Stochastic convergence of random search methods to fixed size Pareto front approximations

European Journal of Operational Research

Volumn 213, Issue 2, 2011, Pages 414-421

  Laumanns, Marco ^a   Zenklusen, Rico ^b  

^a IBM RESEARCH ZURICH   (Switzerland)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Metaheuristics; Multiobjective optimization; Multiple criteria analysis; Search theory

Indexed keywords

ADAPTATION SCHEME; BOUNDED SIZE; CARDINALITIES; CORRESPONDING SOLUTIONS; DOMINANCE RELATION; FIXED SIZE; HIERARCHICAL GRID; LIMIT BEHAVIOR; LIMIT SETS; META HEURISTICS; MULTI OBJECTIVE; MULTIPLE CRITERIA ANALYSIS; NEW SOLUTIONS; PARETO FRONT; PARETO SET; POTENTIAL FUNCTION; RANDOM SEARCH METHOD; SEARCH THEORY; SOLUTION SET;

CONVERGENCE OF NUMERICAL METHODS; HEURISTIC ALGORITHMS; MULTIOBJECTIVE OPTIMIZATION;

PARETO PRINCIPLE;

EID: 79955912058     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2011.03.039     Document Type: Article

References (34)

1. N. Alon, Y. Matias, and M. Szegedy The space complexity of approximating the frequency moments Journal of Computer and System Sciences 58 1 1999 137 147
2. N. Beume, B. Naujoks, and M. Emmerich SMS-EMOA: Multiobjective selection based on dominated hypervolume European Journal of Operational Research 181 3 2007 1653 1669 (Pubitemid 46498552)
3. A. Borodin, and R. El-Yaniv Online Computation and Competitive Analysis 1998 Cambridge University Press
4. K. Bringmann, and T. Friedrich Approximating the least hypervolume contributor: Np-hard in general, but fast in practice M. Ehrgott, C. Fonseca, X. Gandibleux, J.-K. Hao, M. Sevaux, Evolutionary Multi-Criterion Optimization Lecture Notes in Computer Science vol. 5467 2009 Springer Berlin, Heidelberg 6 20 10.1007/978-3-642-01020-0-6
5. K. Bringmann, and T. Friedrich Approximating the volume of unions and intersections of high-dimensional geometric objects Computational Geometry: Theory and Applications 43 6-7 2010 601 610
6. K. Bringmann, and T. Friedrich Tight bounds for the approximation ratio of the hypervolume indicator Parallel Problem Solving from Nature (PPSN XI) LNCS vol. 6238 2010 607 616
7. T.M. Chan A (slightly) faster algorithm for Klee's measure problem SCG'08: Proceedings of the Twenty-Fourth Annual Symposium on Computational Geometry 2008 ACM New York, NY, USA
8. I. Diakonikolas, and M. Yannakakis Small approximate Pareto sets for biobjective shortest paths and other problems SIAM Journal on Computing 39 4 2009 1340 1371
9. M. Ehrgott Approximation algorithms for combinatorial multicriteria optimization problems International Transaction in Operational Research 7 2000 5 31
10. T. Erlebach, H. Kellerer, and U. Pferschy Approximating multiobjective knapsack problems Management Science 48 12 2002 1603 1612
11. Y.G. Evtushenko, and M.A. Potapov Methods of numerical solution of multicriterion problem Soviet mathematics - Doklady 34 1987 420 423
12. T. Hanne On the convergence of multiobjective evolutionary algorithms European Journal Of Operational Research 117 3 1999 553 564
13. T. Hanne A multiobjective evolutionary algorithm for approximating the efficient set European Journal of Operational Research 176 3 2007 1723 1734 (Pubitemid 44573663)
14. P. Hansen Bicriterion path problems T. Gal, G. Fandel, Multiple Criteria Decision Making: Theory and Applications LNEMS 177 1980 Springer-Verlag Berlin 109 127
15. S. Helbig, and D. Pateva On several concepts for -efficiency OR Spektrum 16 3 1994 179 186
16. Knowles, J.D.; 2002. Local-search and hybrid evolutionary algorithms for Pareto optimization. Ph.D. Thesis, The University of Reading, Department of Computer Science, Reading, UK.
17. J.D. Knowles, and D.W. Corne Approximating the non-dominated front using the Pareto Archived Evolution Strategy Evolutionary Computation 8 2 2000 149 172
18. J.D. Knowles, and D. Corne Properties of an adaptive archiving algorithm for storing nondominated vectors IEEE Transactions on Evolutionary Computation 7 2 2003 100 116
19. J.D. Knowles, and D.W. Corne Bounded Pareto archiving: Theory and practice X. Gandibleux, M. Sevaux, K. Sörensen, V. T'Kindt, Metaheuristics for Multiobjective Optimisation Lecture Notes in Economics and Mathematical Systems vol. 535 2004 Springer 39 64
20. V. Koltun, and C.H. Papadimitriou Approximately dominating representatives Theoretical Computer Science 371 3 2007 148 154 (Pubitemid 46215855)
21. M. Laumanns, L. Thiele, K. Deb, and E. Zitzler Combining convergence and diversity in evolutionary multiobjective optimization Evolutionary Computation 10 3 2002 263 282
22. M. López-Ibánez, J. Knowles, and M. Laumanns On sequential online archiving of objective vectors R. Takahashi, Evolutionary Multi-criterion Optimization (EMO 2011) Lecture Notes in Computer Science vol. 6576 2011 Springer Heidelberg, Germany 46 60
23. Papadimitriou, C.H.; Yannakakis, M.; 2000. The complexity of tradeoffs, and optimal access of web sources. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science FOCS 2000, pp. 86-92. (Pubitemid 32075881)
24. M. Peschel, and C. Riedel Use of vector optimization in multiobjective decision making D.E. Bell, R.L. Keeney, H. Raiffa, Conflicting Objectives in Decisions 1977 Wiley Chichester 97 121
25. H. Reuter An approximation method for the efficiency set of multiobjective programming problems Optimization 21 1990 905 911
26. G. Rudolph Evolutionary search for minimal elements in partially ordered finite sets V. Porto, Evolutionary Programming VII. Proceedings of the 7th Annual Conference on Evolutionary Programming 1998 Springer 345 353
27. G. Rudolph, and A. Agapie Convergence properties of some multi-objective evolutionary algorithms Congress on Evolutionary Computation (CEC 2000) vol. 2 2000 IEEE Press 1010 1016
28. G. Ruhe, and B. Fruhwirt -optimality for bicriteria programs and its application to minimum cost flows Computing 44 1990 21 34 (Pubitemid 20694979)
29. Safer, H.M.; Orlin, J.B.; 1995. Fast approximation schemes for multi-criteria combinatorial optimization. Technical Report WP 3756-95, MIT Sloan School of Management.
30. S. Sayin Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming Mathematical Programming, Series A 87 2000 543 560
31. O. Schütze, M. Laumanns, C.A.C. Coello, M. Dellnitz, and E. Talbi Convergence of stochastic search algorithms to finite size Pareto set approximations Journal of Global Optimization 41 4 2008 559 577
32. E. Zitzler, and S. Künzli Indicator-based selection in multiobjective search Conference on Parallel Problem Solving from Nature (PPSN VIII) LNCS vol. 3242 2004 Springer 832 842 (Pubitemid 39750284)
33. E. Zitzler, and L. Thiele Multiobjective optimization using evolutionary algorithms - A comparative case study A.E. Eiben, Parallel Problem Solving from Nature (PPSN V) Lecture Notes in Computer Science vol. 1498 1998 Springer 292 301
34. E. Zitzler, L. Thiele, M. Laumanns, C.M. Foneseca, and V.G. da Fonseca Performance assessment of multiobjective optimizers: An analysis and review Transactions on Evolutionary Computation 7 2 2003 117 132