Quick hypervolume

IEEE Transactions on Evolutionary Computation

Volumn 18, Issue 4, 2014, Pages 481-502

  Russo, Luís M S ^a   Francisco, Alexandre P ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

diversity methods; hypervolume; multiobjective optimization; performance metrics

Indexed keywords

MULTIOBJECTIVE OPTIMIZATION;

DIVERSITY METHOD; HYPERVOLUME; MULTI OBJECTIVE EVOLUTIONARY ALGORITHMS; PERFORMANCE METRICS; STATE OF THE ART;

ALGORITHMS;

EID: 84905566775     PISSN: 1089778X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TEVC.2013.2281525     Document Type: Article

References (40)

1. J. Leskovec, A. Krause, C. Guestrin, C. Faloutsos, J. M. Van Briesen, and N. S. Glance, "Cost-effective outbreak detection in networks, " in Proc. KDD, Aug. 2007, pp. 420-429. (Pubitemid 350229228)
2. B. Schwartz, The Paradox of Choice: Why More Is Less (P. S. Series). New York, NY, USA: Harper Collins, 2005.
3. K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms (Wiley-Interscience Series in Systems and Optimization). New York, NY, USA: Wiley, 2009.
4. A. Zhou, B. Qu, H. Li, S. Zhao, P. Suganthan, and Q. Zhang, "Multiobjective evolutionary algorithms: A survey of the state-of-The-Art, " Swarm Evol. Comput., vol. 1, no. 1, pp. 32-49, 2011.
5. C. Goh, Y. Ong, and K. Tan, Multi-Objective Memetic Algorithms, vol. 171. New York, NY, USA: Springer Verlag, 2009.
6. S. Huband, P. Hingston, L. While, and L. Barone, "An evolution strategy with probabilistic mutation for multi-objective optimization, " in Proc. IEEE Congr. Evol. Comput., Dec. 2003, pp. 2284-2291.
7. J. Knowles, D. Corne, and M. Fleischer, "Bounded archiving using the Lebesgue measure, " in Proc. IEEE Congr. Evol. Comput., Dec. 2003, pp. 2490-2497.
8. N. Beume, M. Emmerich, and B. Noujoks, "An EMO algorithm using the hypervolume measure as selection criterion, " in Proc. Evol. Multi-Objective Optimiz., 2005, pp. 62-76. (Pubitemid 41251756)
9. E. Zitzler and S. Knzli, "Indicator-based selection in multiobjective search, " in Proc. PPSN VIII, vol. 3242. 2004, pp. 832-842. (Pubitemid 39750284)
10. C. A. R. Hoare, "Algorithm 64: Quicksort, " Commun. ACM, vol. 4, no. 7, p. 321, Jul. 1961.
11. P. Briggs and L. Torczon, "An efficient representation for sparse sets, " ACM Lett. Program. Lang. Syst., vol. 2, no. 1-4, pp. 59-69, 1993.
12. J. Bentley, Programming Pearls. Reading, MA, USA: Addison-Wesley Professional, 2000.
13. A. Aho and J. Hopcroft, Design and Analysis of Computer Algorithms. Delhi, India: Pearson Education, 1974.
14. L. While, P. Hingston, L. Barone, and S. Huband, "A faster algorithm for calculating hypervolume, " IEEE Trans. Evol. Comput., vol. 10, no. 1, pp. 29-38, Feb. 2006. (Pubitemid 43174983)
15. M. Mitzenmacher and E. Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge, U.K.: Cambridge Univ., 2005.
16. N. Beume and G. Rudolph, "S-metric calculation by considering dominated hypervolume as Klees measure problem, " Evol. Comput., vol. 17, no. 4, pp. 477-492, 2009.
17. H. Yildiz and S. Suri, "On Klees measure problem for grounded boxes, " in Proc. Symp. Comput. Geometry, 2012, pp. 111-120.
18. L. Bradstreet, L. While, and L. Barone, "A fast way of calculating exact hypervolumes, " IEEE Trans. Evol. Comput., vol. 16, no. 1, pp. 86-95, Feb. 2012.
19. A. P. Guerreiro, C. M. Fonseca, and M. T. M. Emmerich, "A fast dimension-sweep algorithm for the hypervolume indicator in four dimensions, " in Proc. CCCG, Aug. 2012, pp. 77-82.
20. J. Bader and E. Zitzler, "Hype: An algorithm for fast hypervolume-based many-objective optimization, " Evol. Comput., vol. 19, no. 1, pp. 45-76, 2011.
21. J. Wu and S. Azarm, "Metrics for quality assessment of a multiobjective design optimization solution set." J. Mech. Design, vol. 123, no. 1, pp. 18-25, 2001. (Pubitemid 33716175)
22. J. L. Bentley, "Multidimensional divide-And-conquer, " Commun. ACM, vol. 23, pp. 214-229, Apr. 1980.
23. M. Fleischer, "The measure of pareto optimal applications to multiobjective metaheuristics, " in Proc. EMO, 2003, pp. 519-533. (Pubitemid 137634663)
24. C. Fonseca, L. Paquete, and M. Lopez-Ibanez, "An optimal algorithm for a special case of Klees measure problem in three dimensions, " Centre for Intelligent Systems, University of Algarve, Faro, Potugal, Tech. Rep. CSI-RT-I-01/2006, 2006.
25. C. Fonseca, L. Paquete, and M. Lopez-Ibanez, "An improved dimensionsweep algorithm for the hypervolume indicator, " in Proc. IEEE Congr. Evol. Comput., Jul. 2006, pp. 1157-1163. (Pubitemid 47130629)
26. L. While, L. Bradstreet, L. Barone, and P. Hingston, "Heuristics for optimizing the calculation of hypervolume for multi-objective optimization problems, " in Proc. IEEE Congr. Evol. Comput., vol. 3. Sep. 2005, pp. 2225-2232. (Pubitemid 41496126)
27. V. Klee, "Can the measure of-n1 [ai, bi] be computed in less than o(nlogn) steps?" Amer. Math. Monthly, vol. 84, no. 4, pp. 284-285, Apr. 1977.
28. J. L. Bentley, "Algorithms for Klees rectangle problems, " Comput. Sci. Dept., Carnegie Mellon Univ., 1977.
29. M. Overmars and C.-K. Yap, "New upper bounds in Klees measure problem, " in Proc. 29th Annu. Symp. Found. Comput. Sci., Oct. 1988, pp. 550-556.
30. N. Beume, "Hypervolumen-basierte selektion in einem evolutionären algorithmus zur mehrzieloptimierung, " 2006.
31. L. Bradstreet, L. While, and L. Barone, "A fast many-objective hypervolume algorithm using iterated incremental calculations, " in Proc. IEEE Congr. Evol. Comput., Jul. 2010, pp. 1-8.
32. N. Beume, C. Fonseca, M. Lopez-Ibañez, L. Paquete, and J. Vahrenhold, "On the complexity of computing the hypervolume indicator, " IEEE Trans. Evol. Comput., vol. 13, no. 5, pp. 1075-1082, Oct. 2009.
33. L. Bradstreet, L. While, and L. Barone, "A fast incremental hypervolume algorithm, " IEEE Trans. Evol. Comput., vol. 12, no. 6, pp. 714-723, Dec. 2008.
34. Q. Yang and S. Ding, "Novel algorithm to calculate hypervolume indicator of pareto approximation set, " in Proc. Adv. Intell. Comput. Theories Applicat., vol. 2. 2007, pp. 235-244.
35. A. Guerreiro, "Efficient algorithms for the assessment of stochastic multiobjective optimizers, " Masters thesis, Dept. Comput. Sci. Eng., IST, Tech. Univ. Lisbon, Lisbon, Portugal, 2011.
36. K. Bringmann and T. Friedrich, "Approximating the volume of unions and intersections of high-dimensional geometric objects, " Comput. Geometry, vol. 43, no. 6, pp. 601-610, 2010.
37. K. Bringmann and T. Friedrich, "An efficient algorithm for computing hypervolume contributions, " Evol. Comput., vol. 18, no. 3, pp. 383-402, 2010.
38. K. Bringmann and T. Friedrich, "Approximating the least hypervolume contributor: NP-hard in general, but fast in practice, " in Proc. EMO, LNCS 5467. 2009, pp. 6-20.
39. K. Bringmann, "Bringing order to special cases of Klees measure problem, " Comput. Res. Repository, 2013, arXiv:1301.7154
40. V. Grunert da Fonseca, C. Fonseca, and A. Hall, "Inferential performance assessment of stochastic optimisers and the attainment function, " in Proc. Evol. Multi-Criterion Optimiz., 2001, LNCS 1993, pp. 213-225. . (Pubitemid 33241389)