A mutation and crossover adaptation mechanism for differential evolution algorithm

A new adaptive Differential Evolution algorithm called EWMA-DECrF is proposed. In original Differential Evolution algorithm three different control parameter values must be pre-specified by the user a priori; Population size, crossover and mutation scale factor. Choosing good parameters can be very difficult for the user, especially for the practitioners. In the proposed algorithm the mutation scale factor and crossover factor is adapted using a mechanism based on exponential weighting moving average, while the population size is kept fixed as in standard Differential Evolution. The algorithm was evaluated by using the set of 25 benchmark functions provided by CEC2005 special session on real-parameter optimization. It was compared to standard DE/rand/1/bin version and the two other algorithms also based on exponential weighting moving average; EWMA-DE and EWMA-DECr. Results show that proposed algorithm EWMA-DECrF outperformed the other algorithms by its average ranking based on normalized success performance.

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

[2]  Mehmet Fatih Tasgetiren,et al.  Differential evolution algorithm with ensemble of parameters and mutation strategies , 2011, Appl. Soft Comput..

[3]  Ivan Zelinka,et al.  ON STAGNATION OF THE DIFFERENTIAL EVOLUTION ALGORITHM , 2000 .

[4]  Yang Wang,et al.  Repairing the crossover rate in adaptive differential evolution , 2014, Appl. Soft Comput..

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

[6]  Josef Tvrdík,et al.  Competitive Differential Evolution Algorithm in Comparison with Other Adaptive Variants , 2012, SOCO.

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

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

[9]  Josef Tvrdík.  Adaptation in differential evolution: A numerical comparison , 2009, Appl. Soft Comput..

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

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

[12]  Jouni Lampinen,et al.  A mutation adaptation mechanism for Differential Evolution algorithm , 2013, 2013 IEEE Congress on Evolutionary Computation.

[13]  Arthur C. Sanderson,et al.  JADE: Self-adaptive differential evolution with fast and reliable convergence performance , 2007, 2007 IEEE Congress on Evolutionary Computation.

[14]  Adam P. Piotrowski,et al.  Adaptive Memetic Differential Evolution with Global and Local neighborhood-based mutation operators , 2013, Inf. Sci..

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

[16]  SK Mishra,et al.  Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions , 2006 .

[17]  H. Abbass,et al.  PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[18]  Carlos A. Coello Coello,et al.  On the adaptation of the mutation scale factor in differential evolution , 2015, Optim. Lett..

[19]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[21]  Petr Bujok,et al.  Adaptive Variants of Differential Evolution: Towards Control-Parameter-Free Optimizers , 2013, Handbook of Optimization.

[22]  Josef Tvrdík,et al.  Differential evolution with competitive setting of control parameters , 2007 .

[23]  Ponnuthurai N. Suganthan,et al.  Adaptive Differential Evolution with Locality based Crossover for Dynamic Optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[24]  Karl-Dirk Kammeyer,et al.  Parameter Study for Differential Evolution Using a Power Allocation Problem Including Interference Cancellation , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[25]  Zhifeng Hao,et al.  Multi-objective Differential Evolution Algorithm based on Adaptive Mutation and Partition Selection , 2013, J. Comput..

[26]  Saku Kukkonen,et al.  Real-parameter optimization with differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[27]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .