On Continuation Methods for the Numerical Treatment of Multi-Objective Optimization Problems

Dagstuhl Seminar Proceedings

Volumn 4461, Issue , 2005, Pages

  Schütze, Oliver ^a   Dell'Aere, Alessandro ^a   Dellnitz, Michael ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

Author keywords

continuation; k manifolds; multi objective optimization

Indexed keywords

NUMERICAL METHODS;

CONTINUATION; CONTINUATION METHOD; K-MANIFOLD; KARUSH KUHN TUCKERS; MULTI-OBJECTIVE OPTIMIZATION PROBLEM; MULTI-OBJECTIVES OPTIMIZATION; NEIGHBOURHOOD; NUMERICAL TREATMENTS; PREDICTOR CORRECTOR; SOLUTIONS SETS;

MULTIOBJECTIVE OPTIMIZATION;

EID: 84875563769     PISSN: 18624405     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (36)

1. E. L. Allgower and K. Georg. Numerical Continuation Methods. Springer, 1990.
2. E. L. Allgower and P. H. Schmidt. An algorithm for piecewise-linear approximation of an implicitly defined manifold. SIAM Journal of Numerical Analysis, 22:322{ 346, 1987.
3. C. A. Coello Coello and M. S. Lechunga. MOPSO: A proposal for multiple objective particle swarm optimization. In Proceedings of the IEEE World Congress on Computational Intelligence, IEEE Press, 2002.
4. I. Das and J. Dennis. Normal-boundary intersection: A new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM Journal of Optimization, 8:631 { 657, 1998.
5. K. Deb. Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, 2001.
6. K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In Parallel Problem Solving from Nature VI (PPSN-VI), pages 849{858, 2000.
7. K. Deb, S. Pratap, and A. Meyarivan. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In Proceedings of the Parallel Problem Solving from Nature VI Conference, pages 849{858. Springer, 2000.
8. M. Dellnitz, O. Schütze, and T. Hestermeyer. Covering pareto sets by multilevel subdivision techniques. Journal of Optimization Theory and Applications, 124:113{ 155, 2005.
9. M. Dellnitz, O. Schütze, and St. Sertl. Finding zeros by multilevel subdivision techniques. IMA Journal of Numerical Analysis, 22(2):167{185, 2002.
10. P. Deuhard. Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Springer, 2004.
11. J. E. Fieldsend and S. Singh. A multi-objective algorithm based upon particle swarm optimization, an efficient data structure and turbulence. In Proceedings of the 2002 U.K. Workshop on Computational Intelligence, 2002.
12. J. Fliege and A. Heseler. Constructing approximations to the efficient set of convex quadratic multiobjective problems. University of Dortmund, Germany, Technical Report, 2003.
13. C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors. Evolutionary Multi-Criterion Optimization. Second International Conference, EMO 2003. Springer, 2003.
14. J. Guddat, F. Guerra Vasquez, K. Tammer, and K. Wendler. Multiobjective and Stochastic Optimization based on Parametric Optimization. Akademie-Verlag, 1985.
15. M. E. Henderson. Multiple parameter continuation: Computing implicitly defined k-manifolds. International Journal of Bifurcation and Chaos, 12:451{476, 2002.
16. C. Hillermeier. Nonlinear Multiobjective Optimization - A Generalized Homotopy Approach. Birkhäuser, 2001.
17. J. Jahn. Mathematical Vector Optimization in Partially Ordered Linear Spaces. Verlag Peter Lang GmbH, Frankfurt am Main, 1986.
18. W. E. Karush. Minima of functions of several variables with inequalities as side conditions. PhD thesis, University of Chicago, 1939.
19. H. Kuhn and A. Tucker. Nonlinear programming. In J. Neumann, editor, Proceeding of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, pages 481{492, 1951.
20. K. Miettinen. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, 1999.
21. S. Mostaghim. Multi-Objective Evolutionary Algorithms, Data Structures, Convergence and Diversity. PhD thesis, University of Paderborn, 2004.
22. J. A. Nelder and R. Mead. A simplex method for function minimization. Computer Journal, 7:308{313, 1965.
23. R. P. Brent. Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ, 1973.
24. J. Rakowska, R. T. Haftka, and L. T. Watson. Tracing the efficient curve for multi-objective control-structure optimization. Computing Systems in Engineering, 2(6):461{471, 199.
25. W. Rheinboldt. On the computation of multi-dimensional solution manifolds of parametrized equations. Numer. Math., 53:165{181, 1988.
26. W. C. Rheinboldt. Numerical Analysis of Parametrized Nonlinear Equations. Wiley, 1986.
27. S. Schäffler, R. Schultz, and K. Weinzierl. A stochastic method for the solution of unconstrained vector optimization problems. Journal of Optimization Theory and Applications, 114(1):209{222, 2002.
28. K. Schittkowski. EASY-OPT: An interactive optimization system with automatic differentiation - user's guide. Department of Mathematics, University of Bayreuth, Technical Report, 1999.
29. O. Schütze. A new data structure for the nondominance problem in multi-objective optimization. In C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors, Evolutionary Multi-Criterion Optimization (EMO 03), volume 2 of Springer, 2003.
30. O. Schütze. Set Oriented Methods for Global Optimization. PhD thesis, University of Paderborn, 2004.
31. O. Schütze, S. Mostaghim, M. Dellnitz, and J. Teich. Covering Pareto sets by multilevel evolutionary subdivision techniques. In C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors, Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science, 2003.
32. R. E. Steuer. Multiple Criteria Optimization: Theory, Computation, and Applications. John Wiley & Sons, Inc., 1986.
33. R. E. Steuer, editor. Multiple Criteria Decision Making and Risk Analysis Using Microcomputers, chapter The Tchebycheff Procedure of Interactive Multiple Objective Programming, pages 235{249. Springer, Berlin, 1989.
34. V. Pareto. Cours d'Economie Politique. Libraire Droz, Genève, 1964 (first edition in 1896).
35. E. Zitzler, K. Deb, L. Thiele, C. A. Coello Coello, and D. Corne, editors. Evolutionary Multi-Criterion Optimization. First International Conference, EMO 2001. Springer, 2001.
36. E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the strength Pareto evolutionary algorithm. In Evolutionary Methods for Design, Optimisation and Control with Applications to Industrial Problems, pages 95{100. CIMNE, Barcelona, Spain, 2002.