Biogeography-based optimisation with chaos

Abstract The biogeography-based optimisation (BBO) algorithm is a novel evolutionary algorithm inspired by biogeography. Similarly, to other evolutionary algorithms, entrapment in local optima and slow convergence speed are two probable problems it encounters in solving challenging real problems. Due to the novelty of this algorithm, however, there is little in the literature regarding alleviating these two problems. Chaotic maps are one of the best methods to improve the performance of evolutionary algorithms in terms of both local optima avoidance and convergence speed. In this study, we utilise ten chaotic maps to enhance the performance of the BBO algorithm. The chaotic maps are employed to define selection, emigration, and mutation probabilities. The proposed chaotic BBO algorithms are benchmarked on ten test functions. The results demonstrate that the chaotic maps (especially Gauss/mouse map) are able to significantly boost the performance of BBO. In addition, the results show that the combination of chaotic selection and emigration operators results in the highest performance.

[1]  Amir Hossein Gandomi,et al.  Hybrid krill herd algorithm with differential evolution for global numerical optimization , 2014, Neural Computing and Applications.

[2]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[3]  Konstantinos G. Margaritis,et al.  On benchmarking functions for genetic algorithms , 2001, Int. J. Comput. Math..

[4]  Patrick Siarry,et al.  Two-stage update biogeography-based optimization using differential evolution algorithm (DBBO) , 2011, Comput. Oper. Res..

[5]  R. Storn,et al.  Differential Evolution , 2004 .

[6]  Andrew Lewis,et al.  Adaptive gbest-guided gravitational search algorithm , 2014, Neural Computing and Applications.

[7]  Francisco Herrera,et al.  A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization , 2009, J. Heuristics.

[8]  Dan Simon,et al.  Blended biogeography-based optimization for constrained optimization , 2011, Eng. Appl. Artif. Intell..

[9]  Vidroha Debroy,et al.  Genetic Programming , 1998, Lecture Notes in Computer Science.

[10]  Dan Simon,et al.  Biogeography-Based Optimization , 2022 .

[11]  Patrick Siarry,et al.  Biogeography-based optimization for constrained optimization problems , 2012, Comput. Oper. Res..

[12]  Wenyin Gong,et al.  DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization , 2010, Soft Comput..

[13]  Binggang Cao,et al.  Self-Adaptive Chaos Differential Evolution , 2006, ICNC.

[14]  Amir Hossein Alavi,et al.  Krill herd: A new bio-inspired optimization algorithm , 2012 .

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

[16]  L. Liming,et al.  Genetic Algorithm in Chaos , 2001 .

[17]  P. K. Chattopadhyay,et al.  Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch , 2010, IEEE Transactions on Power Systems.

[18]  Chen Tian-Lun,et al.  Application of Chaos in Genetic Algorithms , 2002 .

[19]  Seyed Mohammad Mirjalili,et al.  Chaotic krill herd optimization algorithm , 2014 .

[20]  Xin-She Yang,et al.  Firefly algorithm with chaos , 2013, Commun. Nonlinear Sci. Numer. Simul..

[21]  Amir Hossein Gandomi,et al.  A chaotic particle-swarm krill herd algorithm for global numerical optimization , 2013, Kybernetes.

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

[23]  Andrew Lewis,et al.  Let a biogeography-based optimizer train your Multi-Layer Perceptron , 2014, Inf. Sci..

[24]  Amir Hossein Gandomi,et al.  Stud krill herd algorithm , 2014, Neurocomputing.

[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]  Amir Nakib,et al.  An improved biogeography based optimization approach for segmentation of human head CT-scan images employing fuzzy entropy , 2012, Eng. Appl. Artif. Intell..

[27]  Amir Hossein Alavi,et al.  An effective krill herd algorithm with migration operator in biogeography-based optimization , 2014 .

[28]  Andrew Lewis,et al.  S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization , 2013, Swarm Evol. Comput..

[29]  Patrick Siarry,et al.  Hybridizing Biogeography-Based Optimization With Differential Evolution for Optimal Power Allocation in Wireless Sensor Networks , 2011, IEEE Transactions on Vehicular Technology.

[30]  Siti Zaiton Mohd Hashim,et al.  Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm , 2012, Appl. Math. Comput..

[31]  Amir Hossein Gandomi,et al.  A new improved krill herd algorithm for global numerical optimization , 2014, Neurocomputing.

[32]  V. Jothiprakash,et al.  Optimization of Hydropower Reservoir Using Evolutionary Algorithms Coupled with Chaos , 2013, Water Resources Management.

[33]  Xin-She Yang,et al.  Binary bat algorithm , 2013, Neural Computing and Applications.

[34]  Siti Zaiton Mohd Hashim,et al.  BMOA: Binary Magnetic Optimization Algorithm , 2012 .

[35]  François Michaud,et al.  Having a robot attend AAAI 2000 , 2000, IEEE Intelligent Systems and their Applications.

[36]  S. Mirjalili,et al.  A new hybrid PSOGSA algorithm for function optimization , 2010, 2010 International Conference on Computer and Information Application.

[37]  Seyedali Mirjalili,et al.  Integrating Chaos to Biogeography-Based Optimization Algorithm , 2013 .

[38]  F. Wilcoxon Individual Comparisons by Ranking Methods , 1945 .

[39]  Dan Simon,et al.  Biogeography-based optimization combined with evolutionary strategy and immigration refusal , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[40]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[41]  J. Tennyson In the wake of chaos. Unpredictable order in dynamical systems , 1995 .