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For Real! XCS with Continuous-Valued Inputs

Stone, Christopher; Bull, Larry

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Christopher Stone

Lawrence Bull
School Director (Research & Enterprise) and Professor


Many real-world problems are not conveniently expressed using the ternary representation typically used by Learning Classifier Systems and for such problems an interval-based representation is preferable. We analyse two interval-based representations recently proposed for XCS, together with their associated operators and find evidence of considerable representational and operator bias. We propose a new interval-based representation that is more straightforward than the previous ones and analyse its bias. The representations presented and their analysis are also applicable to other Learning Classifier System architectures. We discuss limitations of the real multiplexer problem, a benchmark problem used for Learning Classifier Systems that have a continuous-valued representation, and propose a new test problem, the checkerboard problem, that matches many classes of real-world problem more closely than the real multiplexer. Representations and operators are compared, using both the real multiplexer and checkerboard problems and we find that representational, operator and sampling bias all affect the performance of XCS in continuous-valued environments.


Stone, C., & Bull, L. (2003). For Real! XCS with Continuous-Valued Inputs. Evolutionary Computation, 11(3), 299-336.

Journal Article Type Article
Publication Date Jan 1, 2003
Deposit Date Jan 22, 2010
Publicly Available Date Nov 15, 2016
Journal Evolutionary Computation
Print ISSN 1063-6560
Publisher Massachusetts Institute of Technology Press (MIT Press)
Peer Reviewed Peer Reviewed
Volume 11
Issue 3
Pages 299-336
Keywords XCS, continuous-valued inputs
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Additional Information Additional Information : Since they can be used to evolve traditional production system rules, Learning Classifier Systems have proven useful tools for data mining and knowledge discovery. This paper explores the most efficient way by which to represent rules consisting of vectors of real numbers, both formally and experimentally, as this is perhaps the most typical form of real-world data sets. The paper presents a new representation which has been widely adopted by the users of these systems. As a consequence, an EPSRC project (GR/T18455/01) to create super-computer implementations of such systems and other machine learning techniques was obtained - the Super Computer Data Mining Toolkit hosted by the AI Group. This is currently being used by the Group to explore Olympic athlete data (EP/43488/01), breast cancer data for a local health trust, bowling technique for the English Cricket Board, and the system identification of complex systems considering memory (EP/E042981/01). Copyright of this article is (c) MIT Press, 2003.


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