Improved smoothed analysis of multiobjective optimization

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2012, Pages 407-426

  Brunsch, Tobias ^a   Röglin, Heiko ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

multi objective optimization; smoothed analysis

Indexed keywords

FEASIBLE SOLUTION; MULTI OBJECTIVE OPTIMIZATIONS (MOO); MULTI-OBJECTIVE OPTIMIZATION PROBLEM; NEW RESULTS; NONLINEAR OBJECTIVE FUNCTIONS; OBJECTIVE FUNCTIONS; PARETO OPTIMAL SOLUTIONS; PERTURBATION PARAMETERS; PRACTICAL EXPERIENCE; SMOOTHED ANALYSIS; WORST-CASE ANALYSIS;

COMPUTATION THEORY; MULTIOBJECTIVE OPTIMIZATION; OPTIMAL SYSTEMS; PARETO PRINCIPLE;

POLYNOMIALS;

EID: 84862594860     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2213977.2214016     Document Type: Conference Paper

References (21)

1. René Beier. Probabilistic Analysis of Discrete Optimization Problems. PhD thesis, Universität des Saarlandes, 2004.
2. René Beier, Heiko Röglin, and Berthold Vöcking. The smoothed number of Pareto optimal solutions in bicriteria integer optimization. In Proceedings of the 12th International Conference on Integer Programming and Combinatorial Optimization (IPCO), pages 53-67, 2007.
3. René Beier and Berthold Vöcking. Random knapsack in expected polynomial time. Journal of Computer and System Sciences, 69(3):306-329, 2004.
4. René Beier and Berthold Vöcking. Typical properties of winners and losers in discrete optimization. SIAM Journal on Computing, 35(4):855-881, 2006.
5. André Berger, Heiko Röglin, and Ruben van der Zwaan. Path trading: Fast algorithms, smoothed analysis, and hardness results. In Proceedings of the 10th International Symposium on Experimental Algorithms (SEA), pages 43-53, 2011.
6. Tobias Brunsch and Heiko Röglin. Lower bounds for the smoothed number of pareto optimal solutions. In Proceedings of the 8th Annual Conference on Theory and Applications of Models of Computation (TAMC), pages 416-427, 2011.
7. H. William Corley and I. Douglas Moon. Shortest paths in networks with vector weights. Journal of Optimization Theory and Application, 46(1):79-86, 1985.
8. Matthias Ehrgott. Integer solutions of multicriteria network ow problems. Investigacao Operacional, 19:229-243, 1999.
9. Matthias Ehrgott. Multicriteria Optimization. Springer, 2005.
10. Navin Goyal and Luis Rademacher. Lower bounds for the average and smoothed number of pareto optima. CoRR, abs/1107.3876, 2011.
11. Pierre Hansen. Bicriterion path problems. In Multiple Criteria Decision Making: Theory and Applications, volume 177 of Lecture Notes in Economics and Mathematical Systems, pages 109-127, 1980.
12. Kathrin Klamroth and Margaret M. Wiecek. Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics, 47(1):57-76, 2000.
13. Ankur Moitra and Ryan O'Donnell. Pareto optimal solutions for smoothed analysts. In Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (STOC), pages 225-234, 2011.
14. Matthias Müller-Hannemann and Karsten Weihe. Pareto shortest paths is often feasible in practice. In Proceedings of the 5th International Workshop on Algorithm Engineering (WAE), pages 185-198, 2001.
15. Adli Mustafa and Mark Goh. Finding integer efficient solutions for bicriteria and tricriteria network ow problems using dinas. Computers & Operations Research, 25(2):139-157, 1998.
16. George L. Nemhauser and Zev Ullmann. Discrete dynamic programming and capital allocation. Management Science, 15(9):494-505, 1969.
17. Heiko Röglin and Shang-Hua Teng. Smoothed analysis of multiobjective optimization. In Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 681-690, 2009.
18. Arvind Sankar, Daniel A. Spielman, and Shang-Hua Teng. Smoothed analysis of the condition numbers and growth factors of matrices. SIAM Journal on Matrix Analysis Applications, 28(2):446-476, 2006.
19. Anders J. V. Skriver and Kim Allan Andersen. A label correcting approach for solving bicriterion shortest-path problems. Computers & Operations Research, 27(6):507-524, 2000.
20. Daniel A. Spielman and Shang-Hua Teng. Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time. Journal of the ACM, 51(3):385-463, 2004.
21. Daniel A. Spielman and Shang-Hua Teng. Smoothed analysis: an attempt to explain the behavior of algorithms in practice. Communications of the ACM, 52(10):76-84, 2009.