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A Heuristic Approach in Solving the Optimal Seating Chart Problem

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Mathematical Optimization Theory and Operations Research: Recent Trends (MOTOR 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1476))

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Abstract

The optimal seating chart problem is a graph partitioning problem with very practical use. It is the problem of finding an optimal seating arrangement for a wedding or a gala dinner. Given the number of tables available and the number of seats per table, the optimal seating arrangement is determined based on the guests’ preferences to seat or not to seat together with other guests at the same table. The problem is easily translated to finding an m-partitioning of a graph of n nodes, such that the number of nodes in each partition is less than or equal to the given upper limit c, and that the sum of edge weights in all partitions is maximized. Although it can be easily formulated as MILP, the problem is extremely difficult to solve even with relatively small instances, which makes it perfect to apply a heuristic method. In this paper, we present research of a novel descent-ascent method for the solution, with comparison to some of the already proposed techniques from the earlier works.

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Acknowledgement

This work was partially supported by the Serbian Ministry of Education, Science and Technological Development through the Mathematical Institute of the Serbian Academy of Sciences and Arts.

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Authors and Affiliations

  1. School of Computing, Union University, Kneza Mihaila 6, 11000, Beograd, Serbia

    Milan Tomić & Dragan Urošević

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, p.p. 367, 11000, Beograd, Serbia

    Dragan Urošević

Authors
  1. Milan Tomić
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  2. Dragan Urošević
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Corresponding author

Correspondence to Milan Tomić .

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Editors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Alexander Strekalovsky

  2. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Yury Kochetov

  3. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Tatiana Gruzdeva

  4. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Andrei Orlov

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Tomić, M., Urošević, D. (2021). A Heuristic Approach in Solving the Optimal Seating Chart Problem. In: Strekalovsky, A., Kochetov, Y., Gruzdeva, T., Orlov, A. (eds) Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2021. Communications in Computer and Information Science, vol 1476. Springer, Cham. https://doi.org/10.1007/978-3-030-86433-0_19

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  • DOI: https://doi.org/10.1007/978-3-030-86433-0_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86432-3

  • Online ISBN: 978-3-030-86433-0

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