Quasi-random Numbers Improve the CMA-ES on the BBOB Testbed

Pseudo-random numbers are usually a good enough approximation of random numbers in evolutionary algorithms. But quasi-random numbers follow a different idea, namely they are aimed at being more regularly distributed than random points. It has been pointed out in earlier papers that quasi-random points provide a significant improvement in evolutionary optimization. In this paper, we experiment quasi-random mutations on a well known test case, namely the Coco/Bbob test case. We also include experiments on translated or rescaled versions of BBOB, on which we get similar improvements.

[1]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[2]  Antoniya Georgieva,et al.  A hybrid meta-heuristic for global optimisation using low-discrepancy sequences of points , 2010, Comput. Oper. Res..

[3]  I. Sobol On the Systematic Search in a Hypercube , 1979 .

[4]  H. Niederreiter Low-discrepancy and low-dispersion sequences , 1988 .

[5]  Shuhei Kimura,et al.  Genetic algorithms using low-discrepancy sequences , 2005, GECCO '05.

[6]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[7]  Fred J. Hickernell,et al.  Randomized Halton sequences , 2000 .

[8]  Olivier Teytaud,et al.  On the huge benefit of quasi-random mutations for multimodal optimization with application to grid-based tuning of neurocontrollers , 2009, ESANN.

[9]  A. Owen Multidimensional variation for quasi-Monte Carlo , 2004 .

[10]  Olivier Teytaud,et al.  When Does Quasi-random Work? , 2008, PPSN.

[11]  Olivier Teytaud,et al.  On the Ultimate Convergence Rates for Isotropic Algorithms and the Best Choices Among Various Forms of Isotropy , 2006, PPSN.

[12]  Hongmei Chi,et al.  On the Scrambled Halton Sequence , 2004, Monte Carlo Methods Appl..

[13]  Steven M. LaValle,et al.  Incremental low-discrepancy lattice methods for motion planning , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[14]  B. Tuffin A new permutation choice in Halton sequences , 1998 .

[15]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[16]  Tony Warnock,et al.  Computational investigations of low-discrepancy point-sets. , 1972 .

[17]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[18]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[19]  R. Cools,et al.  Good permutations for deterministic scrambled Halton sequences in terms of L2-discrepancy , 2006 .

[20]  Olivier Teytaud,et al.  DCMA: yet another derandomization in covariance-matrix-adaptation , 2007, GECCO '07.

[21]  T. Warnock Computational Investigations of Low-Discrepancy Point Sets II , 1995 .

[22]  Bernhard Sendhoff,et al.  Covariance Matrix Adaptation Revisited - The CMSA Evolution Strategy - , 2008, PPSN.