An improved differential evolution to continuous domains and its convergence

ABSTRACT

When differential evolution algorithm is applied in complicated optimization problems, it has the shortages of prematurity and stagnation. An improved differential evolution to obtain solutions quickly is proposed in this paper. The algorithm takes into account the information of problem solving and objective function. Firstly, a hybrid optimization strategy that parallelly executes uniform crossover and Binomial crossover is designed. So individuals can fully represent the solution space. Secondly, a transform function is constructed. This method is utilized to simplify the objective function .It eliminates local minimum and keeps the value of optimized function unchanged under the local minimum. Then its convergence is analyzed theoretically, and is proved to converge to the best solution. This algorithm is also tested by several benchmark functions. The simulation results show that it has perfect property in efficacy and converges faster.

REFERENCES

• 1: Storn, R., Price, K. 1995. Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. Berkeley: International Computer Science Institute.
• 2: Fan.Yu . 2004. "A hybrid optimized algorithm based on differential evolution and genetic algorithm and its applications in pattern synthesis of antenna arrays ". Acta Electronica Sinica, 1997 2000.
• 3: Zhao,G, Q., Peng X, Y. 2007. Design of FIR filters with differential evolution. In Proceedings of the 8th International Conference on Electronic Measurement & Instruments. ICEMI, 1748--1751.
• 4: Krink., Thiemo. 2007. "Using differential evolution to improve the accuracy of bank rating systems ". Computational Statistics and Data Analysis, 68--87.
• 5: Zaharie, D. 2003. Control of population diversity and adaptation in differential evolution algorithms. The 9th Int Conf on Soft Computing. Mendel, 41--46.
• 6: Chiou, J, P., Wang, F, S. 1998. A hybrid method of differential evolution with application to optimal control problems of a bioprocess system. In Proceedings of the of IEEE Int Conf on Evolutionary Computation. New York: IEEE Press,:627--632.
• 7: Cai, X, F., Zhong, S, N. 2005. "Evolutionary uniform optimization algorithm. Journal of Mathematics, 349--354.
• 8: Wang, Y., Fang, K, T. 1996. Application of the number theory in statistics. Beijing: Science Press.
• 9: Wang, L., Zhang, L. 2000." The genetic algorithm with crossover operator employing lattice methods". Computer Engineering and Science, 18--20.
• 10: Lin, D., Li, M, Q., Kou, J, S. 2000. " On the convergence of real--coded genetic algorithms ". Journal of Computer Research & Development, 1321--1327.
• 11: Liu, J, K. 2005 .Advanced PID control and its Matlab simulation. Beijing: Electronics Industry Press.
• 12: Storn, R. 1996. On the usage of differential evolution for function optimization. In Proceedings of the Biennial Conference of the North American Fuzzy Information Processing Society. Piscataway, NJ, New York: IEEE Press, 519--523.

INDEX TERMS

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

General Terms:
Algorithms

Keywords:
differential evolution algorithm