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Empirical study of the improved UNIRANDI local search method

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Abstract

UNIRANDI is a stochastic local search algorithm that performs line searches from starting points along good random directions. In this paper, we focus on a modified version of this method. The new algorithm, addition to the random directions, considers more promising directions in order to speed up the optimization process. The performance of the new method is tested empirically on standard test functions in terms of function evaluations, success rates, error values, and CPU time. It is also compared to the previous version as well as other local search methods. Numerical results show that the new method is promising in terms of robustness and efficiency.

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References

  • Audet C, Dennis JE (2006) Mesh adaptive direct search algorithms for constrained optimization. SIAM J Optim 17:188–217

    Article  Google Scholar 

  • Boender C, Rinnooy Kan A, Timmer G, Stougie L (1982) A stochastic method for global optimization. Math Progr 22:125–140

    Article  Google Scholar 

  • Csendes T (1988) Nonlinear parameter estimation by global optimization–efficiency and reliability. Acta Cybern 8(4):361–370

    Google Scholar 

  • Csendes T, Pál L, Sendín JOH, Banga JR (2008) The GLOBAL optimization method revisited. Optim Lett 2(4):445–454

    Article  Google Scholar 

  • Currie J, Wilson DI (2012) OPTI: lowering the barrier between open source optimizers and the industrial MATLAB user. In: Sahinidis N, Pinto J (eds) Foundations of computer-aided process operations. Savannah, USA

    Google Scholar 

  • Custódio AL, Rocha H, Vicente LN (2010) Incorporating minimum frobenius norm models in direct search. Comput Optim Appl 46:265–278

    Article  Google Scholar 

  • Dolan E, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math Progr 91:201–213

    Article  Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of sixth international symposium micro machine and human science. Nagoya, Japan, pp 39–43

  • Gilmore P, Kelley CT (1995) An implicit filtering algorithm for optimization of functions with many local minima. SIAM J Optim 5:269–285

    Article  Google Scholar 

  • Grippo L, Rinaldi F (2015) A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations. Comput Optim Appl 60(1):1–33

    Article  Google Scholar 

  • Hansen N (2006) The CMA evolution strategy: a comparing review. In: Lozano JA, Larranaga P, Inza I, Bengoetxea E (eds) Towards a new evolutionary computation. Advances on estimation of distribution algorithms. Springer, Berlin, pp 75–102

    Chapter  Google Scholar 

  • Hansen N, Auger A, Finck S, Ros R (2009) Real-parameter black-box optimization benchmarking 2009: Experimental setup. Tech. Rep. RR-6828, INRIA

  • Hansen N, Auger A, Ros R, Finck S, Pošík P (2010) Comparing results of 31 algorithms from the black-box optimization benchmarking bbob-2009. In: GECCO ’10: Proceedings of the 12th annual conference on Genetic and evolutionary computation. ACM, New York, NY, USA, pp 1689–1696

  • Hirsch MJ, Pardalos PM, Resende MGC (2010) Speeding up continuous GRASP. Eur J Oper Res 205(3):507–521

    Article  Google Scholar 

  • Huyer W, Neumaier A (1999) Global optimization by multilevel coordinate search. J Global Optim 14(4):331–355

    Article  Google Scholar 

  • Hvattum LM, Duarte A, Glover F, Martí R (2013) Designing effective improvement methods for scatter search: an experimental study on global optimization. Soft Comput 17(1):49–62

    Article  Google Scholar 

  • Ingber L (1996) Adaptive simulated annealing (ASA): lessons learned. J Control Cybern 25:33–54

    Google Scholar 

  • Järvi T (1973) A random search optimizer with an application to a max-min problem. Publications of the Institute for Applied Mathematics (3), University of Turku, Finland

  • Johnson S (2015) The nlopt nonlinear-optimization package. http://ab-initio.mit.edu/nlopt. Accessed July 2015

  • Kelley CT (1999) Iterative methods for optimization. Frontiers in applied mathematics. SIAM, Philadelphia

    Book  Google Scholar 

  • Liepins GE, Hilliard MR (1989) Genetic algorithms: foundations and applications. Ann Oper Res 21:31–58

    Article  Google Scholar 

  • Montes de Oca MA, Aydin D, Stützle T (2011) An incremental particle swarm for large-scale continuous optimization problems: an example of tuning-in-the-loop (re)design of optimization algorithms. Soft Comput 15(11):2233–2255

    Article  Google Scholar 

  • Moré JJ, Wild SM (2009) Benchmarking derivative-free optimization algorithms. SIAM J Optim 20(1):172–191

    Article  Google Scholar 

  • Nelder JA, Mead R (1965) The downhill simplex method. Comput J 7:308–313

    Article  Google Scholar 

  • Pál L, Csendes T (2015) An improved stochastic local search method in a multistart framework. In: Proceedings of the 10th jubilee ieee international symposium on applied computational intelligence and informatics, Timisoara, pp 117–120

  • Pál L, Csendes T, Markót M, Neumaier A (2012) Black-box optimization benchmarking of the global method. Evol Comput 20(4):609–639

    Article  Google Scholar 

  • Pošík P, Huyer W, Pál L (2012) A comparison of global search algorithms for continuous black box optimization. Evol Comput 20(4):509–541

    Article  Google Scholar 

  • Powell MJD (1964) An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput J 7(2):155–162

    Article  Google Scholar 

  • Powell MJD (2006) The NEWUOA software for unconstrained optimization without derivatives. Large scale nonlinear optimization. Springer, Berlin, pp 255–297

    Book  Google Scholar 

  • Powell MJD (2009) The BOBYQA algorithm for bound constrained optimization without derivatives. Tech. Rep. NA2009/06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C. The art of scientific computing, 2nd edn. Cambridge University Press, New York

    Google Scholar 

  • Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE T Evolut Comput 12(1):64–79

    Article  Google Scholar 

  • Rios L, Sahinidis N (2013) Derivative-free optimization: a review of algorithms and comparison of software implementations. J Global Optim 56(3):1247–1293

    Article  Google Scholar 

  • Rosenbrock HH (1960) An automatic method for finding the greatest or least value of a function. Comput J 3(3):175–184

    Article  Google Scholar 

  • Storn R, Price K (1997) Differential evolutiona simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    Article  Google Scholar 

  • Torczon VJ (1997) On the convergence of pattern search algorithms. SIAM J Optim 7:1–25

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Sapientia Foundation - Institute for Scientific Research with the Grant No. 252/11/28/04/2015.

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Authors and Affiliations

  1. Faculty of Economics, Socio-Human Sciences and Engineering, Sapientia - Hungarian University of Transylvania, 530104, Miercurea Ciuc, Romania

    László Pál

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  1. László Pál
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Correspondence to László Pál.

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Pál, L. Empirical study of the improved UNIRANDI local search method. Cent Eur J Oper Res 25, 929–952 (2017). https://doi.org/10.1007/s10100-017-0470-2

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