A new differential evolution with improved mutation strategy

The paper employs Lagrange's mean value theorem of differential Calculus to design a new strategy for the selection of parameter vectors in the Differential Evolution (DE) algorithm. Classical differential evolution selects parameter vectors randomly to obtain the donor vectors. These donor vectors thus cannot be directly used as trial solution to the optimization problem. The recombination step indeed is very useful to generate potential trial solutions. The proposed algorithm eliminates the recombination step as the trial solutions can be directly generated by the extended mutation step only. Performance analysis of the proposed algorithm with respect to standard benchmark functions reveals that both in expected convergence time and accuracy in solutions, the proposed algorithm outperforms classical DE/rand/1. Besides extension in mutation strategy, an adaptive selection strategy in the scaling factor F also improves the performance of the proposed algorithm. In addition, the proposed algorithm outperforms classical DE in noisy optimization problem. Further, the number of function evaluation with scaled up dimensions of the optimization problem adds insignificantly small complexity in comparison to that in classical differential evolution to meet up a prescribed level of accuracy in solution quality.

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

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

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

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

[5]  Gary B. Fogel,et al.  Noisy optimization problems - a particular challenge for differential evolution? , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[6]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[7]  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.

[8]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

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

[10]  Xin Yao,et al.  Self-adaptive differential evolution with neighborhood search , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

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

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

[13]  Daniel A. Ashlock,et al.  Evolutionary computation for modeling and optimization , 2005 .

[14]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

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