Central European Journal of Operations Research

, Volume 25, Issue 4, pp 929–952 | Cite as

Empirical study of the improved UNIRANDI local search method

Original Paper

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.

Keywords

Direct search Local search Global optimization Benchmarking 

Notes

Acknowledgements

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

References

  1. Audet C, Dennis JE (2006) Mesh adaptive direct search algorithms for constrained optimization. SIAM J Optim 17:188–217CrossRefGoogle Scholar
  2. Boender C, Rinnooy Kan A, Timmer G, Stougie L (1982) A stochastic method for global optimization. Math Progr 22:125–140CrossRefGoogle Scholar
  3. Csendes T (1988) Nonlinear parameter estimation by global optimization–efficiency and reliability. Acta Cybern 8(4):361–370Google Scholar
  4. Csendes T, Pál L, Sendín JOH, Banga JR (2008) The GLOBAL optimization method revisited. Optim Lett 2(4):445–454CrossRefGoogle Scholar
  5. 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, USAGoogle Scholar
  6. Custódio AL, Rocha H, Vicente LN (2010) Incorporating minimum frobenius norm models in direct search. Comput Optim Appl 46:265–278CrossRefGoogle Scholar
  7. Dolan E, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math Progr 91:201–213CrossRefGoogle Scholar
  8. 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 39–43Google Scholar
  9. Gilmore P, Kelley CT (1995) An implicit filtering algorithm for optimization of functions with many local minima. SIAM J Optim 5:269–285CrossRefGoogle Scholar
  10. Grippo L, Rinaldi F (2015) A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations. Comput Optim Appl 60(1):1–33CrossRefGoogle Scholar
  11. 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 75–102CrossRefGoogle Scholar
  12. Hansen N, Auger A, Finck S, Ros R (2009) Real-parameter black-box optimization benchmarking 2009: Experimental setup. Tech. Rep. RR-6828, INRIAGoogle Scholar
  13. 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 1689–1696Google Scholar
  14. Hirsch MJ, Pardalos PM, Resende MGC (2010) Speeding up continuous GRASP. Eur J Oper Res 205(3):507–521CrossRefGoogle Scholar
  15. Huyer W, Neumaier A (1999) Global optimization by multilevel coordinate search. J Global Optim 14(4):331–355CrossRefGoogle Scholar
  16. 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):49–62CrossRefGoogle Scholar
  17. Ingber L (1996) Adaptive simulated annealing (ASA): lessons learned. J Control Cybern 25:33–54Google Scholar
  18. 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, FinlandGoogle Scholar
  19. Johnson S (2015) The nlopt nonlinear-optimization package. http://ab-initio.mit.edu/nlopt. Accessed July 2015
  20. Kelley CT (1999) Iterative methods for optimization. Frontiers in applied mathematics. SIAM, PhiladelphiaCrossRefGoogle Scholar
  21. Liepins GE, Hilliard MR (1989) Genetic algorithms: foundations and applications. Ann Oper Res 21:31–58CrossRefGoogle Scholar
  22. 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):2233–2255CrossRefGoogle Scholar
  23. Moré JJ, Wild SM (2009) Benchmarking derivative-free optimization algorithms. SIAM J Optim 20(1):172–191CrossRefGoogle Scholar
  24. Nelder JA, Mead R (1965) The downhill simplex method. Comput J 7:308–313CrossRefGoogle Scholar
  25. 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 117–120Google Scholar
  26. Pál L, Csendes T, Markót M, Neumaier A (2012) Black-box optimization benchmarking of the global method. Evol Comput 20(4):609–639CrossRefGoogle Scholar
  27. Pošík P, Huyer W, Pál L (2012) A comparison of global search algorithms for continuous black box optimization. Evol Comput 20(4):509–541CrossRefGoogle Scholar
  28. Powell MJD (1964) An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput J 7(2):155–162CrossRefGoogle Scholar
  29. Powell MJD (2006) The NEWUOA software for unconstrained optimization without derivatives. Large scale nonlinear optimization. Springer, Berlin, pp 255–297CrossRefGoogle Scholar
  30. 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, CambridgeGoogle Scholar
  31. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C. The art of scientific computing, 2nd edn. Cambridge University Press, New YorkGoogle Scholar
  32. Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE T Evolut Comput 12(1):64–79CrossRefGoogle Scholar
  33. Rios L, Sahinidis N (2013) Derivative-free optimization: a review of algorithms and comparison of software implementations. J Global Optim 56(3):1247–1293CrossRefGoogle Scholar
  34. Rosenbrock HH (1960) An automatic method for finding the greatest or least value of a function. Comput J 3(3):175–184CrossRefGoogle Scholar
  35. Storn R, Price K (1997) Differential evolutiona simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359CrossRefGoogle Scholar
  36. Torczon VJ (1997) On the convergence of pattern search algorithms. SIAM J Optim 7:1–25CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Faculty of Economics, Socio-Human Sciences and EngineeringSapientia - Hungarian University of TransylvaniaMiercurea CiucRomania

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