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A general variable neighborhood search approach for the minimum load coloring problem

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Abstract

The minimum load coloring problem consists of finding a 2-coloring function that assign either a color red or blue to each node of a graph such that the (maximum) load is minimized, i.e., to reduce as much as possible the number of edges with, at least, one endpoint colored in red (symmetrically, in blue). This \(\mathcal {NP}\)-complete problem arises in Wavelength Division Multiplexing (WDM) technology and it has been used for broadcast WDM networks. In this paper, several procedures based on the Variable Neighborhood Search (VNS) methodology are proposed and compared on a set of random graphs and DIMACS benchmarks. Experimental results show that the proposed VNS variant exhibits a remarkable performance in comparison with the state-of-the-art methods. In particular, our approach achieves the best results in 48 out of 52 considered instances by employing, on average, less than 7 seconds. These results are further confirmed by conducting statistical tests.

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Notes

  1. GVNS and MS-GVNS were implemented in C++ and executed on an Intel Core i7 (2.5 GHz) with 8GB RAM.

  2. TALS was implemented in Visual C++ 6.0, and executed over a Intel Pentium (R) G630 Processor 2.70 MHz with 4 GB of RAM under Windows 7 System.

  3. MA was implemented in C++, and executed over a PC with Intel Pentium (R) G630 processor 2.70 GHz and 4 GB memory under Windows 7 (64 bits).

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Funding

This work has been partially supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (MCIU/AEI/FEDER, UE) under Grant Ref. PGC2018-095322-B-C22; and Comunidad de Madrid y Fondos Estructurales de la Unión Europea with Grant Ref. P2018/TCS-4566. This research has also been partially supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan, Grant No. BR10965172.

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Authors and Affiliations

  1. Department of Computer Sciences, Universidad Rey Juan Carlos, C/. Tulipán, s/n, Móstoles, 28933, Madrid, Spain

    Alberto Herrán, J. Manuel Colmenar & Abraham Duarte

  2. Department of Industrial Engineering and Research Center on Digital Supply Chain and Operations Management, Khalifa University, Abu Dhabi, UAE

    Nenad Mladenović

Authors
  1. Alberto Herrán
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  2. J. Manuel Colmenar
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  3. Nenad Mladenović
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  4. Abraham Duarte
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Correspondence to J. Manuel Colmenar.

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Herrán, A., Colmenar, J.M., Mladenović, N. et al. A general variable neighborhood search approach for the minimum load coloring problem. Optim Lett 17, 2065–2086 (2023). https://doi.org/10.1007/s11590-022-01861-1

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