Improved CMA-ES with Memory based Directed Individual Generation for Real Parameter Optimization

Covariance Matrix Adaptation and Evolution Strategy (CMA-ES) is an efficient method of optimization that iteratively generates new individuals around an ever-adaptive recombination point. Although it ensures speed and high rate of exploitation, CMA-ES suffers a major drawback as the scheme of generating new members scattered around an influential mean may often lead to members drawn to local minima. The result is that while precision of better solutions increases, the ability to reform is lost. In this paper we incorporate a directional feature to the generation wise perturbation of individuals in standard version of CMA-ES that utilizes potentially useful information from previous generation to retain the influence of old recombination point. Coupled with a modified population size we attempt to form an algorithm that amalgamates the effectiveness of CMA-ES along with the ability to explore. The performance is tested on IEEE CEC (Congress on Evolutionary Computation) 2013 Special Session on Real-Parameter Optimization in 10, 30 and 50 dimensions. The results obtained clearly indicates that the proposed algorithm addressed as CMA-ES with Memory based Directed Individual Generation (CMA-ES-DIG) is able to perform excessively well on majority of the test cases in a statistically meaningful way.

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

[2]  Thomas Bäck,et al.  A robust optimization approach using Kriging metamodels for robustness approximation in the CMA-ES , 2010, IEEE Congress on Evolutionary Computation.

[3]  Otmar Scherzer,et al.  The CMA-ES on Riemannian Manifolds to Reconstruct Shapes in 3-D Voxel Images , 2010, IEEE Transactions on Evolutionary Computation.

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

[5]  S. Rahnamayan,et al.  Efficiency competition on N-queen problem: DE vs. CMA-ES , 2008, 2008 Canadian Conference on Electrical and Computer Engineering.

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

[7]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[8]  D. Werner,et al.  Exploiting Rotational Symmetry for the Design of Ultra-Wideband Planar Phased Array Layouts , 2013, IEEE Transactions on Antennas and Propagation.

[9]  Ho-fung Leung,et al.  Improving CMA-ES by random evaluation on the minor eigenspace , 2010, IEEE Congress on Evolutionary Computation.

[10]  Ponnuthurai N. Suganthan,et al.  A differential covariance matrix adaptation evolutionary algorithm for global optimization , 2011, 2011 IEEE Symposium on Differential Evolution (SDE).

[11]  Krzysztof Walczak Hybrid Differential Evolution with covariance matrix adaptation for digital filter design , 2011, 2011 IEEE Symposium on Differential Evolution (SDE).

[12]  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.

[13]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[14]  Ofer M. Shir,et al.  Self-Adaptive Niching CMA-ES with Mahalanobis Metric , 2007, 2007 IEEE Congress on Evolutionary Computation.

[15]  Marc Parizeau,et al.  Black-box optimization of sensor placement with elevation maps and probabilistic sensing models , 2011, 2011 IEEE International Symposium on Robotic and Sensors Environments (ROSE).

[16]  Christian Igel,et al.  A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies , 2006, GECCO.