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Breakout local search for the Steiner tree problem with revenue, budget and hop constraints

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  • Fu, Zhang-Hua
  • Hao, Jin-Kao

Abstract

The Steiner tree problem (STP) is one of the most popular combinatorial optimization problems with various practical applications. In this paper, we propose a Breakout Local Search (BLS) algorithm for an important generalization of the STP: the Steiner tree problem with revenue, budget and hop constraints (STPRBH), which consists of determining a subtree of a given undirected graph which maximizes the collected revenues, subject to both budget and hop constraints. Starting from a probabilistically constructed initial solution, BLS uses a Neighborhood Search (NS) procedure based on several specifically designed move operators for local optimization, and employs an adaptive diversification strategy to escape from local optima. The diversification mechanism is implemented by adaptive perturbations, guided by dedicated information of discovered high-quality solutions. Computational results based on 240 benchmarks show that BLS produces competitive results with respect to several previous approaches. For the 56 most challenging instances with unknown optimal results, BLS succeeds in improving 49 and matching one best known results within reasonable time. For the 184 instances which have been solved to optimality, BLS can also match 167 optimal results.

Suggested Citation

  • Fu, Zhang-Hua & Hao, Jin-Kao, 2014. "Breakout local search for the Steiner tree problem with revenue, budget and hop constraints," European Journal of Operational Research, Elsevier, vol. 232(1), pages 209-220.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:1:p:209-220
    DOI: 10.1016/j.ejor.2013.06.048
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    References listed on IDEAS

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    1. Costa, Alysson M. & Cordeau, Jean-François & Laporte, Gilbert, 2008. "Fast heuristics for the Steiner tree problem with revenues, budget and hop constraints," European Journal of Operational Research, Elsevier, vol. 190(1), pages 68-78, October.
    2. S. Voß, 1999. "The Steiner tree problem with hop constraints," Annals of Operations Research, Springer, vol. 86(0), pages 321-345, January.
    3. Avella, Pasquale & Villacci, Domenico & Sforza, Antonio, 2005. "A Steiner arborescence model for the feeder reconfiguration in electric distribution networks," European Journal of Operational Research, Elsevier, vol. 164(2), pages 505-509, July.
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    Cited by:

    1. Alessandro Hill & Roberto Baldacci & Edna Ayako Hoshino, 2019. "Capacitated ring arborescence problems with profits," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 357-389, June.
    2. 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.
    3. Zhang-Hua Fu & Jin-Kao Hao, 2015. "Dynamic Programming Driven Memetic Search for the Steiner Tree Problem with Revenues, Budget, and Hop Constraints," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 221-237, May.

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