Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions

A Rosenbrock artificial bee colony algorithm (RABC) that combines Rosenbrock's rotational direction method with an artificial bee colony algorithm (ABC) is proposed for accurate numerical optimization. There are two alternative phases of RABC: the exploration phase realized by ABC and the exploitation phase completed by the rotational direction method. The proposed algorithm was tested on a comprehensive set of complex benchmark problems, encompassing a wide range of dimensionality, and it was also compared with several algorithms. Numerical results show that the new algorithm is promising in terms of convergence speed, success rate, and accuracy. The proposed RABC is also capable of keeping up with the direction changes in the problems.

[1]  Bernhard Sendhoff,et al.  Lamarckian memetic algorithms: local optimum and connectivity structure analysis , 2009, Memetic Comput..

[2]  Huanwen Tang,et al.  A single-point mutation evolutionary programming , 2004, Inf. Process. Lett..

[3]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[4]  Jorge J. Moré,et al.  Testing Unconstrained Optimization Software , 1981, TOMS.

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

[6]  Bilal Alatas,et al.  Chaotic bee colony algorithms for global numerical optimization , 2010, Expert Syst. Appl..

[7]  Mario A. Muñoz,et al.  An artificial beehive algorithm for continuous optimization , 2009, HIS 2009.

[8]  Ferrante Neri,et al.  An Adaptive Multimeme Algorithm for Designing HIV Multidrug Therapies , 2007, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[9]  Andy J. Keane,et al.  Meta-Lamarckian learning in memetic algorithms , 2004, IEEE Transactions on Evolutionary Computation.

[10]  Ajith Abraham,et al.  Adaptive Computational Chemotaxis in Bacterial Foraging Optimization: An Analysis , 2009, IEEE Transactions on Evolutionary Computation.

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

[12]  Dervis Karaboga,et al.  A modified Artificial Bee Colony algorithm for real-parameter optimization , 2012, Inf. Sci..

[13]  Sam Kwong,et al.  Gbest-guided artificial bee colony algorithm for numerical function optimization , 2010, Appl. Math. Comput..

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

[15]  Alok Singh,et al.  A swarm intelligence approach to the quadratic minimum spanning tree problem , 2010, Inf. Sci..

[16]  Junjie Li,et al.  Virus coevolution partheno-genetic algorithms for optimal sensor placement , 2008, Adv. Eng. Informatics.

[17]  Andrew Lim,et al.  Example-based learning particle swarm optimization for continuous optimization , 2012, Information Sciences.

[18]  Francisco Herrera,et al.  Real-Coded Memetic Algorithms with Crossover Hill-Climbing , 2004, Evolutionary Computation.

[19]  A. Kai Qin,et al.  Self-adaptive differential evolution algorithm for numerical optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[20]  Junjie Li,et al.  Structural inverse analysis by hybrid simplex artificial bee colony algorithms , 2009 .

[21]  J. R. Palmer An Improved Procedure for Orthogonalising the Search Vectors in Rosenbrock's and Swann's Direct Search Optimisation Methods , 1969, Comput. J..

[22]  Georgios Dounias,et al.  Honey bees mating optimization algorithm for the Euclidean traveling salesman problem , 2011, Inf. Sci..

[23]  Efrén Mezura-Montes,et al.  Differential evolution in constrained numerical optimization: An empirical study , 2010, Inf. Sci..

[24]  Mehmet Fatih Tasgetiren,et al.  A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem , 2011, Inf. Sci..

[25]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[26]  F. Herrera,et al.  Real-parameter crossover operators with multiple descendents: An experimental study , 2008 .

[27]  Francisco Herrera,et al.  A taxonomy for the crossover operator for real‐coded genetic algorithms: An experimental study , 2003, Int. J. Intell. Syst..

[28]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[29]  Rafael Martí,et al.  Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions , 2005, J. Glob. Optim..

[30]  Masao Fukushima,et al.  Tabu Search directed by direct search methods for nonlinear global optimization , 2006, Eur. J. Oper. Res..

[31]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[32]  M.M.A. Salama,et al.  Opposition-Based Differential Evolution , 2008, IEEE Transactions on Evolutionary Computation.

[33]  Maoguo Gong,et al.  Baldwinian learning in clonal selection algorithm for optimization , 2010, Inf. Sci..

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

[35]  Carlos García-Martínez,et al.  Global and local real-coded genetic algorithms based on parent-centric crossover operators , 2008, Eur. J. Oper. Res..

[36]  Yu Wang,et al.  Self-adaptive learning based particle swarm optimization , 2011, Inf. Sci..

[37]  Wei Hou,et al.  Evolutionary programming using a mixed mutation strategy , 2007, Inf. Sci..

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

[39]  Bogdan Filipic,et al.  The differential ant-stigmergy algorithm , 2012, Inf. Sci..

[40]  Reza Akbari,et al.  A novel bee swarm optimization algorithm for numerical function optimization , 2010 .

[41]  Patrick Siarry,et al.  A hybrid method combining continuous tabu search and Nelder-Mead simplex algorithms for the global optimization of multiminima functions , 2005, Eur. J. Oper. Res..

[42]  Xia Li,et al.  An improved shuffled frog-leaping algorithm with extremal optimisation for continuous optimisation , 2012, Inf. Sci..

[43]  Francisco Herrera,et al.  Hybrid crossover operators with multiple descendents for real‐coded genetic algorithms: Combining neighborhood‐based crossover operators , 2009, Int. J. Intell. Syst..

[44]  N. Garc'ia-Pedrajas,et al.  CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features , 2005, J. Artif. Intell. Res..

[45]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[46]  Tsung-Ying Sun,et al.  Effective Learning Rate Adjustment of Blind Source Separation Based on an Improved Particle Swarm Optimizer , 2008, IEEE Transactions on Evolutionary Computation.

[47]  Chien-Chih Liao,et al.  A memetic algorithm for extending wireless sensor network lifetime , 2010, Inf. Sci..

[48]  Amit Konar,et al.  On Stability of the Chemotactic Dynamics in Bacterial-Foraging Optimization Algorithm , 2009, IEEE Trans. Syst. Man Cybern. Part A.

[49]  Ferrante Neri,et al.  Memetic Compact Differential Evolution for Cartesian Robot Control , 2010, IEEE Computational Intelligence Magazine.

[50]  T. Seeley The Wisdom of the Hive , 1995 .

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

[52]  Carol Grant Gould,et al.  The Honey Bee , 1988 .

[53]  Patrick Siarry,et al.  A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions , 2000, J. Heuristics.

[54]  Yew-Soon Ong,et al.  A Probabilistic Memetic Framework , 2009, IEEE Transactions on Evolutionary Computation.

[55]  Erwie Zahara,et al.  A hybrid genetic algorithm and particle swarm optimization for multimodal functions , 2008, Appl. Soft Comput..

[56]  Haiping Ma,et al.  An analysis of the equilibrium of migration models for biogeography-based optimization , 2010, Inf. Sci..

[57]  Jim E. Smith,et al.  Coevolving Memetic Algorithms: A Review and Progress Report , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[58]  Ville Tirronen,et al.  Super-fit control adaptation in memetic differential evolution frameworks , 2009, Soft Comput..

[59]  Ajith Abraham,et al.  Stability analysis of the reproduction operator in bacterial foraging optimization , 2010, Theor. Comput. Sci..

[60]  Manoj Kumar Tiwari,et al.  Swarm Intelligence, Focus on Ant and Particle Swarm Optimization , 2007 .

[61]  Hongzhi Liu,et al.  An improved artificial bee colony algorithm , 2013, 2013 25th Chinese Control and Decision Conference (CCDC).

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

[63]  Yongzhi Yang,et al.  A Single Component Mutation Evolutionary Programming , 2010, Appl. Math. Comput..

[64]  V. Torczon,et al.  Direct search methods: then and now , 2000 .

[65]  Ville Tirronen,et al.  An Enhanced Memetic Differential Evolution in Filter Design for Defect Detection in Paper Production , 2008, Evolutionary Computation.

[66]  Patrick Siarry,et al.  Genetic and Nelder-Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions , 2003, Eur. J. Oper. Res..

[67]  Marco Dorigo,et al.  Ant colony optimization for continuous domains , 2008, Eur. J. Oper. Res..

[68]  Liang Gao,et al.  Cellular particle swarm optimization , 2011, Inf. Sci..

[69]  Patrick Lyonnet,et al.  A new heuristic approach for non-convex optimization problems , 2010, Inf. Sci..

[70]  Fred W. Glover,et al.  ' s personal copy Continuous Optimization Finding local optima of high-dimensional functions using direct search methods , 2008 .

[71]  Lale Özbakır,et al.  Artificial Bee Colony Algorithm and Its Application to Generalized Assignment Problem , 2007 .

[72]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[73]  P. N. Suganthan,et al.  Ensemble of niching algorithms , 2010, Inf. Sci..

[74]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

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

[76]  Chun Chen,et al.  Multiple trajectory search for Large Scale Global Optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).