Abstract
We propose a new data structure for the efficient computation of the nondominance problem which occurs in most multi-objective optimization algorithms. The strength of our data structure is illustrated by a comparison both to the linear list approach and the quad tree approach on a category of problems. The computational results indicate that our method is particularly advantageous in the case where the proportion of the nondominated vectors versus the total set of criterion vectors is not too large.
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References
J. L. Bentley. Multidimensional binary search trees used for associative searching. Communications of the ACM, pages 509–517, 1975.
J. L. Bentley and J. H. Friedmann. Data structures for range searching. Computing Surveys, 4: 398–409, 1979.
M. Dellnitz, R. Elsässer, T. Hestermeyer, O. Schütze, and S. Sertl. Covering Pareto sets with multilevel subdivision techniques. to appear, 2002.
R. M. Everson, J.E. Fieldsend, and S. Singh. Full elite sets for multi-objective optimization. In I. C. Parmee, editor, Adaptive Computing in Design and Manufacture V, Springer, 2002.
F. P. Preparata and M. I. Shamos. Computational Geometry — An Introduction. Springer Verlag, 1988.
J. Fieldsend, R.M. Everson, and S. Singh. Using unconstrained elite archives for multi-objective optimisation. to appear, 2003.
R. A. Finkel and J. L. Bentley. Quad trees, a datastructure for retrieval on composite keys. Acta Informatica, 4:1–9, 1974.
P. Gupta, R. Janardan, M. Smid, and B. Dasgupta. The rectangle enclosure and point-dominance problems revisited. Int. J. Comput. Geom. Appl., 5:437–455, 1997.
W. Habenicht. Quad trees, a datatructure for discrete vector optimization problems. Lecture Notes in Economics and Mathematical Systems, 209:136–145, 1983.
M. de Berg and M. van Kreveld and M. Overmars and O. Scharzkopf. Computational Geometry: algorithms and applications. Springer Verlag, 1997.
E. M. McCreight. Priority search trees. SIAM Journal on Computing, 14:257–276, 1985.
S. Mostaghim, J. Teich, and A. Tyagi. Comparison of data structures for storing pareto-sets in moeas. Int. J. Comput. Geom. Appl., 5:437–455, 2002.
M. Sun and R. E. Steuer. InterQuad: An interactive quad tree based procedure for solving the discrete alternative multiple criteria problem. European Journal of Operational Research, 89:462–472, 1996.
M. Sun and R. E. Steuer. Quad trees and linear lists for identifying nondominated criterion vectors. INFORMS J. Comp., 8:367–375, 1996.
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Schütze, O. (2003). A New Data Structure for the Nondominance Problem in Multi-objective Optimization. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds) Evolutionary Multi-Criterion Optimization. EMO 2003. Lecture Notes in Computer Science, vol 2632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_36
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DOI: https://doi.org/10.1007/3-540-36970-8_36
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