zbMATH — the first resource for mathematics

Empirical study of the improved UNIRANDI local search method. (English) Zbl 1390.90591
Summary: 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.

90C59 Approximation methods and heuristics in mathematical programming
90C26 Nonconvex programming, global optimization
90C60 Abstract computational complexity for mathematical programming problems
Full Text: DOI
[1] Audet, C; Dennis, JE, Mesh adaptive direct search algorithms for constrained optimization, SIAM J Optim, 17, 188-217, (2006) · Zbl 1112.90078
[2] Boender, C; Rinnooy Kan, A; Timmer, G; Stougie, L, A stochastic method for global optimization, Math Progr, 22, 125-140, (1982) · Zbl 0525.90076
[3] Csendes, T, Nonlinear parameter estimation by global optimization-efficiency and reliability, Acta Cybern, 8, 361-370, (1988) · Zbl 0654.90074
[4] Csendes, T; Pál, L; Sendín, JOH; Banga, JR, The GLOBAL optimization method revisited, Optim Lett, 2, 445-454, (2008) · Zbl 1160.90660
[5] Currie, J; Wilson, DI; Sahinidis, N (ed.); Pinto, J (ed.), OPTI: lowering the barrier between open source optimizers and the industrial MATLAB user, (2012), USA
[6] Custódio, AL; Rocha, H; Vicente, LN, Incorporating minimum Frobenius norm models in direct search, Comput Optim Appl, 46, 265-278, (2010) · Zbl 1190.90280
[7] Dolan, E; Moré, JJ, Benchmarking optimization software with performance profiles, Math Progr, 91, 201-213, (2002) · Zbl 1049.90004
[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 39-43 · Zbl 0525.90076
[9] Gilmore, P; Kelley, CT, An implicit filtering algorithm for optimization of functions with many local minima, SIAM J Optim, 5, 269-285, (1995) · Zbl 0828.65064
[10] Grippo, L; Rinaldi, F, A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations, Comput Optim Appl, 60, 1-33, (2015) · Zbl 1316.90065
[11] Hansen, N; Lozano, JA (ed.); Larranaga, P (ed.); Inza, I (ed.); Bengoetxea, E (ed.), The CMA evolution strategy: a comparing review, 75-102, (2006), Berlin
[12] Hansen N, Auger A, Finck S, Ros R (2009) Real-parameter black-box optimization benchmarking 2009: Experimental setup. Tech. Rep. RR-6828, INRIA · Zbl 0132.11702
[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 1689-1696
[14] Hirsch, MJ; Pardalos, PM; Resende, MGC, Speeding up continuous GRASP, Eur J Oper Res, 205, 507-521, (2010) · Zbl 1189.90055
[15] Huyer, W; Neumaier, A, Global optimization by multilevel coordinate search, J Global Optim, 14, 331-355, (1999) · Zbl 0956.90045
[16] Hvattum, LM; Duarte, A; Glover, F; Martí, R, Designing effective improvement methods for scatter search: an experimental study on global optimization, Soft Comput, 17, 49-62, (2013)
[17] Ingber, L, Adaptive simulated annealing (ASA): lessons learned, J Control Cybern, 25, 33-54, (1996) · Zbl 0860.93035
[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, Finland · Zbl 0956.90045
[19] Johnson S (2015) The nlopt nonlinear-optimization package. http://ab-initio.mit.edu/nlopt. Accessed July 2015 · Zbl 1189.90055
[20] Kelley CT (1999) Iterative methods for optimization. Frontiers in applied mathematics. SIAM, Philadelphia
[21] Liepins, GE; Hilliard, MR, Genetic algorithms: foundations and applications, Ann Oper Res, 21, 31-58, (1989) · Zbl 0796.68167
[22] Montes de Oca, MA; Aydin, D; Stützle, T, 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, 2233-2255, (2011)
[23] Moré, JJ; Wild, SM, Benchmarking derivative-free optimization algorithms, SIAM J Optim, 20, 172-191, (2009) · Zbl 1187.90319
[24] Nelder, JA; Mead, R, The downhill simplex method, Comput J, 7, 308-313, (1965) · Zbl 0229.65053
[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 117-120 · Zbl 1112.90078
[26] Pál, L; Csendes, T; Markót, M; Neumaier, A, Black-box optimization benchmarking of the global method, Evol Comput, 20, 609-639, (2012)
[27] Pošík, P; Huyer, W; Pál, L, A comparison of global search algorithms for continuous black box optimization, Evol Comput, 20, 509-541, (2012)
[28] Powell, MJD, An efficient method for finding the minimum of a function of several variables without calculating derivatives, Comput J, 7, 155-162, (1964) · Zbl 0132.11702
[29] Powell MJD (2006) The NEWUOA software for unconstrained optimization without derivatives. Large scale nonlinear optimization. Springer, Berlin, pp 255-297 · Zbl 1108.90005
[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, Cambridge
[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 York
[32] Rahnamayan, S; Tizhoosh, HR; Salama, MMA, Opposition-based differential evolution, IEEE T Evolut Comput, 12, 64-79, (2008)
[33] Rios, L; Sahinidis, N, Derivative-free optimization: a review of algorithms and comparison of software implementations, J Global Optim, 56, 1247-1293, (2013) · Zbl 1272.90116
[34] Rosenbrock, HH, An automatic method for finding the greatest or least value of a function, Comput J, 3, 175-184, (1960)
[35] Storn, R; Price, K, Differential evolutiona simple and efficient heuristic for global optimization over continuous spaces, J Glob Optim, 11, 341-359, (1997) · Zbl 0888.90135
[36] Torczon, VJ, On the convergence of pattern search algorithms, SIAM J Optim, 7, 1-25, (1997) · Zbl 0884.65053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.