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A hybrid breakout local search and reinforcement learning approach to the vertex separator problem

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  • Benlic, Una
  • Epitropakis, Michael G.
  • Burke, Edmund K.

Abstract

The Vertex Separator Problem (VSP) is an NP-hard problem which emerges from a variety of important domains and applications. In this paper, we present an improved Breakout Local Search for VSP (named BLS-RLE). The distinguishing feature of this approach is a new parameter control mechanism that draws upon ideas from reinforcement learning theory to reach an interdependent decision on the number and on the type of perturbation moves. The mechanism complies with the principle of first carrying out intensification and then employing minimal diversification only if needed, it uses a dedicated sampling strategy for a rapid convergence towards a limited set of parameter values that appear to be the most convenient for the given state of search. Extensive experimental evaluations and statistical comparisons on a wide range of benchmark instances show significant improvement in performance of the proposed algorithm over the existing BLS algorithm for VSP. Indeed, out of the 422 tested instances, BLS-RLE was able to attain the best-known solution in 93.8% of the cases, which is around 20% higher compared to the existing BLS. In addition, we provide detailed analyses to evaluate the importance of the key elements of the proposed method and to justify the degree of diversification introduced during perturbation.

Suggested Citation

  • Benlic, Una & Epitropakis, Michael G. & Burke, Edmund K., 2017. "A hybrid breakout local search and reinforcement learning approach to the vertex separator problem," European Journal of Operational Research, Elsevier, vol. 261(3), pages 803-818.
    • Handle: RePEc:eee:ejores:v:261:y:2017:i:3:p:803-818
    DOI: 10.1016/j.ejor.2017.01.023
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    References listed on IDEAS

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    1. Hager, William W. & Hungerford, James T., 2015. "Continuous quadratic programming formulations of optimization problems on graphs," European Journal of Operational Research, Elsevier, vol. 240(2), pages 328-337.
    2. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    3. Mohamed Didi Biha & Marie-Jean Meurs, 2011. "An exact algorithm for solving the vertex separator problem," Journal of Global Optimization, Springer, vol. 49(3), pages 425-434, March.
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    Cited by:

    1. Li, Mingjie & Hao, Jin-Kao & Wu, Qinghua, 2024. "A flow based formulation and a reinforcement learning based strategic oscillation for cross-dock door assignment," European Journal of Operational Research, Elsevier, vol. 312(2), pages 473-492.
    2. Rodriguez-Tello, Eduardo & Lardeux, Frédéric & Duarte, Abraham & Narvaez-Teran, Valentina, 2019. "Alternative evaluation functions for the cyclic bandwidth sum problem," European Journal of Operational Research, Elsevier, vol. 273(3), pages 904-919.
    3. Karimi-Mamaghan, Maryam & Mohammadi, Mehrdad & Meyer, Patrick & Karimi-Mamaghan, Amir Mohammad & Talbi, El-Ghazali, 2022. "Machine learning at the service of meta-heuristics for solving combinatorial optimization problems: A state-of-the-art," European Journal of Operational Research, Elsevier, vol. 296(2), pages 393-422.
    4. Karimi-Mamaghan, Maryam & Mohammadi, Mehrdad & Pasdeloup, Bastien & Meyer, Patrick, 2023. "Learning to select operators in meta-heuristics: An integration of Q-learning into the iterated greedy algorithm for the permutation flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1296-1330.
    5. Mu He & Qinghua Wu & Yongliang Lu, 2022. "Breakout local search for the cyclic cutwidth minimization problem," Journal of Heuristics, Springer, vol. 28(5), pages 583-618, December.

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