Mishra, SK (2006): Repulsive Particle Swarm Method on Some Difficult Test Problems of Global Optimization.

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Abstract
In this paper we test a particular variant of the (Repulsive) Particle Swarm method on some rather difficult global optimization problems. A number of these problems are collected from the extant literature and a few of them are newly introduced. First, we introduce the Particle Swarm method of global optimization and its variant called the 'Repulsive Particle Swarm' (RPS) method. Then we endow the particles with some stronger local search abilities  much like tunneling  so that each particle can make a search in its neighborhood to optimize itself. Next, we introduce the test problems, the existing as well as the new ones. We also give plots of some of these functions to help appreciation of the optimization problem. Finally, we present the results of the RPS optimization exercise and compare the results with those obtained by using the Genetic algorithm (GA)and/or Simulated annealing (SA) method. We append the (Fortran) computer program that we have developed and used in this exercise.
Our findings indicate that neither the RPS nor the GA/SA method can assuredly find the optimum of an arbitrary function. In case of the Needleeye and the Corana functions both methods perform equally well while in case of Bukin's 6th function both yield the values of decision variables far away from the right ones. In case of zerosum function, GA performs better than the RPS. In case of the Perm #2 function, both of the methods fail when the dimension grows larger. In several cases, GA falters or fails while RPS succeeds. In case of N#1 through N#5 and the ANNs XOR functions the RPS performs better than the Genetic algorithm.
It is needed that we find out some criteria to classify the problems that suit (or does not suit) a particular method. This classification will highlight the comparative advantages of using a particular method for dealing with a particular class of problems.
Item Type:  MPRA Paper 

Institution:  NorthEastern Hill University, Shillong (India) 
Original Title:  Repulsive Particle Swarm Method on Some Difficult Test Problems of Global Optimization 
Language:  English 
Keywords:  Repulsive Particle Swarm; Global optimization; nonconvex functions; Bounded rationality; local optima; Bukin; Corana; Rcos; Freudenstein Roth; Goldenstein Price; ANNs XOR; Perm; Power sum; Zero sum; Needleeye; Genetic algorithms; variants; Fortran; computer program; benchmark; test 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C65  Miscellaneous Mathematical Tools C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C69  Other C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling 
Item ID:  1742 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  11. Feb 2007 
Last Modified:  12. Feb 2013 00:14 
References:  · Bauer, J.M.: “Harnessing the Swarm: Communication Policy in an Era of Ubiquitous Networks and Disruptive Technologies”, Communications and Strategies, 45, 2002. · Bukin, A. D.: New Minimization Strategy For NonSmooth Functions, Budker Institute of Nuclear Physics preprint BUDKERINP199779, Novosibirsk 1997. · Eberhart R.C. and Kennedy J.: “A New Optimizer using Particle Swarm Theory”, Proceedings Sixth Symposium on Micro Machine and Human Science, pp. 39–43. IEEE Service Center, Piscataway, NJ, 1995. · Fleischer, M.: “Foundations of Swarm Intelligence: From Principles to Practice”, Swarming Network Enabled C4ISR, arXiv:nlin.AO/0502003 v1 2 Feb 2005. · Hayek, F.A.: The Road to Serfdom, Univ. of Chicago Press, Chicago, 1944. · Jung, B.S. and Karney, B.W.: “Benchmark Tests of Evolutionary Computational Algorithms”, Environmental Informatics Archives (International Society for Environmental Information Sciences), 2, pp. 731742, 2004. · Mishra, S.K.: “Some Experiments on Fitting of Gielis Curves by Simulated Annealing and Particle Swarm Methods of Global Optimization”, Social Science Research Network (SSRN): http://ssrn.com/abstract=913667, Working Papers Series, 2006 (a). · Mishra, S.K.: “Least Squares Fitting of ChacónGielis Curves by the Particle Swarm Method of Optimization”, Social Science Research Network (SSRN), Working Papers Series, http://ssrn.com/abstract=917762 , 2006 (b). · Mishra, S.K.: “Performance of Repulsive Particle Swarm Method in Global Optimization of Some Important Test Functions: A Fortran Program” , Social Science Research Network (SSRN), Working Papers Series, http://ssrn.com/abstract=924339 , 2006 (c). · Mishra, S.K.: “Some New Test Functions for Global Optimization and Performance of Repulsive Particle Swarm Method”, Social Science Research Network (SSRN): http://ssrn.com/abstract=927134, Working Papers Series, 2006 (d). · Nagendra, S.: Catalogue of Test Problems for Optimization Algorithm Verification, Technical Report 97CRD110, General Electric Company, 1997. · Parsopoulos, K.E. and Vrahatis, M.N., “Recent Approaches to Global Optimization Problems Through Particle Swarm Optimization”, Natural Computing, 1 (23), pp. 235 306, 2002. · Prigogine, I. and Strengers, I.: Order Out of Chaos: Man’s New Dialogue with Nature, Bantam Books, Inc. NY, 1984. · Silagadge, Z.K.: “Finding TwoDimensional Peaks”, Working Paper, Budkar Insttute of Nuclear Physics, Novosibirsk, Russia, arXive:physics/0402085 V3 11 Mar 2004. · Simon, H.A.: Models of Bounded Rationality, Cambridge Univ. Press, Cambridge, MA, 1982. · Smith, A.: The Theory of the Moral Sentiments, The Adam Smith Institute (2001 eversion), 1759. · Sumper, D.J.T.: “The Principles of Collective Animal Behaviour”, Phil. Trans. R. Soc. B. 361, pp. 522, 2006. · Veblen, T.B.: "Why is Economics Not an Evolutionary Science" The Quarterly Journal of Economics, 12, 1898. · Veblen, T.B.: The Theory of the Leisure Class, The New American library, NY. (Reprint, 1953), 1899. · Vesterstrøm, J. and Thomsen, R.: “A comparative Study of Differential Evolution, Particle Swarm Optimization, and Evolutionary Algorithms on Numerical Benchmark Problems”, Congress on Evolutionary Computation, 2004. CEC2004, 2, pp. 19801987, 2004. · Whitley, D., Mathias, K., Rana, S. and Dzubera, J.: “Evaluating Evolutionary Algorithms”, Artificial Intelligence, 85, pp. 245276, 1996. · Yao, X. and Liu, Y.: “Fast Evolutionary Programming”, in Fogel, LJ, Angeline, PJ and Bäck, T (eds) Proc. 5th Annual Conf. on Evolutionary programming, pp. 451460, MIT Press, Mass, 1996. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/1742 