DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization

Differential evolution (DE) is a fast and robust evolutionary algorithm for global optimization. It has been widely used in many areas. Biogeography-based optimization (BBO) is a new biogeography inspired algorithm. It mainly uses the biogeography-based migration operator to share the information among solutions. In this paper, we propose a hybrid DE with BBO, namely DE/BBO, for the global numerical optimization problem. DE/BBO combines the exploration of DE with the exploitation of BBO effectively, and hence it can generate the promising candidate solutions. To verify the performance of our proposed DE/BBO, 23 benchmark functions with a wide range of dimensions and diverse complexities are employed. Experimental results indicate that our approach is effective and efficient. Compared with other state-of-the-art DE approaches, DE/BBO performs better, or at least comparably, in terms of the quality of the final solutions and the convergence rate. In addition, the influence of the population size, dimensionality, different mutation schemes, and the self-adaptive control parameters of DE are also studied.

[1]  Andries Petrus Engelbrecht,et al.  Empirical analysis of self-adaptive differential evolution , 2007, Eur. J. Oper. Res..

[2]  Hisao Ishibuchi,et al.  Hybrid Evolutionary Algorithms , 2007 .

[3]  Swagatam Das,et al.  Automatic Clustering Using an Improved Differential Evolution Algorithm , 2007 .

[4]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

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

[6]  Uday K. Chakraborty,et al.  Advances in Differential Evolution , 2010 .

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

[8]  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.

[9]  Hitoshi Iba,et al.  Accelerating Differential Evolution Using an Adaptive Local Search , 2008, IEEE Transactions on Evolutionary Computation.

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

[11]  Hitoshi Iba,et al.  Enhancing differential evolution performance with local search for high dimensional function optimization , 2005, GECCO '05.

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

[13]  Francisco Herrera,et al.  Two-Loop Real-Coded Genetic Algorithms with Adaptive Control of Mutation Step Sizes , 2000, Applied Intelligence.

[14]  Bilal Alatas,et al.  MODENAR: Multi-objective differential evolution algorithm for mining numeric association rules , 2008, Appl. Soft Comput..

[15]  Weicai Zhong,et al.  A multiagent genetic algorithm for global numerical optimization , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Xin Yao,et al.  Fast Evolution Strategies , 1997, Evolutionary Programming.

[17]  M. M. Ali,et al.  Differential evolution algorithms using hybrid mutation , 2007, Comput. Optim. Appl..

[18]  Francisco Herrera,et al.  A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability , 2009, Soft Comput..

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

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

[21]  Yangyang Li,et al.  Quantum-Inspired Immune Clonal Algorithm for Global Optimization , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[22]  Carlos García-Martínez,et al.  Hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification: Overview and progress report , 2010, Comput. Oper. Res..

[23]  Godfrey C. Onwubolu,et al.  Differential Evolution: A Handbook for Global Permutation-Based Combinatorial Optimization , 2009 .

[24]  Jouni Lampinen,et al.  A Trigonometric Mutation Operation to Differential Evolution , 2003, J. Glob. Optim..

[25]  Janez Demsar,et al.  Statistical Comparisons of Classifiers over Multiple Data Sets , 2006, J. Mach. Learn. Res..

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

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

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

[29]  William Fuller Brown,et al.  Methods of Statistical Analysis , 1939 .

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

[31]  Amit Konar,et al.  Two improved differential evolution schemes for faster global search , 2005, GECCO '05.

[32]  Wenyin Gong,et al.  ODE: A Fast and Robust Differential Evolution Based on Orthogonal Design , 2006, Australian Conference on Artificial Intelligence.

[33]  Amin Nobakhti,et al.  A simple self-adaptive Differential Evolution algorithm with application on the ALSTOM gasifier , 2008, Appl. Soft Comput..

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

[35]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[36]  Janez Brest,et al.  Population size reduction for the differential evolution algorithm , 2008, Applied Intelligence.

[37]  Jason Teo,et al.  Exploring dynamic self-adaptive populations in differential evolution , 2006, Soft Comput..

[38]  S. García,et al.  An Extension on "Statistical Comparisons of Classifiers over Multiple Data Sets" for all Pairwise Comparisons , 2008 .

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

[40]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[41]  Ling. Huang.  Self adaptive differential evolution , 2010 .

[42]  Jason Teo,et al.  Self-adaptive population sizing for a tune-free differential evolution , 2009, Soft Comput..

[43]  Andries Petrus Engelbrecht,et al.  Self-adaptive Differential Evolution , 2005, CIS.

[44]  Xin Yao,et al.  Making a Difference to Differential Evolution , 2008, Advances in Metaheuristics for Hard Optimization.

[45]  Stefan Janaqi,et al.  Generalization of the strategies in differential evolution , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[46]  Jiang-She Zhang,et al.  A dynamic clustering based differential evolution algorithm for global optimization , 2007, Eur. J. Oper. Res..

[47]  Riccardo Poli,et al.  Evolving Problems to Learn About Particle Swarm Optimizers and Other Search Algorithms , 2006, IEEE Transactions on Evolutionary Computation.

[48]  E. D. Van Rest,et al.  Methods of Statistical Analysis , 1954 .

[49]  Thomas Bäck,et al.  An Overview of Evolutionary Algorithms for Parameter Optimization , 1993, Evolutionary Computation.

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

[51]  Francisco Herrera,et al.  Tackling Real-Coded Genetic Algorithms: Operators and Tools for Behavioural Analysis , 1998, Artificial Intelligence Review.

[52]  Vitaliy Feoktistov.  Differential Evolution: In Search of Solutions , 2006 .

[53]  Jouni Lampinen,et al.  A Fuzzy Adaptive Differential Evolution Algorithm , 2005, Soft Comput..