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Analysis of Convergence for Free Search Algorithm in Solving Complex Function Optimization Problems

  • Lu Li
  • Zihou Zhang
  • Xingyu Wang
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 107)

Abstract

Free Search (FS) algorithm is efficient in solving complex function optimization problems. Convergence of FS is analyzed in two different cases: continuous and discrete space. For continuous space, convergence of FS did not exist for all functions, such as functions containing singular points. However, taking advantage of measure theory, convergence of FS could be shown when functions satisfy continuous and Lipschitz conditions. For discrete space, making use of random process theory, convergence of FS was got in finite search space and FS was characterized by Markov property. Simulation of multi-model Shubert function is done. Compared with Genetic Algorithm (GA), FS is superior in convergence speed, accuracy and robustness. The analytic and experimental results on FS provide useful evidence for further understanding and properly tackling optimization problems of complex functions.

Keywords

Free search algorithm Convergence of algorithms Optimization problems of complex functions Markov chain Genetic algorithm 

Notes

Acknowledgements

This paper was supported by Shanghai Leading Academic Discipline Project, No.B504 and Special Fund of Shanghai University of Engineering Science.

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.College of Fundamental StudiesUniversity of Engineering ScienceShanghaiChina
  2. 2.School of Information Science and Engineering, East China University of Science and TechnologyShanghaiChina

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