Some modifications of low-dimensional simplex evolution and their convergence

References

• Ali , M. M. , Khompatraporn , C. and Zabinsky , Z. B. 2005 . A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems . J. Global Optim. , 31 : 635 – 672 .
   Web of Science ®Google Scholar
• Chakraborty , U. K. , Kalyanmoy , D. and Chakraborty , M. 1996 . Analysis of selection algorithms: a Markov chain approach . Evol. Comput. , 4 : 133 – 167 .
   Web of Science ®Google Scholar
• Davis , T. E. and Principe , J. C. 1993 . A Markov chain framework for the simple genetic algorithm . Evol. Comput. , 1 : 269 – 288 .
   Web of Science ®Google Scholar
• Fogel , D. B. 2006 . Evolutionary Computation: Toward a New Philosophy of Machine Intelligence , Piscataway, NJ : 3rd ed., Wiley-IEEE Press .
   Google Scholar
• Fogel , L. J. , Owens , A. J. and Walsh , M. J. 1965 . Artificial intelligence through a simulation of evolution , Edited by: M. , Maxfield , Callahan , A. and Fogel , L. J. 131 – 155 . Washington DC : Spartan Books . Biophysics and Cybernetic Systems: Proc. 2nd Cybernetic Sciences Symposium
   Google Scholar
• Garcia , S. , Fernandez , A. , Luengo , J. and Herrera , F. 2009 . A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability . Soft Comput. , 13 : 959 – 977 .
   Web of Science ®Google Scholar
• Gutknecht , M. H. 2007 . A brief introduction to krylov space methods for solving linear systems . Frontiers of Computational Science, Springer Berlin Heidelberg, , : 53 – 62 .
   Google Scholar
• Hedar , A. and Fukushima , M. 2003 . Minimizing multimodal functions by simplex coding genetic algorithm . Optim. Method Softw. , 18 : 265 – 282 .
   Web of Science ®Google Scholar
• Holland , J. H. 1992 . Adaption in Natural and Artificial Systems , Cambridge, MA : MIT Press .
   Google Scholar
• Kaelo , P. and Ali , M. M. 2006 . A numerical study of some modified differential evolution algorithms . Eur. J. Oper. Res. , 169 : 1176 – 1181 .
   Web of Science ®Google Scholar
• Kennedy , J. and Eberhart , R. Particle swarm optimization . Vol. 4 , pp. 1942 – 1948 . Proc, IEEE Int'l. Conf. on Neural Networks
   Google Scholar
• Luo , C. T. and Yu , B. Low dimensional simplex evolution: a hybrid heuristic for global optimization . Global Optim. (DOI:10.1007/s10898-011-96781)
   Google Scholar
• Luo , C. T. and Yu , B. 2007 . Solving min UR problem by triangle evolution algorithm with archiving and Niche techniques . J. Inform. Comput. Sci. , 4 ( 1 ) : 195 – 203 .
   Google Scholar
• 2010 . Global Optimization Toolbox 3 Users Guide , Natick, MA : The MathWorks, Inc. .
   Google Scholar
• Meyer , C. D. 2000 . Matrix Analysis and Applied Linear Algebra , Philadelphia, PA : SIAM .
   Google Scholar
• Poli , R. and McPhee , N. F. 2003 . General schema theory for genetic programming with subtree-swapping crossover: Part II . Evol. Comput. , 11 : 169 – 206 .
   Web of Science ®Google Scholar
• Rechenberg , I. 1973 . Evolutions strategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , Stuttgart : Frommann-Holzboog Verlag .
   Google Scholar
• Renders , J. M. and Bersini , H. 1994 . Hybridizing genetic algorithms with hill-climbing methods for global optimization: Two possible ways, Proc. 1st IEEE Conf. Evolutionary Computation. Vol. 1 . 1994 . pp. 312 – 317 .
   Google Scholar
• Rudolph , G. 1994 . Convergence analysis of canonical genetic algorithms . IEEE Trans. Neural Network , 5 : 96 – 101 .
   PubMed Web of Science ®Google Scholar
• Schmitt , L. M. 2004 . Theory of genetic algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling . Theor. Comput. Sci. , 310 : 181 – 231 .
   Web of Science ®Google Scholar
• Storn , R. and Price , K. 1997 . DE-a simple and efficient heuristic for global optimization over continuous space . J. Global Optim. , 11 : 341 – 359 .
   Web of Science ®Google Scholar
• Suganthan , P. N. , Hansen , N. , Liang , J. J. , Deb , K. , Chen , Y.-P. , Auger , A. and Tiwari , S. 2005 . Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization , Singapore : Technical Report, Nanyang Technological University .
   Google Scholar
• Yu , B. , Luo , C. T. and Zhang , Y. 2007 . Studies on Complicated System of Inequalities with Possible Inconsistency . Frontiers Science Series , 49 : 147 – 148 .
   Google Scholar