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Diophantine Benchmarks for the B-Cell Algorithm

  • P. Bull
  • A. Knowles
  • G. Tedesco
  • A. Hone
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4163)

Abstract

The B-cell algorithm (BCA) due to Kelsey and Timmis is a function optimization algorithm inspired by the process of somatic mutation of B cell clones in the natural immune system. So far, the BCA has been shown to be perform well in comparison with genetic algorithms when applied to various benchmark optimisation problems (finding the optima of smooth real functions). More recently, the convergence of the BCA has been shown by Clark, Hone and Timmis, using the theory of Markov chains. However, at present the theory does not predict the average number of iterations that are needed for the algorithm to converge. In this paper we present some empirical convergence results for the BCA, using a very different non-smooth set of benchmark problems. We propose that certain Diophantine equations, which can be reformulated as an optimization problem in integer programming, constitute a much harder set of benchmarks for evolutionary algorithms. In the light of our empirical results, we also suggest some modifications that can be made to the BCA in order to improve its performance.

Keywords

Markov Chain Model Diophantine Equation Natural Immune System Diophantine Problem Smooth Real Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • P. Bull
    • 1
  • A. Knowles
    • 2
  • G. Tedesco
    • 3
  • A. Hone
    • 4
  1. 1.Department of Computer ScienceUniversity of AberystwythAberystwythU.K.
  2. 2.Department of ElectronicsUniversity of YorkU.K.
  3. 3.School of Computer ScienceUniversity of NottinghamNottinghamU.K.
  4. 4.Institute of Mathematics, Statistics & Actuarial ScienceUniversity of KentCanterburyU.K.

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