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

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  • Mishra, Sudhanshu

Abstract

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.

Suggested Citation

  • Mishra, Sudhanshu, 2006. "Some new test functions for global optimization and performance of repulsive particle swarm method," MPRA Paper 2718, University Library of Munich, Germany.
    • 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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    Citations

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    Cited by:

    1. Weitao Sun & Yuan Dong, 2011. "Study of multiscale global optimization based on parameter space partition," Journal of Global Optimization, Springer, vol. 49(1), pages 149-172, January.
    2. Timothy Haas, 2020. "Developing political-ecological theory: The need for many-task computing," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-26, November.
    3. Beopsoo Kim & Nikita Rusetskii & Haesung Jo & Insu Kim, 2021. "The Optimal Allocation of Distributed Generators Considering Fault Current and Levelized Cost of Energy Using the Particle Swarm Optimization Method," Energies, MDPI, vol. 14(2), pages 1-18, January.
    4. 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.
    5. Mishra, SK, 2006. "Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multi-modal Benchmark Functions," MPRA Paper 1743, University Library of Munich, Germany.
    6. Linas Stripinis & Remigijus Paulavičius, 2022. "Experimental Study of Excessive Local Refinement Reduction Techniques for Global Optimization DIRECT-Type Algorithms," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
    7. Mehmet Hakan Satman & Emre Akadal, 2020. "Machine Coded Compact Genetic Algorithms for Real Parameter Optimization Problems," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 8(1), pages 43-58, June.
    8. 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, vol. 55(1), pages 165-188, January.
    9. Mishra, SK, 2012. "Global optimization of some difficult benchmark functions by cuckoo-hostco-evolution meta-heuristics," MPRA Paper 40615, University Library of Munich, Germany.
    10. Ziadi, Raouf & Bencherif-Madani, Abdelatif & Ellaia, Rachid, 2016. "Continuous global optimization through the generation of parametric curves," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 65-83.

    More about this item

    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;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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