S-metric calculation by considering dominated hypervolume as Klee's measure problem

Evolutionary Computation

Volumn 17, Issue 4, 2009, Pages 477-492

  Beume, Nicola ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Computational geometry; Evolutionary algorithms; Hypervolume indicator; Multi objective optimization; Performance assessment; S metric

Indexed keywords

ALGORITHM; ARTICLE; COMPARATIVE STUDY; COMPUTER ANALYSIS;

ALGORITHMS; COMPUTING METHODOLOGIES;

EID: 72249110751     PISSN: 10636560     EISSN: 15309304     Source Type: Journal    
DOI: 10.1162/evco.2009.17.4.17402     Document Type: Article

References (31)

1. Bader, J., and Zitzler, E. (2008). HypE: An algorithm for fast hypervolume-based many-objective optimization. TIK Report 286, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Switzerland.
2. Bentley, J. L. (1977). Algorithms for Klee's rectangle problem. Unpublished notes, Department of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania.
3. Beume, N. (2006). Hypervolumen-basierteSelektion in einem evolutionären Algorithmus zur Mehrzieloptimierung. Diploma thesis, University of Dortmund, Dortmund, Germany.
4. Beume, N., Fonseca, C. M., López-Ibáñez, M., Paquete, L., and Vahrenhold, J. (2009). On the complexity of computing the hypervolume indicator. IEEE Transactions on Evolutionary Computation, 13(5): 1075-1082.
5. Beume, N., Naujoks, B., and Emmerich, M. (2007). SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research, 181(3):1653-1669.
6. Beume, N., and Rudolph, G. (2006a). Faster S-metric calculation by considering dominated hypervolume as Klee's measure problem. In Proceedings of the Second IASTED Conference on Computational Intelligence, pp. 231-236.
7. Beume, N., and Rudolph, G. (2006b). Faster S-metric calculation by considering dominated hypervolume as Klee's measure problem. Technical Report of the Collaborative Research Centre 531 Computational Intelligence CI-216/06. Dortmund, Germany: University of Dortmund.
8. Bradstreet, L., While, L., and Barone, L. (2008). A fast incremental hypervolume algorithm. IEEE Transactions on Evolutionary Computation, 12(6):714-723.
9. Bringmann, K., and Friedrich, T. (2008). Approximating the volume of unions and intersections of high-dimensional geometric objects. In Proceedings of the 19th International Symposium on Algorithms and Computation (ISAAC 2008), Vol. 5369 of LNCS, pp. 436-447. Berlin: Springer.
10. Bringmann, K., and Friedrich, T. (2009). Approximating the least hypervolume contributor: NP- hard in general, but fast in practice. In Proceedings of EMO 2009, Fifth International Conference on Evolutionary Multi-Criterion Optimization, LNCS, pp. 6-20. Berlin: Springer.
11. Chan, T. M. A (slightly) faster algorithm for Klee's measure problem. In SCG'08: Proceedings of the Twenty-Fourth Annual Symposium on Computational Geometry, pp. 94-100. College Park MD, ACM.
12. Coello Coello, C. A., Van Veldhuizen, D. A., and Lamont, G. B. (2002). Evolutionary algorithms for solving multi-objective problems. New York: Kluwer Academic Publishers.
13. Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley.
14. Edelsbrunner, H., and Overmars, M. H. (1985). Batched dynamic solutions to decomposable searching problems. Journal of Algorithms, 6(4):515-542.
15. Fleischer, M.(2003).The measure of Paretooptima. Applications to multi-objective metaheuristics. In Proceedings of EMO 2003, Second International Conference on Evolutionary Multi-Criterion Optimization, Vol. 2632 of LNCS, pp. 519-533. Berlin: Springer.
16. Fonseca, C. M., Paquete, L., and López-Ibáñez, M. (2006). An improved dimension-sweep algorithm for the hypervolume indicator. In Proceedings of the 2006 Congress on Evolutionary Computation (CEC'06), pp. 1157-1163.
17. i]. In Communications of the ACM, Vol. 21, pp. 540-544.
18. Igel, C., Hansen, N., and Roth, S. (2007). Covariance matrix adaptation for multi-objective optimization. Evolutionary Computation, 15(1):1-28.
19. i] be computed in less than O(nlogn) steps? In American Mathematical Monthly, Vol. 84, pp. 284-285.
20. Knowles, J. D. (2002). Local search and hybrid evolutionary algorithms for Pareto optimization. PhD thesis, University of Reading, Reading, UK.
21. Laumanns, M., Rudolph, G., and Schwefel, H.-P. (1999). Approximating the Pareto set: Concepts, diversity issues, and performance assessment. Technical Report of the Collaborative Research Centre 531 Computational Intelligence CI-72/99. Dortmund, Germany: University of Dortmund.
22. Overmars, M. H., and Yap, C.-K. (1991). New upper bounds in Klee's measure problem. SIAM Journal on Computing, 20(6):1034-1045.
23. While, L. (2005). A new analysis of the LebMeasure algorithm for calculating hypervolume. In Proceedings of EMO 2005, Third International Conference on Evolutionary Multi-Criterion Optimization, Vol. 3410 of Lecture Notes in Computer Science, pp. 326-340. Berlin: Springer.
24. While, L., Bradstreet, L., Barone, L., and Hingston, P. (2005). Heuristics for optimising the calculation of hypervolume for multi-objective optimisation problems. In Proceedings of the 2005 Congress on Evolutionary Computation (CEC'05), Vol. 3, pp. 2225-2232.
25. While, L., Hingston, P., Barone, L., and Huband, S. (2006). A faster algorithm for calculating hypervolume. IEEE Transactions on Evolutionary Computation, 10(1):29-38.
26. Zitzler, E. (2001). Hypervolume metric calculation. Computer Engineering and Networks Laboratory (TIK), Zürich. Retrieved from ftp://ftp.tik.ee.ethz.ch/pub/people/zitzler/hypervol.c.
27. Zitzler, E., Brockhoff, D., and Thiele, L. (2007). The hypervolume indicator revisited: On the design of Pareto-compliant indicators via weighted integration. In Proceedings of EMO 2007, Fourth International Conference on Evolutionary Multi-CriterionOptimization, Vol. 4403 of LNCS, pp. 862-876. Berlin: Springer.
28. Zitzler, E., and Künzli, S. (2004). Indicator-based selection in multiobjective search. In Proceedings of PPSN VIII, Eighth International Conference on Parallel Problem Solving from Nature, Vol. 1498 of LNCS, pp. 832-842. Berlin: Springer.
29. Zitzler, E., and Thiele, L. (1998). Multiobjective optimization using evolutionary algorithms-A comparative case study. In Proceedings of PPSN V, Fifth International Conference on Parallel Problem Solving from Nature, Vol. 1498 of LNCS, pp. 292-301. Berlin: Springer.
30. Zitzler, E., Thiele, L., and Bader, J. (2008). Spam: Set preference algorithm for multiobjective optimization. In Proceedings of PPSN X, Tenth International Conference on Parallel Problem Solving from Nature, Vol. 5199 of LNCS, pp. 847-858. Berlin: Springer.
31. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C. M., and Grunert da Fonseca, V. (2003). Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation, 7(2):117-132.