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Conference of the Spanish Association for Artificial Intelligence

CAEPIA 2016: Advances in Artificial Intelligence pp 68–78Cite as

Predicting Hardness of Travelling Salesman Problem Instances

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9868))

Abstract

Travelling Salesman Problem is a classical combinatorial problem which is used to check the performance of heuristics and metaheuristics. However, for fairly comparing the performance of these algorithms, it is necessary an in-depth understanding of the hardness of the Travelling Salesman Problem instances. This requires to recognize which attributes allow a correct prediction of the hardness of the instances of Travelling Salesman Problem. In this work, the hardness of the instances was predicted based on the statistical distribution of the distance between the cities, the areas arisen from the Dirichlet tessellation, and the areas from the Delaunay triangulation. As a consequence of this work, the attributes which separate the ease and difficult instances of the Travelling Salesman Problem are stated.

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Notes

  1. 1.

    The area of the Delaunay triangles are normalized to the total area covered by the cities.

  2. 2.

    The mean squared error (MSE) is the average of the squares of the differences between the predicted and actual values, \(MSE=\frac{1}{N}\sum _N (\hat{y}_i-y_i)^2\), where N is the number of samples and \(\hat{y}_i\) is the prediction of the value \(y_i\).

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Acknowledgement

The research leading to these results has received funding by the Spanish Ministry of Economy and Competitiveness (MINECO) for funding support through the grant FPA2013-47804-C2-1-R, and “Unidad de Excelencia María de Maeztu”: CIEMAT - FÍSICA DE PARTÍCULAS through the grant MDM-2015-0509.

Author information

Authors and Affiliations

  1. Department of Fundamental Research, Centro de Investigaciones Energéticas Medioambientales y Tecnológicas, Madrid, Spain

    Miguel Cárdenas-Montes

Authors
  1. Miguel Cárdenas-Montes
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Corresponding author

Correspondence to Miguel Cárdenas-Montes .

Editor information

Editors and Affiliations

  1. Artificial Intelligence Center, University of Oviedo, Gijón, Spain

    Oscar Luaces

  2. University of Castilla-La Mancha , Albacete, Spain

    José A. Gámez

  3. Public University of Navarre , Pamplona, Spain

    Edurne Barrenechea

  4. Universidad Pablo de Olavide , Sevilla, Spain

    Alicia Troncoso

  5. Public University of Navarre , Pamplona, Navarra, Spain

    Mikel Galar

  6. University of Salamanca , Salamanca, Spain

    Héctor Quintián

  7. University of Salamanca , Salamanca, Spain

    Emilio Corchado

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Cárdenas-Montes, M. (2016). Predicting Hardness of Travelling Salesman Problem Instances. In: Luaces , O., et al. Advances in Artificial Intelligence. CAEPIA 2016. Lecture Notes in Computer Science(), vol 9868. Springer, Cham. https://doi.org/10.1007/978-3-319-44636-3_7

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  • DOI: https://doi.org/10.1007/978-3-319-44636-3_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44635-6

  • Online ISBN: 978-3-319-44636-3

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