Improved Alopex-based evolutionary algorithm by Gaussian copula estimation of distribution algorithm and its application to the Butterworth filter design

ABSTRACT The application of evolutionary algorithms (EAs) is becoming widespread in engineering optimisation problems because of their simplicity and effectiveness. The Alopex-based evolutionary algorithm (AEA) possesses the basic characteristics of heuristic search algorithms but is lacking in adequate information about the fitness landscape of the input domain, reducing the convergence speed. To improve the performance of AEA, the Gaussian copula estimation of distribution algorithm (EDA) is embedded into the original AEA in this paper. With the help of Gaussian copula EDA, precise probability models are built utilising the best solutions, which can increase the convergence speed, and at the same time, keep the population diversity as much as possible. The simulation results on the benchmark functions and the application to the Butterworth filter design demonstrate the efficiency and effectiveness of the proposed algorithm, compared with several other EAs.

[1]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[2]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[3]  Lingling Huang,et al.  A novel artificial bee colony algorithm with Powell's method , 2013, Appl. Soft Comput..

[4]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[5]  Jinung An,et al.  Estimation of particle swarm distribution algorithms: Combining the benefits of PSO and EDAs , 2012, Inf. Sci..

[6]  Subhabrata Chakraborti,et al.  Nonparametric Statistical Inference , 2011, International Encyclopedia of Statistical Science.

[7]  Yunlong Zhu,et al.  A novel bionic algorithm inspired by plant root foraging behaviors , 2015, Appl. Soft Comput..

[8]  Kusum Deep,et al.  Quadratic approximation based hybrid genetic algorithm for function optimization , 2008, Appl. Math. Comput..

[9]  Roberto Marcondes Cesar Junior,et al.  Inexact graph matching for model-based recognition: Evaluation and comparison of optimization algorithms , 2005, Pattern Recognit..

[10]  S. Baluja,et al.  Using Optimal Dependency-Trees for Combinatorial Optimization: Learning the Structure of the Search Space , 1997 .

[11]  Xin-She Yang,et al.  Flower pollination algorithm: A novel approach for multiobjective optimization , 2014, ArXiv.

[12]  E Harth,et al.  Alopex: a stochastic method for determining visual receptive fields. , 1974, Vision research.

[13]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[14]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[15]  Pedro Larrañaga,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

[16]  Pedro Larrañaga,et al.  Feature Subset Selection by Bayesian network-based optimization , 2000, Artif. Intell..

[17]  Fei Li,et al.  Alopex-based evolutionary algorithm and its application to reaction kinetic parameter estimation , 2011, Comput. Ind. Eng..

[18]  Bin Li,et al.  Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems , 2010, Inf. Sci..

[19]  Yuping Wang,et al.  An Evolutionary Algorithm for Global Optimization Based on Level-Set Evolution and Latin Squares , 2007, IEEE Transactions on Evolutionary Computation.

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

[21]  R. Clemen,et al.  Correlations and Copulas for Decision and Risk Analysis , 1999 .

[22]  R. V. Rao,et al.  Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems , 2012 .

[23]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[24]  Alaa F. Sheta,et al.  Analogue filter design using differential evolution , 2010, Int. J. Bio Inspired Comput..

[25]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[26]  Zelda B. Zabinsky,et al.  A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems , 2005, J. Glob. Optim..

[27]  A. Mood,et al.  The statistical sign test. , 1946, Journal of the American Statistical Association.

[28]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[29]  Junjie Li,et al.  Artificial bee colony algorithm and pattern search hybridized for global optimization , 2013, Appl. Soft Comput..

[30]  Qingfu Zhang,et al.  DE/EDA: A new evolutionary algorithm for global optimization , 2005, Inf. Sci..

[31]  Athanasios V. Vasilakos,et al.  Optimal filter design using an improved artificial bee colony algorithm , 2014, Inf. Sci..

[32]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.