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Some new test functions for global optimization and performance of repulsive particle swarm method


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  • Mishra, Sudhanshu


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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 2718.

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Date of creation: 23 Aug 2006
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Handle: RePEc:pra:mprapa:2718

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.
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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;

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Cited by:
  1. Mishra, SK, 2012. "Global optimization of some difficult benchmark functions by cuckoo-hostco-evolution meta-heuristics," MPRA Paper 40615, University Library of Munich, Germany.
  2. Mishra, SK, 2006. "Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multi-modal Benchmark Functions," MPRA Paper 449, University Library of Munich, Germany.
  3. Sudhanshu K Mishra, 2013. "Global Optimization of Some Difficult Benchmark Functions by Host-Parasite Coevolutionary Algorithm," Economics Bulletin, AccessEcon, vol. 33(1), pages 1-18.
  4. Massimiliano Kaucic, 2013. "A multi-start opposition-based particle swarm optimization algorithm with adaptive velocity for bound constrained global optimization," Journal of Global Optimization, Springer, Springer, vol. 55(1), pages 165-188, January.
  5. Weitao Sun & Yuan Dong, 2011. "Study of multiscale global optimization based on parameter space partition," Journal of Global Optimization, Springer, Springer, vol. 49(1), pages 149-172, January.


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