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Coevolutionary bid-based genetic programming for problem decomposition in classification

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Abstract

In this work a cooperative, bid-based, model for problem decomposition is proposed with application to discrete action domains such as classification. This represents a significant departure from models where each individual constructs a direct input-outcome map, for example, from the set of exemplars to the set of class labels as is typical under the classification domain. In contrast, the proposed model focuses on learning a bidding strategy based on the exemplar feature vectors; each individual is associated with a single discrete action and the individual with the maximum bid ‘wins’ the right to suggest its action. Thus, the number of individuals associated with each action is a function of the intra-action bidding behaviour. Credit assignment is designed to reward correct but unique bidding strategies relative to the target actions. An advantage of the model over other teaming methods is its ability to automatically determine the number of and interaction between cooperative team members. The resulting model shares several traits with learning classifier systems and as such both approaches are benchmarked on nine large classification problems. Moreover, both of the evolutionary models are compared against the deterministic Support Vector Machine classification algorithm. Performance assessment considers the computational, classification, and complexity characteristics of the resulting solutions. The bid-based model is found to provide simple yet effective solutions that are robust to wide variations in the class representation. Support Vector Machines and classifier systems tend to perform better under balanced datasets albeit resulting in black-box solutions.

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Notes

  1. Hereafter, we will use ‘class’ and ‘action’ interchangeably.

  2. As opposed to the test data employed for assessing the generalization performance of the trained classifier.

  3. Compared to a parallel implementation, training overhead increases minimally as Step 2(c) in Fig. 1 is executed |L| times more often where L is the set of class labels.

  4. An alternative approach might take the form of an auction-based model for credit assignment. Such models are based on the concept of ‘wealth’ [38]. However, it becomes increasingly difficult to establish robust mechanisms for deriving the ‘wealth’ property when the subset of exemplars from which wealth-based performance metrics are derived is continuously varying—as is the case of the competitive coevolutionary paradigm central to scaling the BGP model to large problem domains.

  5. For efficiency, micro-classifiers representing identical condition-action rules are recorded as a single macro-classifier. Each macro-classifier has an associated numerosity which is used to weigh calculations accordingly. Here, the algorithm is described in terms of micro-classifiers.

  6. Otherwise the test data would have been used to build the model compromising the independence of the test partition.

  7. All datasets with more than two classes will be ‘unbalanced’ since each class can at best (i.e., when the number of exemplars belonging to each class is the same) account for \(\frac{1}{\# of classes}\) of all exemplars.

  8. The removal of introns, which were found to account for between 60% to 90% of instructions in linear GP [51], was not performed.

  9. Given that 1,250,000 new learners are generated when training learners of each action for 50,000 generations, Step 2 of the learning algorithm, on THY roughly one in 127, 116, and 173 new learners is accepted into the population when training for action 0, 1, and 2 respectively.

  10. Although a small mutation in a program’s genotype may yield a disproportionally large change in its phenotype.

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Acknowledgements

This work was conducted while Peter Lichodzijewski held a Precarn Graduate Scholarship and a Killam Postgraduate Scholarship. Malcolm. I. Heywood would like to thank the Natural Sciences and Engineering Research Council of Canada, The Mathematics of Information Technology and Complex Systems network, and the Canadian Foundation for Innovation for their financial support.

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  1. Faculty of Computer Science, Dalhousie University, 6050 University Ave., Halifax, NS, Canada, B3H 1W5

    Peter Lichodzijewski & Malcolm I. Heywood

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Correspondence to Peter Lichodzijewski.

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Lichodzijewski, P., Heywood, M.I. Coevolutionary bid-based genetic programming for problem decomposition in classification. Genet Program Evolvable Mach 9, 331–365 (2008). https://doi.org/10.1007/s10710-008-9067-9

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