Mishra, Sudhanshu (2006): Some new test functions for global optimization and performance of repulsive particle swarm method.
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In this paper we introduce some new test functions to assess the performance of global optimization methods. These functions have been selected partly because several of them are aesthetically appealing and partly because a few of them are really difficult to optimize, while all the functions are multi-modal. Each function has been graphically presented to appreciate its geometrical appearance. To optimize these functions we have used the Repulsive Particle Swarm (RPS) method. We have also appended a computer program of the RPS method. Except two functions, namely the 'crowned cross' and the 'cross-legged table' functions all other new test functions are optimized by the RPS program.The program has also been tested with success on a number of well-established benchmark functions. However, the program fails miserably in optimizing the Bukin and a couple of other functions.
Note: Readers should beware of the plagiarism by one Mr. Sanjeev K Singh, Tezpur University, Assam, who, in his article "A Comparative Study of Genetic Algorithm, Improved-Repulsive Particle Swarm Optimization and Simulated Annealing" published in the proceedings of Advances in Computational Optimization and Analysis of Systems (COSA 2007), 6-9 February, 2007 Outreach Centre, IIT, Kanpur, attributes introduction of some new functions (Bird function, Penholder function, Cross function, etc) and the improved Particle Swarm method to himself.
|Item Type:||MPRA Paper|
|Institution:||North-Eastern Hill University, Shillong (India)|
|Original Title:||Some new test functions for global optimization and performance of repulsive particle swarm method|
|Keywords:||Repulsive particle swarm method; Global optimization; New test functions; Bird function; Pen-holder function; Crowned cross function; Cross-legged table function; Cross function; Cross in tray function; Carrom table function; Holder table function; Test-tube holder function|
|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 > C8 - Data Collection and Data Estimation Methodology; Computer Programs > C88 - Other Computer Software
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
|Depositing User:||Sudhanshu Kumar Mishra|
|Date Deposited:||13. Apr 2007|
|Last Modified:||08. Jan 2014 07:24|
· Ackley, D. H.: A Connectionist Machine for Genetic Hill-Climbing, Kluwer Academic Publishers, Boston, 1987. · 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 Non-Smooth Functions, Budker Institute of Nuclear Physics preprint BUDKER-INP-1997-79, Novosibirsk 1997.. · Chichinadze, V.: “The y -transform for Solving Linear and Nonlinear Programming Problems”, Automata, 5, 347–355, 1969. · Easom, E. E.: A Survey of Global Optimization Techniques, M. Eng. thesis, Univ. Louisville, Louisville, KY, 1990. · 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. · Giunta, A. A.: Aircraft Multidisciplinary Design Optimization using Design of Experiments Theory and Response Surface Modeling Methods, MAD Center Report 97-05-01, Virginia Polytechnic Institute & State Univ. Blacksburg, VA, 1997. · Hayek, F.A.: The Road to Serfdom, Univ. of Chicago Press, Chicago, 1944. · Huang, V.L., Suganthan, P.N. and Liang, J.J. “Comprehensive Learning Particle Swarm Optimizer for Solving Multi-objective Optimization Problems”, International Journal of Intelligent Systems, 21, pp.209–226 (Wiley Periodicals, Inc. Published online in Wiley InterScience www.interscience.wiley.com) , 2006 · Jung, B.S. and Karney, B.W.: “Benchmark Tests of Evolutionary Computational Algorithms”, Environmental Informatics Archives (International Society for Environmental Information Sciences), 2, pp. 731-742, 2004. · Kuester, J.L. and Mize, J.H.: Optimization Techniques with Fortran, McGraw-Hill Book Co. New York, 1973. · Liang, J.J. and Suganthan, P.N. “Dynamic Multi-Swarm Particle Swarm Optimizer”, International Swarm Intelligence Symposium, IEEE # 0-7803-8916-6/05/$20.00. pp. 124-129, 2005. · Madsen, K. and Zilinskas, J.: Testing Branch-and-Bound Methods for Global Optimization, IMM technical report 05, Technical University of Denmark, 2000. · 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 Chacón-Gielis 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). · Nagendra, S.: Catalogue of Test Problems for Optimization Algorithm Verification, Technical Report 97-CRD-110, General Electric Company, 1997. · Parsopoulos, K.E. and Vrahatis, M.N., “Recent Approaches to Global Optimization Problems Through Particle Swarm Optimization”, Natural Computing, 1 (2-3), pp. 235-306, 2002. · Prigogine, I. and Strengers, I.: Order Out of Chaos: Man’s New Dialogue with Nature, Bantam Books, Inc. NY, 1984. · Schwefel, H.P.: Numerical Optimization of Computer Models, Wiley & Sons, Chichester, 1981. · Silagadge, Z.K.: “Finding Two-Dimensional 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 e-version), 1759. · Styblinski, M. and Tang, T.: “Experiments in Nonconvex Optimization: Stochastic Approximation with Function Smoothing and Simulated Annealing”, Neural Networks, 3, 467-483, 1990. · Sumper, D.J.T.: “The Principles of Collective Animal Behaviour”, Phil. Trans. R. Soc. B. 361, pp. 5-22, 2006. · Veblen, T.B.: The Theory of the Leisure Class, The New American library, NY. (Reprint, 1953), 1899. · Whitley, D., Mathias, K., Rana, S. and Dzubera, J.: “Evaluating Evolutionary Algorithms”, Artificial Intelligence, 85, 245-276, 1996.