Optimization of the Multi-Threaded Interval Algorithm for the Pareto-Set Computation

• Autorzy: Kubica B. J. , Wodniak A.
• Języki publikacji: EN

Abstrakty

EN

Previous investigations of the authors surveyed the possibility of applying interval methods to seek the Paretofront of a multicriterial nonlinear problem. An efficient algorithm has been proposed and its implementation in a multicore environment has been done and tested. This paper has two goals. First one is to tune the developed algorithm to increase the speedup of the multi-threaded variant. The second one is to extend the algorithm to compute not only the Paretofront (in the criteria space), but also the Pareto-set (in the decision space). Numerical results for suitable test problems are presented.

Słowa kluczowe

EN

interval computations; multicriterial analysis; multithreaded programming; Pareto set; POSIX threads; shared-memory parallelization

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2010
• Tom: nr 1
• Strony: 70--75
• Opis fizyczny: Bibliogr. 16 poz., tab.

Twórcy

autor

Kubica B. J.

autor

Wodniak A.

• Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska st 15/19, 00-665 Warsaw, Poland,

Bibliografia

• [1] L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis. London: Springer, 2001.
• [2] V. Barichard and J. K. Hao, “Population and Interval Constraint Propagation Algorithm”, in Second International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003), Faro, Portugal, April 8–11, 2003, LNCS, vol. 2632. Berlin-Heidelberg: Springer, 2003, pp. 81–101.
• [3] G. R. Ruetsch, “An interval algorithm for multi-objective optimization”, Struct. Multidiscip. Opt., vol. 30, no. 1, pp. 27–37, 2005.
• [4] B. J. Kubica and A. Woźniak, “Interval methods for computing the Pareto-front of a multicriterial problem”, in The Seventh International Conference on Parallel Processing and Applied Mathematics PPAM 2007, Gdańsk, Poland, September 2007, LNCS, vol. 4967. Berlin-Heidelberg: Springer, 2008, pp. 1382–1391.
• [5] M. Marks and E. Niewiadomska-Szynkiewicz, “Multiobjective approach to localization in wireless sensor networks”, J. Telecommun. Inform. Technol., no. 3, pp. 59–67, 2009.
• [6] W. Ogryczak, “Reference point method with importance weighted partial achievements”, J. Telecommun. Inform. Technol., no. 4, pp. 17–25, 2008.
• [7] C. Gomes da Silva and J. C. N. Cl´imaco, “A note on the computation of ordered supported non-dominated solutions in the bi-criteria minimum spanning tree problems”, J. Telecommun. Inform. Technol., no. 4, pp. 11–15, 2007.
• [8] B. J. Kubica and A. Woźniak, “A multi-threaded interval algorithm for the Pareto-front computation in a multi-core environment”, in PARA 2008 Conf., Trondheim, Norway, 2008.
• [9] E. Hansen, Global Optimization Using Interval Analysis. New York: Marcel Dekker, 1992.
• [10] R. B. Kearfott, Rigorous Global Search: Continuous Problems. Dordrecht: Kluwer, 1996.
• [11] R. B. Kearfott, M. T. Nakao, A. Neumaier, S. M. Rump, S. P. Shary, and P. van Hentenryck, “Standardized notation in interval analysis”, http://www.mat.univie.ac.at/ neum/software/int/notation.ps.gz
• [12] L. Jaulin and E. Walter, “Set inversion via interval analysis for nonlinear bounded-error estimation”, Automatica, vol. 29, no. 4, pp. 1053–1064, 1993.
• [13] I. Y. Kim and O. L. deWeck, “Adaptive weighted-sum method for biobjective optimization: Pareto front generation”, Struct. Multidiscip. Opt., vol. 29, no. 2, pp. 149–158, 2005.
• [14] “C-XSC library”, http://www.xsc.de
• [15] “POSIX threads programming”, https://computing.llnl.gov/tutorials/pthreads
• [16] E. Zitzler, M. Laumanns, and M. Thiele, “SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization”, in Evolutionary Methods for Design Optimization and Control, K. Giannakoglou, D. Tsahalis, J. Periaux, K. Papailiou, and T. Fogarty, Eds. Barcelona: CIMNE, 2002.