Differential Evolution with Grid-Based Parameter Adaptation

The reduction of human intervention in tuning metaheuristic optimization algorithms has been an ongoing research pursuit. Differential Evolution is a very popular algorithm that counts a large number of variants. However, its efficiency has been shown to depend on the type of its crossover operators (binomial or exponential), mutation operators, as well as on the two parameters that dominate these procedures. Making proper decisions on these parameters has proved to be a laborious, problem-dependent task. We propose a parameter adaptation technique that allows the algorithm to dynamically determine the most suitable crossover type and parameter values during its execution. The technique is based on a search procedure in the discretized parameter search space, using estimations of the algorithm’s performance. The proposed approach is tested and statistically validated on an established high-dimensional test suite. Also, comparisons with other algorithms are reported, verifying the competitiveness of the proposed approach.

[1]  Josef Tvrdík,et al.  Competitive differential evolution applied to CEC 2013 problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[2]  A. E. Eiben,et al.  Evolutionary Algorithm Parameters and Methods to Tune Them , 2012, Autonomous Search.

[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]  Janez Brest,et al.  Self-adaptive differential evolution algorithm using population size reduction and three strategies , 2011, Soft Comput..

[5]  Ponnuthurai N. Suganthan,et al.  Self-adaptive differential evolution with multi-trajectory search for large-scale optimization , 2011, Soft Comput..

[6]  Michael N. Vrahatis,et al.  Particle Swarm Optimization and Intelligence: Advances and Applications , 2010 .

[7]  Alex S. Fukunaga,et al.  Improving the search performance of SHADE using linear population size reduction , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[8]  Ville Tirronen,et al.  Shuffle or update parallel differential evolution for large-scale optimization , 2011, Soft Comput..

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

[10]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

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

[12]  Alex S. Fukunaga,et al.  Success-history based parameter adaptation for Differential Evolution , 2013, 2013 IEEE Congress on Evolutionary Computation.

[13]  Francisco Herrera,et al.  Editorial scalability of evolutionary algorithms and other metaheuristics for large-scale continuous optimization problems , 2011, Soft Comput..

[14]  Daniela Zaharie,et al.  Influence of crossover on the behavior of Differential Evolution Algorithms , 2009, Appl. Soft Comput..

[15]  Arnold Neumaier,et al.  VXQR: derivative-free unconstrained optimization based on QR factorizations , 2011, Soft Comput..

[16]  Francisco J. Rodríguez,et al.  Role differentiation and malleable mating for differential evolution: an analysis on large-scale optimisation , 2011, Soft Comput..

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

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

[19]  Enrique Alba,et al.  Restart particle swarm optimization with velocity modulation: a scalability test , 2011, Soft Comput..

[20]  Xiaodong Li,et al.  Benchmark Functions for the CEC'2010 Special Session and Competition on Large-Scale , 2009 .

[21]  Anyong Qing.  Differential Evolution: Fundamentals and Applications in Electrical Engineering , 2009 .

[22]  D. Zaharie.  A Comparative Analysis of Crossover Variants in Differential Evolution , 2007 .

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

[24]  Xin Yao,et al.  Scalability of generalized adaptive differential evolution for large-scale continuous optimization , 2010, Soft Comput..

[25]  Ville Tirronen,et al.  Scale factor inheritance mechanism in distributed differential evolution , 2009, Soft Comput..

[26]  Antonio LaTorre,et al.  Multiple Offspring Sampling in Large Scale Global Optimization , 2012, 2012 IEEE Congress on Evolutionary Computation.

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

[28]  Thomas Stützle,et al.  An incremental particle swarm for large-scale continuous optimization problems: an example of tuning-in-the-loop (re)design of optimization algorithms , 2011, Soft Comput..

[29]  Zhijian Wu,et al.  Enhanced opposition-based differential evolution for solving high-dimensional continuous optimization problems , 2011, Soft Comput..

[30]  Fred W. Glover,et al.  EM323: a line search based algorithm for solving high-dimensional continuous non-linear optimization problems , 2011, Soft Comput..

[31]  Janez Brest,et al.  Self-adaptive differential evolution algorithm with a small and varying population size , 2012, 2012 IEEE Congress on Evolutionary Computation.

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

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

[34]  Holger H. Hoos,et al.  Automated Algorithm Configuration and Parameter Tuning , 2012, Autonomous Search.

[35]  Francisco Gortázar,et al.  Path relinking for large-scale global optimization , 2011, Soft Comput..

[36]  Zbigniew Michalewicz,et al.  Parameter Control in Evolutionary Algorithms , 2007, Parameter Setting in Evolutionary Algorithms.

[37]  Antonio LaTorre,et al.  A MOS-based dynamic memetic differential evolution algorithm for continuous optimization: a scalability test , 2011, Soft Comput..

[38]  Francisco Herrera,et al.  Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains , 2011, Soft Comput..

[39]  Petr Bujok,et al.  Controlled restart in differential evolution applied to CEC2014 benchmark functions , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[40]  J. Tvrdík,et al.  COMPETITIVE DIFFERENTIAL EVOLUTION , 2006 .

[41]  D. Petcu,et al.  Parallel implementation of multi-population differential evolution , 2004 .