Diophantine benchmarks for the b-cell algorithm

  • Authors:

  • P. Bull;A. Knowles;G. Tedesco;A. Hone

  • Affiliations:

  • Department of Computer Science, University of Aberystwyth, Aberystwyth, U.K.;Department of Electronics, University of York, York, U.K.;School of Computer Science, University of Nottingham, Nottingham, U.K.;Institute of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, U.K.

  • Venue:
  • ICARIS'06 Proceedings of the 5th international conference on Artificial Immune Systems
  • Year:
  • 2006

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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.