An approximation algorithm for convex multi-objective programming problems

Journal of Global Optimization

Volumn 50, Issue 3, 2011, Pages 397-416

  Ehrgott, Matthias ^a   Shao, Lizhen ^b   Schöbel, Anita ^c  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY BEIJING   (China)

^c UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

nondominated point; Convex optimization Approximation algorithm; Multi objective optimization

Indexed keywords

FEASIBLE SET; MULTI OBJECTIVE; MULTI-OBJECTIVE LINEAR PROGRAMMING; MULTI-OBJECTIVE PROGRAMMING PROBLEM; NON-DIFFERENTIABLE; NON-DOMINATED SETS; NONLINEAR PROGRAMMING PROBLEM; OBJECTIVE FUNCTIONS; OBJECTIVE SPACE; OUTER APPROXIMATION ALGORITHM;

APPROXIMATION ALGORITHMS; CONVEX OPTIMIZATION; LINEAR PROGRAMMING; NONLINEAR PROGRAMMING;

MULTIOBJECTIVE OPTIMIZATION;

EID: 80051669720     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-010-9588-7     Document Type: Article

References (15)

1. Bazaraa, M.S.: Nonlinear Programming Theory and Algorithms. John Wiley and Sons Inc, (1993)
2. Benson, H.P.: Hybrid approach for solvingmultiple-objective linear programs in outcome space. J.Optim. Theory Appl. 98, 17-35 (1998) (Pubitemid 128357611)
3. Benson, H.P.: An outer approximation algorithmfor generating all efficient extreme points in the outcome set of a multiple objective linear programming problem. J. Global Optim. 13, 1-24 (1998) (Pubitemid 128508071)
4. Chen, P.C., Hansen, P., Jaumard, B.: On-line and off-line vertex enumeration by adjacency lists. Oper. Res. Lett. 10, 403-409 (1991)
5. Chinchuluun, A., Pardalos, M.: A survey of recent developments in multiobjective optimization. Ann. Oper. Res. 154, 29-50 (2007)
6. Ehrgott, M.: Multicriteria Optimization. Springer, (2005)
7. Ehrgott, M., Ruzika, S.: Improved ε-constraintmethod formultiobjective programming. J. Optim. Theory Appl. 138(3), 375-396 (2008)
8. Ehrgott,M.,Wiecek,M.:Multiobjective programming. In: Figueira, J., Greco, S., Ehrgott,M. (eds.)Multicriteria Decision Analysis: State of the Art Surveys., pp. 667-722. Springer Science + Business Media, New York (2005)
9. Ehrgott,M., Löhne, A., Shao, L.: A dual variant of Benson's outer approximation algorithm. Report 654, Department of Engineering Science, The University of Auckland (2007)
10. Geoffrion, A.: Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22, 618-630 (1968)
11. Miettinen, K., Makela, M.M., Kaario, K.: Experiments with classification-based scalarizing functions in interactive multiobjective optimization. Eur. J. Oper. Res. 175, 931-947 (2006) (Pubitemid 44345085)
12. Miettinen, K.M.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, (1999)
13. Papadimitriou, C., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources. In: Blum, A. (ed) Proceedings of the 41st Annual Sympsium on Foundations of Computer Science, pp. 86-92. IEEE Computer Society (2000) (Pubitemid 32075881)
14. Ruzika, S., Wiecek, M.M.: Approximation methods in multiobjective programming. J. Optim. Theory Appl. 126(3), 473-501 (2005) (Pubitemid 41152032)
15. Shao, L., Ehrgott, M.: Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning. Math. Methods Oper. Res. 68, 257-276 (2008). doi:10.1007/s00186-008- 0220-2