Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization

Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies and their associated control parameter values. Employing a trial-and-error scheme to search for the most suitable strategy and its associated parameter settings requires high computational costs. Moreover, at different stages of evolution, different strategies coupled with different parameter settings may be required in order to achieve the best performance. In this paper, we propose a self-adaptive DE (SaDE) algorithm, in which both trial vector generation strategies and their associated control parameter values are gradually self-adapted by learning from their previous experiences in generating promising solutions. Consequently, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different phases of the search process/evolution. The performance of the SaDE algorithm is extensively evaluated (using codes available from P. N. Suganthan) on a suite of 26 bound-constrained numerical optimization problems and compares favorably with the conventional DE and several state-of-the-art parameter adaptive DE variants.

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

[2]  M. Montaz Ali,et al.  Population set-based global optimization algorithms: some modifications and numerical studies , 2004, Computers & Operations Research.

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

[4]  R. W. Derksen,et al.  Differential Evolution in Aerodynamic Optimization , 1999 .

[5]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

[6]  Amit Konar,et al.  Differential Evolution with Local Neighborhood , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[7]  Joni-Kristian Kämäräinen,et al.  Differential Evolution Training Algorithm for Feed-Forward Neural Networks , 2003, Neural Processing Letters.

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

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

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

[11]  Nikolaus Hansen,et al.  Compilation of Results on the 2005 CEC Benchmark Function Set , 2005 .

[12]  Xin Yao,et al.  Large scale evolutionary optimization using cooperative coevolution , 2008, Inf. Sci..

[13]  Rainer Storn,et al.  Differential evolution design of an IIR-filter , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

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

[15]  Arthur C. Sanderson,et al.  Minimal representation multisensor fusion using differential evolution , 1997, Proceedings 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation CIRA'97. 'Towards New Computational Principles for Robotics and Automation'.

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

[17]  James E. Baker,et al.  Reducing Bias and Inefficienry in the Selection Algorithm , 1987, ICGA.

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

[19]  René Thomsen,et al.  A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[20]  Peter J. Angeline,et al.  Adaptive and Self-adaptive Evolutionary Computations , 1995 .

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

[22]  Jim Smith,et al.  Operator and parameter adaptation in genetic algorithms , 1997, Soft Comput..

[23]  Xiaodong Li,et al.  Solving Rotated Multi-objective Optimization Problems Using Differential Evolution , 2004, Australian Conference on Artificial Intelligence.

[24]  R. Storn,et al.  On the usage of differential evolution for function optimization , 1996, Proceedings of North American Fuzzy Information Processing.

[25]  Fabio A. González,et al.  Using Adaptive Operators in Genetic Search , 2003, GECCO.


[27]  Peter Ross,et al.  Adapting Operator Settings in Genetic Algorithms , 1998, Evolutionary Computation.

[28]  Jing J. Liang,et al.  Novel composition test functions for numerical global optimization , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[29]  Kenneth V. Price,et al.  An introduction to differential evolution , 1999 .

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

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

[32]  Vitaliy Feoktistov,et al.  Differential Evolution: In Search of Solutions (Springer Optimization and Its Applications) , 2006 .

[33]  Bryant A. Julstrom,et al.  What Have You Done for Me Lately? Adapting Operator Probabilities in a Steady-State Genetic Algorithm , 1995, ICGA.

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

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

[36]  Janez Brest,et al.  Performance comparison of self-adaptive and adaptive differential evolution algorithms , 2007, Soft Comput..

[37]  Xiao-Feng Xie,et al.  DEPSO: hybrid particle swarm with differential evolution operator , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

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

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

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

[41]  Dana Petcu,et al.  Adaptive Pareto Differential Evolution and Its Parallelization , 2003, PPAM.