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Partitioning of supply/demand graphs with capacity limitations: an ant colony approach

Author

Listed:
  • Raka Jovanovic

    (Hamad bin Khalifa University)

  • Abdelkader Bousselham

    (Hamad bin Khalifa University)

  • Stefan Voß

    (University of Hamburg
    Pontificia Universidad Católica de Valparaíso)

Abstract

In recent years there has been a growing interest for the problem of the minimal partitioning of graphs with supply and demand, due to its close connection to electrical distribution systems, especially in the context of smartgrids. In this paper we present a new version of the problem which is more suitable for practical applications in modeling such systems. More precisely, the constraint of having a unique supply node in a subgraph (partition) is substituted with a limit on the number of subgraphs and the capacity for each of them. The problem is initially solved by a two stage greedy method. With the goal of further improving the quality of found solutions, a corresponding GRASP and an ant colony optimization algorithm are developed. Due to the novelty of the problem, we include a description of a method for generating test instances with known optimal solutions. In our computational experiments we evaluate the performance of the proposed algorithms on both trees and general graphs. The tests show that the proposed ant colony approach manages to frequently find optimal solutions. It has an average relative error of less than 2 % when compared to known optimal solutions. Moreover, it outperform the GRASP.

Suggested Citation

  • Raka Jovanovic & Abdelkader Bousselham & Stefan Voß, 2018. "Partitioning of supply/demand graphs with capacity limitations: an ant colony approach," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 224-249, January.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:1:d:10.1007_s10878-015-9945-z
    DOI: 10.1007/s10878-015-9945-z
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    References listed on IDEAS

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    1. Raka Jovanovic & Abdelkader Bousselham & Stefan Voß, 2015. "A heuristic method for solving the problem of partitioning graphs with supply and demand," Annals of Operations Research, Springer, vol. 235(1), pages 371-393, December.
    2. Stefan Voßs & Andreas Fink & Cees Duin, 2005. "Looking Ahead with the Pilot Method," Annals of Operations Research, Springer, vol. 136(1), pages 285-302, April.
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    Cited by:

    1. Jianming Zhu & Shuyue Liu & Smita Ghosh, 2019. "Model and algorithm of routes planning for emergency relief distribution in disaster management with disaster information update," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 208-223, July.

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