Multiple Chaos Embedded Gravitational Search Algorithm

This paper proposes a novel multiple chaos embedded gravitational search algorithm (MCGSA) that simultaneously utilizes multiple different chaotic maps with a manner of local search. The embedded chaotic local search can exploit a small region to refine solutions obtained by the canonical gravitational search algorithm (GSA) due to its inherent local exploitation ability. Meanwhile it also has a chance to explore a huge search space by taking advantages of the ergodicity of chaos. To fully utilize the dynamic properties of chaos, we propose three kinds of embedding strategies. The multiple chaotic maps are randomly, parallelly, or memory-selectively incorporated into GSA, respectively. To evaluate the effectiveness and efficiency of the proposed MCGSA, we compare it with GSA and twelve variants of chaotic GSA which use only a certain chaotic map on a set of 48 benchmark optimization functions. Experimental results show that MCGSA performs better than its competitors in terms of convergence speed and solution accuracy. In addition, statistical analysis based on Friedman test indicates that the parallelly embedding strategy is the most effective for improving the performance of GSA. key words: chaos, gravitational search algorithm, local search, optimization, meta-heuristics

[1]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

[2]  María José del Jesús,et al.  KEEL: a software tool to assess evolutionary algorithms for data mining problems , 2008, Soft Comput..

[3]  Amir Hossein Gandomi,et al.  Chaotic Krill Herd algorithm , 2014, Inf. Sci..

[4]  Kwok-Wo Wong,et al.  An improved particle swarm optimization algorithm combined with piecewise linear chaotic map , 2007, Appl. Math. Comput..

[5]  Amir Hossein Gandomi,et al.  Chaotic bat algorithm , 2014, J. Comput. Sci..

[6]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[7]  Humberto Bustince,et al.  A gravitational approach to edge detection based on triangular norms , 2010, Pattern Recognit..

[8]  Yan Wang,et al.  Gravitational search algorithm combined with chaos for unconstrained numerical optimization , 2014, Appl. Math. Comput..

[9]  Qiaoyan Wen,et al.  Hybrid chaotic ant swarm optimization , 2009 .

[10]  R. Arul,et al.  Chaotic self-adaptive differential harmony search algorithm based dynamic economic dispatch , 2013 .

[11]  Weiping Zhang,et al.  Forecasting of turbine heat rate with online least squares support vector machine based on gravitational search algorithm , 2013, Knowl. Based Syst..

[12]  Mohammad Saleh Tavazoei,et al.  Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms , 2007, Appl. Math. Comput..

[13]  Patrick Siarry,et al.  A survey on optimization metaheuristics , 2013, Inf. Sci..

[14]  Jianzhong Zhou,et al.  Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm , 2011 .

[15]  Xin Yao,et al.  Recent Advances in Evolutionary Computation , 2006, Journal of Computer Science and Technology.

[16]  Tao Jiang,et al.  Improved chaotic gravitational search algorithms for global optimization , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[17]  Sepideh Samadzadegan.  Particle Swarm Optimization : A Survey , 2012 .

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

[19]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[20]  Francisco Herrera,et al.  Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power , 2010, Inf. Sci..

[21]  Jiujun Cheng,et al.  Ant colony optimization with clustering for solving the dynamic location routing problem , 2016, Appl. Math. Comput..

[22]  Sakti Prasad Ghoshal,et al.  A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems , 2012 .

[23]  Jilei Zhou,et al.  Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization , 2014, Commun. Nonlinear Sci. Numer. Simul..

[24]  Jin Xu,et al.  Chaotic Fruit Fly Optimization Algorithm , 2014, ICSI.

[25]  Andrew Lewis,et al.  Biogeography-based optimisation with chaos , 2014, Neural Computing and Applications.

[26]  Zheng Tang,et al.  A Multi-Learning Immune Algorithm for Numerical Optimization , 2015, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[27]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[28]  Hao Tian,et al.  Improved gravitational search algorithm for unit commitment considering uncertainty of wind power , 2014, Energy.

[29]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[30]  A. Gandomi,et al.  Imperialist competitive algorithm combined with chaos for global optimization , 2012 .

[31]  A. Rezaee Jordehi,et al.  An efficient chaotic water cycle algorithm for optimization tasks , 2015, Neural Computing and Applications.

[32]  Hossein Nezamabadi-pour,et al.  A gravitational search algorithm for multimodal optimization , 2014, Swarm Evol. Comput..

[33]  Hui Qin,et al.  Comparison of different chaotic maps in particle swarm optimization algorithm for long-term cascaded hydroelectric system scheduling , 2009 .

[34]  Bo Fu,et al.  T–S Fuzzy Model Identification With a Gravitational Search-Based Hyperplane Clustering Algorithm , 2012, IEEE Transactions on Fuzzy Systems.

[35]  Muhammad Khurram Khan,et al.  An effective memetic differential evolution algorithm based on chaotic local search , 2011, Inf. Sci..

[36]  Luigi Fortuna,et al.  Chaotic sequences to improve the performance of evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[37]  Farookh Khadeer Hussain,et al.  Support vector regression with chaos-based firefly algorithm for stock market price forecasting , 2013, Appl. Soft Comput..