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An ant colony optimization algorithm for continuous optimization: application to feed-forward neural network training

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Abstract

Ant colony optimization (ACO) is an optimization technique that was inspired by the foraging behaviour of real ant colonies. Originally, the method was introduced for the application to discrete optimization problems. Recently we proposed a first ACO variant for continuous optimization. In this work we choose the training of feed-forward neural networks for pattern classification as a test case for this algorithm. In addition, we propose hybrid algorithm variants that incorporate short runs of classical gradient techniques such as backpropagation. For evaluating our algorithms we apply them to classification problems from the medical field, and compare the results to some basic algorithms from the literature. The results show, first, that the best of our algorithms are comparable to gradient-based algorithms for neural network training, and second, that our algorithms compare favorably with a basic genetic algorithm.

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Notes

  1. Note that this paper is an extension of the work published in [7, 32]. The extension consists in a more detailed explanation of the algorithm itself, the conduction of a fourfold cross-validation for all applications to test instances, and the conduction of tests for determining the statistical significance of the obtained results.

  2. Note that k can not be smaller than the number of dimensions of the problem being solved. This is due to the explicit handling of correlation among variables as explained in Sect. 3: In order to be able to rotate the coordinate system properly, the number of solutions available has to be at least equal to the number of dimensions.

  3. Such pseudo-random number generators are routinely available for most programming languages.

  4. At step i, only dimensions i through n are used.

  5. http://www.r-project.org

  6. Due to the limited resources for tuning, the chosen configuration for each race is not necessarily significantly better than all the others. The limit of 100 experiments per race did sometimes not allow reaching that level of assurance. However, the chosen configuration was definitely not significantly worse than any of the others.

  7. Note that Alba and Chicano did not perform a fourfold cross-validation. They only performed the first one of our four cross-validation experiments. Therefore, the results of our ACO algorithms in these tables refer to the results of the first of our four cross-validation experiments.

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Acknowledgments

This work was supported by the Spanish CICYT project OPLINK (grant TIN-2005-08818-C04), and by the Ramón y Cajal program of the Spanish Ministry of Science and Technology of which Christian Blum is a research fellow. This work was also partially supported by the ANTS project, an Action de Recherche Concertée funded by the Scientific Research Directorate of the French Community of Belgium.

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Authors and Affiliations

  1. IRIDIA, CoDE, Université Libre de Bruxelles, Brussels, Belgium

    Krzysztof Socha

  2. ALBCOM, LSI, Universitat Politècnica de Catalunya, Barcelona, Spain

    Christian Blum

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  1. Krzysztof Socha
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  2. Christian Blum
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Correspondence to Krzysztof Socha.

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Socha, K., Blum, C. An ant colony optimization algorithm for continuous optimization: application to feed-forward neural network training. Neural Comput & Applic 16, 235–247 (2007). https://doi.org/10.1007/s00521-007-0084-z

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