Finite life span for improving the selection scheme in evolution strategies

Evolution strategies traditionally employ the comma or the plus scheme for selection. The concept of intermediate selection schemes was introduced in 1995, in which individuals may survive limited but more than one generation; however, research on this topic has remained dormant. During the recent decade, the comma scheme has emerged as the preferred choice at least for continuous optimization. The objective of this article is to explore pros and cons of both extreme as well as intermediate selection schemes in coping with different types of difficulties that may arise in global optimization of multimodal functions. A specific test suite is developed which allows for studying different selection schemes when facing particular challenges. A modified variant of the previously proposed intermediate selection scheme in which fitness of survivors iteratively degrades is proposed. The degrading rate is controlled by a strategy parameter, called the aging factor. The resulting algorithm is tested on the whole suite using different values of the aging factor. The comparison of results reveals the drastic problem dependence of the optimal aging factor; however, when all situations are considered, an intermediate selection scheme significantly outperforms both the comma and the plus schemes.

[1]  Hans-Georg Beyer,et al.  Performance analysis of evolutionary optimization with cumulative step length adaptation , 2004, IEEE Transactions on Automatic Control.

[2]  Nikolaus Hansen,et al.  Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed , 2009, GECCO '09.

[3]  Thomas Bäck,et al.  How to Do Recombination in Evolution Strategies: An Empirical Study , 2009, IWINAC.

[4]  Oliver Kramer,et al.  A Review of Constraint-Handling Techniques for Evolution Strategies , 2010, Appl. Comput. Intell. Soft Comput..

[5]  L. Darrell Whitley,et al.  Evaluating Evolutionary Algorithms , 1996, Artif. Intell..

[6]  Ying Tan,et al.  Artificial Immune System , 2016 .

[7]  Carlos A. Coello Coello,et al.  An empirical study about the usefulness of evolution strategies to solve constrained optimization problems , 2008, Int. J. Gen. Syst..

[8]  Oliver Kramer,et al.  Premature Convergence in Constrained Continuous Search Spaces , 2008, PPSN.

[9]  Ali Ahrari,et al.  On the utility of randomly generated functions for performance evaluation of evolutionary algorithms , 2010, Optim. Lett..

[10]  Thomas Bäck,et al.  Contemporary Evolution Strategies , 2013, Natural Computing Series.

[11]  Jesús Marín,et al.  How landscape ruggedness influences the performance of real-coded algorithms: a comparative study , 2012, Soft Comput..

[12]  Marcus Gallagher,et al.  A general-purpose tunable landscape generator , 2006, IEEE Transactions on Evolutionary Computation.

[13]  Ali Ahrari,et al.  An improved evolution strategy with adaptive population size , 2015 .

[14]  Anne Auger,et al.  Impacts of invariance in search: When CMA-ES and PSO face ill-conditioned and non-separable problems , 2011, Appl. Soft Comput..

[15]  Thomas Jansen,et al.  On the role of age diversity for effective aging operators , 2011, Evol. Intell..

[16]  Marek Kisiel-Dorohinicki,et al.  Maintaining Population Diversity in Evolution Strategy for Engineering Problems , 2008, IEA/AIE.

[17]  Hans-Georg Beyer,et al.  Self-adaptation of evolution strategies under noisy fitness evaluations , 2006, Genetic Programming and Evolvable Machines.

[18]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[19]  Hans-Georg Beyer,et al.  A Comparison of Evolution Strategies with Other Direct Search Methods in the Presence of Noise , 2003, Comput. Optim. Appl..

[20]  Thomas Jansen,et al.  Maximal age in randomized search heuristics with aging , 2009, GECCO.

[21]  Xiaodong Li,et al.  A framework for generating tunable test functions for multimodal optimization , 2011, Soft Comput..

[22]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[23]  Thomas Stützle,et al.  Computational results for an automatically tuned CMA-ES with increasing population size on the CEC’05 benchmark set , 2012, Soft Computing.

[24]  Bernardetta Addis,et al.  A new class of test functions for global optimization , 2007, J. Glob. Optim..

[25]  Hans-Georg Beyer,et al.  Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge , 2008, Natural Computing.

[26]  Hans-Georg Beyer,et al.  On the Behaviour of Evolution Strategies Optimising Cigar Functions , 2010, Evolutionary Computation.

[27]  Dirk V. Arnold,et al.  Weighted multirecombination evolution strategies , 2006, Theor. Comput. Sci..

[28]  Cláudio F. Lima,et al.  On the utility of the multimodal problem generator for assessing the performance of evolutionary algorithms , 2006, GECCO '06.

[29]  Günter Rudolph,et al.  Contemporary Evolution Strategies , 1995, ECAL.

[30]  Hans-Georg Beyer,et al.  The Dynamics of Self-Adaptive Multirecombinant Evolution Strategies on the General Ellipsoid Model , 2014, IEEE Transactions on Evolutionary Computation.

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

[32]  Francisco Herrera,et al.  A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization , 2009, J. Heuristics.

[33]  Masoud Shariat Panahi,et al.  On the limitations of classical benchmark functions for evaluating robustness of evolutionary algorithms , 2010, Appl. Math. Comput..

[34]  Anne Auger,et al.  Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009 , 2010, GECCO '10.

[35]  Thomas Bäck,et al.  Evolutionary computation: comments on the history and current state , 1997, IEEE Trans. Evol. Comput..

[36]  Günter Rudolph,et al.  When parameter tuning actually is parameter control , 2011, GECCO '11.

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

[38]  Marco Locatelli,et al.  On the Multilevel Structure of Global Optimization Problems , 2005, Comput. Optim. Appl..

[39]  Thomas Jansen,et al.  Comparing Different Aging Operators , 2009, ICARIS.

[40]  Oliver Kramer,et al.  Evolutionary self-adaptation: a survey of operators and strategy parameters , 2010, Evol. Intell..

[41]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[42]  Ofer M. Shir,et al.  Niching in Evolution Strategies and Its Application to Laser Pulse Shaping , 2005, Artificial Evolution.

[43]  Dirk V. Arnold,et al.  Improving Evolution Strategies through Active Covariance Matrix Adaptation , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[44]  Thomas Jansen,et al.  On benefits and drawbacks of aging strategies for randomized search heuristics , 2011, Theor. Comput. Sci..

[45]  Yaroslav D. Sergeyev,et al.  Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization , 2003, TOMS.