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Methodology of Solving Selected Routing Problems

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Graph-Based Modelling in Science, Technology and Art

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 107))

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Abstract

The article presents the methodology of solving selected routing problems, which include the traveling salesman problem (TSP) and the arc routing problem (ARP). Graphs are used to model problems, which have become a natural language useful for describing the created models. Basic theorems of graph theory are used to solve routing tasks. TSP is reduced to the task of determining the Hamilton cycle in the complete graph, and ARP to the task of determining the Euler cycle in the Euler graph. TSP is NP—hard problem. ARP tasks may become such in complex cases. Artificial immune systems are used as a tool supporting solving the formulated problems. The proposed tools are very effective also for large tasks. The concepts and theorems of graph theory are used here to reduce a given problem to a form that is most convenient to be solved by the adopted method. TSP and ARP solving methods have a wide range of applications, including in transport logistics and in the organization of production. In addition, TSP can be used in the control of CNC machines and even in DNA sequencing.

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Authors and Affiliations

  1. Faculty of Transport, Silesian University of Technology, Gliwice, Poland

    Bogna Mrówczyńska

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  1. Bogna Mrówczyńska
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Correspondence to Bogna Mrówczyńska .

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  1. Faculty of Mechanical Engineering and Computer Science, University of Bielsko-Biala, Bielsko-Biała, Poland

    Stanisław Zawiślak

  2. Department of Fundamentals of Machine Building, University of Bielsko-Biala, Bielsko-Biała, Poland

    Jacek Rysiński

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Mrówczyńska, B. (2022). Methodology of Solving Selected Routing Problems. In: Zawiślak, S., Rysiński, J. (eds) Graph-Based Modelling in Science, Technology and Art. Mechanisms and Machine Science, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-030-76787-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-76787-7_5

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