A Divisive Multi-level Differential Evolution

It is generally accepted that the clustering-based differential evolution (CDE) algorithm exhibits better performance in comparison with the standard differential evolution. However, such clustering method mechanism that is only based on input data may lead to some limitations such as premature convergence. In this study, we propose a divisive multi-level differential evolution algorithm (DMDE) to alleviate this drawback. The proposed divisive method is based not only input data but also the output fitness. In particular, DMDE becomes the conventional CDE when the output fitness in not considered in the process of clustering. Several benchmark functions are included to evaluate the performance of the proposed DMDE. Experimental results show that the proposed DMDE exhibits a promising performance when compared with CDE, especially in case of high-dimensional continuous optimization problems.

[1]  Andries Petrus Engelbrecht,et al.  Differential evolution in high-dimensional search spaces , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

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

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

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

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

[7]  Yong Wang,et al.  Combining Multiobjective Optimization With Differential Evolution to Solve Constrained Optimization Problems , 2012, IEEE Transactions on Evolutionary Computation.

[8]  Chen Duo Research on Optimization of Control Parameters for Genetic Algorithm Based on Fitness Landscape , 2010 .

[9]  Jiang Ping,et al.  Parameters Optimization of Active Disturbance Rejection Controller with Genetic Algorithm for Cascade Speed Control System , 2011, 2011 Fourth International Conference on Intelligent Computation Technology and Automation.

[10]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

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

[12]  Ponnuthurai N. Suganthan,et al.  Differential Evolution Algorithm with Ensemble of Parameters and Mutation and Crossover Strategies , 2010, SEMCCO.

[13]  Wenyin Gong,et al.  A clustering-based differential evolution for global optimization , 2011, Appl. Soft Comput..

[14]  Zbigniew Michalewicz,et al.  Parameter control in evolutionary algorithms , 1999, IEEE Trans. Evol. Comput..

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

[16]  Meie Shen,et al.  Differential Evolution With Two-Level Parameter Adaptation , 2014, IEEE Transactions on Cybernetics.

[17]  Safieddin Safavi-Naeini,et al.  A hybrid evolutionary programming method for circuit optimization , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Kay Chen Tan,et al.  Multimodal Optimization Using a Biobjective Differential Evolution Algorithm Enhanced With Mean Distance-Based Selection , 2013, IEEE Transactions on Evolutionary Computation.

[19]  Lalit M. Patnaik,et al.  Adaptive probabilities of crossover and mutation in genetic algorithms , 1994, IEEE Trans. Syst. Man Cybern..

[20]  Mourad Allad,et al.  Fuzzy controller parameters optimization by using genetic algorithm for the control of inverted pendulum , 2015, 2015 3rd International Conference on Control, Engineering & Information Technology (CEIT).

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

[22]  Jun Zhang,et al.  Clustering-Based Adaptive Crossover and Mutation Probabilities for Genetic Algorithms , 2007, IEEE Transactions on Evolutionary Computation.

[23]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.

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