CFP last date
20 December 2024
Reseach Article

A Fast Algorithm for Finding the Non Dominated Set in Multi objective Optimization

by K.K.Mishra, Sandeep Harit
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 1 - Number 25
Year of Publication: 2010
Authors: K.K.Mishra, Sandeep Harit
10.5120/460-764

K.K.Mishra, Sandeep Harit . A Fast Algorithm for Finding the Non Dominated Set in Multi objective Optimization. International Journal of Computer Applications. 1, 25 ( February 2010), 35-39. DOI=10.5120/460-764

@article{ 10.5120/460-764,
author = { K.K.Mishra, Sandeep Harit },
title = { A Fast Algorithm for Finding the Non Dominated Set in Multi objective Optimization },
journal = { International Journal of Computer Applications },
issue_date = { February 2010 },
volume = { 1 },
number = { 25 },
month = { February },
year = { 2010 },
issn = { 0975-8887 },
pages = { 35-39 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume1/number25/460-764/ },
doi = { 10.5120/460-764 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T19:48:32.704730+05:30
%A K.K.Mishra
%A Sandeep Harit
%T A Fast Algorithm for Finding the Non Dominated Set in Multi objective Optimization
%J International Journal of Computer Applications
%@ 0975-8887
%V 1
%N 25
%P 35-39
%D 2010
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The working of single objective optimization algorithm and multi objective optimization algorithm is quite different. This difference is due to number of optimal solution approached by both the algorithms. In single objective optimization problem there will be a single optimal solution, even though in multi model optimization there may be more than one solution but we are interested in only one optimal solution, where as in multi objective optimization problem, there will be many set of optimal solutions. These sets are called different non dominated front, and every non dominated front will contain a set of non dominated solutions thus there are two tasks of an ideal multi objective optimization algorithm (i) To find multiple non dominated fronts (or to identify different set of non dominated solutions). (ii) To seek for Pareto optimal solutions with a good diversity in objective and decision variable values.

References
  1. Jun Du, Zhihua Cai and Yunliang Chen," A Sorting Based Algorithm for Finding Non-Dominated Set in Multi-Objective Optimization" Third International Conference on Natural Computation (ICNC 2007)
  2. K. Deb, "Multi-objective Optimization Using Evolutionary Algorithms," JOHN WILEY&SONS, LTD, 2001 pp.33-43, 2000.
  3. . K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan. Afast elitist non-dominated sorting genetic algorithm for multi-objectv e optimization: NSGA-II. In Proceeding of the 6th International Conference on Parallel Problem Solving from Nature, Pages 849-858, 2000.
  4. . L. Ding. S.Zeng. and L. Kang, "A fast algorithm on finding the non-dominated set in multi-objectve optimization.", In Proceedings of International Conference on Evolutionary Computation, pages 2565-2571, 2003
  5. A. Freitas," A critical review of multi-objective optimization in data mining: a position paper. ",SIGKDD Explorations, 6(2): 77-86, 2004.
  6. J. Knowles and D. Corne,"Reducing local optima in single-objective problems by multiobjectivization", In Proceedings of the 1st International Conference on Evolutionary Multi-Criterion Optimization, pages 269-283, 2001.
  7. H. Kung. F. Luccio, and F. Preparata,"On finding the maxima of a set of vectors.", Journal of the Association Computing Machinery, 22(4) : 469-476, 1975.
  8. E. Zitzler, M. Laumanns, and L. Thiele,"Spea2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization.", In Proceedings of the Evolutionary Methods for Design, Optimization, and Control, 19-26, Barcelona, Spain, 2002.
  9. . C. Fonseca, M. and P. J. Fleming " Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization," In S. Forrest (Ed.), Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, California, pp. 416C423. Morgan Kaufmann. , 2003
  10. . J. Horn, and N. Nafpliotis " Multiobjective optimization using the niched Pareto genetic algorithm," IlliGAL Report 93005, Illinois Genetic Algorithms Laboratory, University of Illinois, Urbana, Champaign.,1993
  11. . J. Horn, N. Nafpliotis, and D. E. Goldberg" A niched Pareto genetic algorithm for multiobjective optimization," In Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Computation, Volume 1, Piscataway, NJ, pp. 82C87. IEEE. ,1994
  12. . R. C. Purshouse, P. J. Fleming " The Multi-objective Genetic Algorithm Applied to Benchmark Problems-an Analysis," Research Report No. 796. Department of Automatic Control and Systems Engineering University of Sheffield, Sheffield, S1 3JD, UK. 2001
  13. . J. D. Schaffer "Multiple objective optimization with vector evaluated genetic algorithms," In J. J. Grefenstette (Ed.),Proceedings of an International Conference on Genetic Algorithms and Their Applications, Pittsburgh, PA, pp. 93C100. sponsored by Texas Instruments and U.S. Navy Center for Applied Research in Artificial Intelligence (NCARAI), 1985
  14. . N. Srinivas and K. Deb , " Multiobjective optimization using non-dominated sorting in genetic algorithms," Evolutionary Computation 2(3), 221C248, 1985
  15. . A. Tiwari and R. Roy(2002) " Generalised Regression GA for Handling Inseparable Function Interaction: Algorithm and Applications," Proceedings of the seventh international conference on parallel problem solving from nature. ( PPSN VII). Granada, Spain
  16. . E. Zitzler" Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications," Ph. D. thesis, Swiss Federal Institute of Technology (ETH) Zurich, Switzerland. TIK-Schriftenreihe Nr. 30, Diss ETH No. 13398, Shaker Verlag, Aachen, Germany, 1999
  17. . E. Zitzler, M. Laumanns and L. Thiele," SPEA2: Improving the Strength Pareto Evolutionary Algorithm," TIK-Report 103. ETH Zentrum, Gloriastrasse 35, CH-8092 Zurich, Switzerland. 1999.
Index Terms

Computer Science
Information Sciences

Keywords

FAST ALGORITHM MULTIOBJECTIVE OPTIMIZATION