Hybrid differential evolution and the simplified quadratic interpolation for global optimization

ABSTRACT

To improve the searching ability and convergence speed of differential evolution (DE), we combined a search operation for enhancing the performance of the original DE. The simplified quadratic interpolation (SQI) is employed to improve the local search ability and the accuracy of the minimum function value, and to reduce greatly the computational overhead of the algorithm. The classic benchmark test functions are employed to evaluate the performance of the proposed method. We also provide a comparison of the proposed method to fuzzy adaptive differential evolution (FADE). Experimental results confirm that the proposed method outperforms the original DE and FADE in terms of convergence speed, solution quality, and solution stability.

REFERENCES

• 1: Rainer Storn , Kenneth Price, Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, v.11 n.4, p.341-359, December 1997 [doi>10.1023/A:1008202821328]
• 2: Kenneth Price , Rainer M. Storn , Jouni A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series), Springer-Verlag New York, Inc., Secaucus, NJ, 2005
• 3: H.K. Kim, J.K. Chong, and K.Y. Park, Differential evolution strategy for constrained global optimization and application to practical engineering problems, IEEE Trans. Magn., 43(4):1565--1568, April 2007.
• 4: Shiwen Yang , Yeow Beng Gan , Anyong Qing, Antenna-array pattern nulling using a differential evolution algorithm: Original Articles, International Journal of RF and Microwave Computer-Aided Engineering, v.14 n.1, p.57-63, January 2004 [doi>10.1002/mmce.v14:1]
• 5: ,W. L. Price, Global optimization by controlled random search, J. Optim. Theory Appl.,40: 33--348, 1983.
• 6: J.P. Chiou, and F. S. Wang, Hybrid method of evolutionary algorithms for static and dynamic optimization problems with applications to a fed-batch fermentation process. Comput. Chem. Eng., 23(9):1277--1291,1999.
• 7: Nasimul Noman , Hitoshi Iba, Enhancing differential evolution performance with local search for high dimensional function optimization, Proceedings of the 2005 conference on Genetic and evolutionary computation, June 25-29, 2005, Washington DC, USA [doi>10.1145/1068009.1068174]
• 8: H. Li, Y.C. Jiao, and Y.P. Wang, Integrating the simplified interpolation into the genetic algorithm for constrained optimization problems, Springer-Verlag Berlin Heidelberg, 247--254, 2005.
• 9: M. M. Ali , A. Törn , S. Viitanen, A Numerical Comparison of Some Modified Controlled Random SearchAlgorithms, Journal of Global Optimization, v.11 n.4, p.377-385, December 1997 [doi>10.1023/A:1008236920512]
• 10: J. Liu , J. Lampinen, A Fuzzy Adaptive Differential Evolution Algorithm, Soft Computing - A Fusion of Foundations, Methodologies and Applications, v.9 n.6, p.448-462, June 2005 [doi>10.1007/s00500-004-0363-x]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Global optimization

General Terms:
Algorithms, Experimentation, Performance

Keywords:
differential evolution, global optimization, simplified quadratic interpolation