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Global Optimization of Some Difficult Benchmark Functions by Host-Parasite Coevolutionary Algorithm

Author

Listed:
  • Sudhanshu K Mishra

    (North-Eastern Hill University, Shillong, India)

Abstract

This paper proposes a novel method of global optimization based on host-parasite co-evolution. It also develops a Fortran-77 code for the algorithm. The algorithm has been tested on 100 benchmark functions (of which the results of 32 relatively harder problems have been reported). In its search ability, the proposed method is comparable to the Differential Evolution method of global optimization. The method has been used for solving the 'completing the incomplete correlation matrix' problem encountered in financial economics. It is found that the proposed methods as well as the Differential Evolution method solves the problem, but the proposed method provides results much faster than the Differential Evolution method.

Suggested Citation

  • 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.
    • Handle: RePEc:ebl:ecbull:eb-12-00599
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    References listed on IDEAS

    as
    1. 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.
    2. Mishra, SK, 2004. "Optimal solution of the nearest correlation matrix problem by minimization of the maximum norm," MPRA Paper 1783, University Library of Munich, Germany.
    3. Raoul Pietersz & Patrick Groenen, 2004. "Rank reduction of correlation matrices by majorization," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 649-662.
    4. 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.
    5. Mishra, SK, 2007. "Minimization of Keane’s Bump Function by the Repulsive Particle Swarm and the Differential Evolution Methods," MPRA Paper 3098, University Library of Munich, Germany, revised 05 May 2007.
    6. Chesney, Marc & Scott, Louis, 1989. "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 267-284, September.
    7. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1999. "Random matrix theory," Science & Finance (CFM) working paper archive 500052, Science & Finance, Capital Fund Management.
    8. Ingram Olkin, 1981. "Range restrictions for product-moment correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 469-472, December.
    9. Grubisic, I. & Pietersz, R., 2005. "Efficient Rank Reduction of Correlation Matrices," ERIM Report Series Research in Management ERS-2005-009-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    10. Ormerod, Paul & Mounfield, Craig, 2000. "Random matrix theory and the failure of macro-economic forecasts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 497-504.
    11. Mishra, SK, 2007. "Completing correlation matrices of arbitrary order by differential evolution method of global optimization: A Fortran program," MPRA Paper 2000, University Library of Munich, Germany.
    12. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    14. Mishra, SK, 2006. "Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions," MPRA Paper 1005, University Library of Munich, Germany.
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    Citations

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    Cited by:

    1. Nayak, Purusottam & Mishra, SK, 2014. "A state level analysis of the status of social sector in India," MPRA Paper 58144, University Library of Munich, Germany.
    2. Sudhanshu K. MISHRA, 2017. "Almost equi-marginal principle based composite index of globalization: China, India and Pakistan," Journal of Economic and Social Thought, KSP Journals, vol. 4(3), pages 335-351, Seprember.
    3. Mishra, SK, 2017. "A New Kind of Two-Stage Least Squares Based on Shapley Value Regression," MPRA Paper 83534, University Library of Munich, Germany.
    4. Mishra, Sudhanshu K, 2014. "What happens if in the principal component analysis the Pearsonian is replaced by the Brownian coefficient of correlation?," MPRA Paper 56861, University Library of Munich, Germany.
    5. Sudhanshu K. MISHRA, 2017. "Measuring degree of globalization of African Countries on almost equimarginal contribution principle," Journal of Economics Bibliography, KSP Journals, vol. 4(4), pages 345-353, December.
    6. Sudhanshu K. MISHRA, 2016. "BA Note on Construction of a Composite Index by Optimization of Shapley Value Shares of the Constituent Variables," Turkish Economic Review, KSP Journals, vol. 3(3), pages 466-472, September.
    7. Sudhanshu K. Mishra, 2018. "A Study on Regime Type and Globalization in Simultaneous Equation Framework," Journal of Economics and Financial Analysis, Tripal Publishing House, vol. 2(1), pages 99-128.
    8. H. R. E. H. Bouchekara, 2020. "Most Valuable Player Algorithm: a novel optimization algorithm inspired from sport," Operational Research, Springer, vol. 20(1), pages 139-195, March.
    9. Sudhanshu K. MISHRA, 2016. "Shapley Value Regression and the Resolution of Multicollinearity," Journal of Economics Bibliography, KSP Journals, vol. 3(3), pages 498-515, September.

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    More about this item

    Keywords

    cuckoo-host co-evolution; cuckoo search; global optimization; differential evolution; levy flight; benchmark functions;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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