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An efficient evolutionary algorithm for the ring star problem

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  • Calvete, Herminia I.
  • Galé, Carmen
  • Iranzo, José A.

Abstract

This paper addresses the ring star problem (RSP). The goal is to locate a cycle through a subset of nodes of a network aiming to minimize the sum of the cost of installing facilities on the nodes on the cycle, the cost of connecting them and the cost of assigning the nodes not on the cycle to their closest node on the cycle. A fast and efficient evolutionary algorithm is developed which is based on a new formulation of the RSP as a bilevel programming problem with one leader and two independent followers. The leader decides which nodes to include in the ring, one follower decides about the connections of the cycle and the other follower decides about the assignment of the nodes not on the cycle. The bilevel approach leads to a new form of chromosome encoding in which genes are associated to values of the upper level variables. The quality of each chromosome is evaluated by its fitness, by means of the objective function of the RSP. Hence, in order to compute the value of the lower level variables, two optimization problems are solved for each chromosome. The computational results show the efficiency of the algorithm in terms of the quality of the solutions yielded and the computing time. A study to select the best configuration of the algorithm is presented. The algorithm is tested on a set of benchmark problems providing very accurate solutions within short computing times. Moreover, for one of the problems a new best solution is found.

Suggested Citation

  • Calvete, Herminia I. & Galé, Carmen & Iranzo, José A., 2013. "An efficient evolutionary algorithm for the ring star problem," European Journal of Operational Research, Elsevier, vol. 231(1), pages 22-33.
    • Handle: RePEc:eee:ejores:v:231:y:2013:i:1:p:22-33
    DOI: 10.1016/j.ejor.2013.05.013
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    References listed on IDEAS

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    6. Naji-Azimi, Zahra & Salari, Majid & Toth, Paolo, 2012. "An Integer Linear Programming based heuristic for the Capacitated m-Ring-Star Problem," European Journal of Operational Research, Elsevier, vol. 217(1), pages 17-25.
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    Cited by:

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    3. Xujin Chen & Xiaodong Hu & Xiaohua Jia & Zhongzheng Tang & Chenhao Wang & Ying Zhang, 0. "Algorithms for the metric ring star problem with fixed edge-cost ratio," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-25.
    4. Anupam Mukherjee & Partha Sarathi Barma & Joydeep Dutta & Goutam Panigrahi & Samarjit Kar & Manoranjan Maiti, 2022. "A multi-objective antlion optimizer for the ring tree problem with secondary sub-depots," Operational Research, Springer, vol. 22(3), pages 1813-1851, July.
    5. Calvete, Herminia I. & Galé, Carmen & Iranzo, José A., 2016. "MEALS: A multiobjective evolutionary algorithm with local search for solving the bi-objective ring star problem," European Journal of Operational Research, Elsevier, vol. 250(2), pages 377-388.
    6. Xujin Chen & Xiaodong Hu & Xiaohua Jia & Zhongzheng Tang & Chenhao Wang & Ying Zhang, 2021. "Algorithms for the metric ring star problem with fixed edge-cost ratio," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 499-523, October.

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