haimes, Y.Y.1    Lasdon, L.S.2    Wismer, D.A.3
  • 15
    • 0043246267 scopus 로고
    • An interactive algorithm for nonlinear vector optimization
    • 0712.90061 10.1007/BF01447324 1055657
    • S. Helbig 1990 An interactive algorithm for nonlinear vector optimization Appl. Math. Optim. 22 2 147 151 0712.90061 10.1007/BF01447324 1055657
    • (1990) Appl. Math. Optim. , vol.22 , Issue.2 , pp. 147-151
    • Helbig, S.1
  • 16
    • 0001367459 scopus 로고
    • Approximation of the efficient point set by perturbation of the ordering cone
    • 0737.90051 1114292
    • S. Helbig 1991 Approximation of the efficient point set by perturbation of the ordering cone Z. Oper. Res. 35 3 197 220 0737.90051 1114292
    • (1991) Z. Oper. Res. , vol.35 , Issue.3 , pp. 197-220
    • Helbig, S.1
  • 17
    • 33749615861 scopus 로고    scopus 로고
    • Multiobjective optimization: Survey of methods and industrial applications
    • 1160.90651 10.1007/3-540-26949-5-1
    • 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
    • (2005) Surv. Math. Ind. , vol.11 , pp. 1-42
    • Hillermeier, C.1    Jahn, J.2
  • 18
    • 0001802186 scopus 로고
    • Reference point approximation method for the solution of bicriterial nonlinear optimization problems
    • 0795.90056 10.1007/BF00939894 1168998
    • 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
    • (1992) J. Optim. Theory Appl. , vol.74 , Issue.1 , pp. 87-103
    • Jahn, J.1    Merkel, A.2
  • 21
    • 0344339136 scopus 로고    scopus 로고
    • Quantitative parametric connections between methods for generating noninferior solutions in multiobjective optimization
    • 0998.90072 10.1016/S0377-2217(98)00018-6
    • D. Li J.-B. Yang M.P. Biswal 1999 Quantitative parametric connections between methods for generating noninferior solutions in multiobjective optimization Eur. J. Oper. Res. 117 84 99 0998.90072 10.1016/S0377-2217(98) 00018-6
    • (1999) Eur. J. Oper. Res. , vol.117 , pp. 84-99
    • Li, D.1    Yang, J.-B.2    Biswal, M.P.3
  • 22
    • 17444429941 scopus 로고    scopus 로고
    • On min-norm and min-max methods of multi-objective optimization
    • DOI 10.1007/s10107-003-0462-y
    • 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 (Pubitemid 40537669)
    • (2005) Mathematical Programming , vol.103 , Issue.1 , pp. 1-33
    • Lin, J.G.1
  • 25
    • 0021406619 scopus 로고
    • Scalarizing vector optimization problems
    • 0505.90072 10.1007/BF00934564 739432
    • A. Pascoletti P. Serafini 1984 Scalarizing vector optimization problems J. Optim. Theory Appl. 42 4 499 524 0505.90072 10.1007/BF00934564 739432
    • (1984) J. Optim. Theory Appl. , vol.42 , Issue.4 , pp. 499-524
    • Pascoletti, A.1    Serafini, P.2
  • 26
    • 2342571370 scopus 로고
    • On the approximation of solutions to multiple criteria decision making problems
    • M. Zeleny (eds). Springer Berlin
    • Polak, E.: On the approximation of solutions to multiple criteria decision making problems. In: Zeleny, M. (ed.) Multiple Crit. Decis. Making, 22nd Int. Meet. TIMS, Kyoto 1975, pp. 271-282. Springer, Berlin (1976)
    • (1976) Multiple Crit. Decis. Making, 22nd Int. Meet. TIMS, Kyoto 1975 , pp. 271-282
    • Polak, E.1
  • 27
    • 23844480435 scopus 로고    scopus 로고
    • Approximation methods in multiobjective programming
    • DOI 10.1007/s10957-005-5494-4
    • S. Ruzika M.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 (Pubitemid 41152032)
    • (2005) Journal of Optimization Theory and Applications , vol.126 , Issue.3 , pp. 473-501
    • Ruzika, S.1    Wiecek, M.M.2
  • 29
    • 0023538157 scopus 로고
    • Continuous dependence of solutions on a parameter in a scalarization method
    • 0616.90075 10.1007/BF00941178 917406
    • A. Sterna-Karwat 1987 Continuous dependence of solutions on a parameter in a scalarization method J. Optim. Theory Appl. 55 3 417 434 0616.90075 10.1007/BF00941178 917406
    • (1987) J. Optim. Theory Appl. , vol.55 , Issue.3 , pp. 417-434
    • Sterna-Karwat, A.1
  • 30
    • 84974465205 scopus 로고
    • Lipschitz and differentiable dependence of solutions on a parameter in a scalarization method
    • 0616.49017 10.1017/S1446788700028639 877805
    • A. Sterna-Karwat 1987 Lipschitz and differentiable dependence of solutions on a parameter in a scalarization method J. Aust. Math. Soc. A 42 353 364 0616.49017 10.1017/S1446788700028639 877805
    • (1987) J. Aust. Math. Soc. A , vol.42 , pp. 353-364
    • Sterna-Karwat, A.1
  • 31
    • 4444306693 scopus 로고
    • Ein Trennungskonzept und seine Anwendung auf Vektoroptimierungsprobleme
    • University of Halle, Germany
    • Weidner, P.: Ein Trennungskonzept und seine Anwendung auf Vektoroptimierungsprobleme. Professorial dissertation. University of Halle, Germany (1990)
    • (1990) Professorial Dissertation
    • Weidner, P.1
  • 32
    • 0007228693 scopus 로고
    • Efficiency in multiple objective optimization problems
    • 0362.90092 10.1007/BF01593807 449751
    • R.E. Wendell D.N. Lee 1977 Efficiency in multiple objective optimization problems Math. Program. 12 406 414 0362.90092 10.1007/BF01593807 449751
    • (1977) Math. Program. , vol.12 , pp. 406-414
    • Wendell, R.E.1    Lee, D.N.2
  • 33
    • 84939004610 scopus 로고
    • Optimality and non-scalared-valued performance criteria
    • 10.1109/TAC.1963.1105511
    • L. Zadeh 1963 Optimality and non-scalared-valued performance criteria IEEE Trans. Automatic Contr. 8 59 60 10.1109/TAC.1963.1105511
    • (1963) IEEE Trans. Automatic Contr. , vol.8 , pp. 59-60
    • Zadeh, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.