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A hybrid ant colony system algorithm for solving the ring star problem

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Abstract

The ring star problem (RSP) involves finding a minimum-length cycle over a set of nodes, for which each node that is non-visited on a cycle is assigned to its closest node on the cycle. The goal is to minimize routing and assignment costs. This study proposes a mathematical model to formulate RSP by using bi-level programming ideas, which consist of one leader and one follower sub-problems. The leader sub-problem refers to constructing a cycle over a subset of nodes in the network, whereas the follower sub-problem is related to assigning the remaining nodes to the nodes on the cycle. An efficient hybrid ant colony system (ACS) algorithm is developed on the basis of the bi-level programming formulations, in which ACS with assignment pheromone is proposed to solve the leader sub-problem. Lastly, the hybrid ACS is tested on 153 benchmark instances. Results show the good performance of the proposed approach.

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Acknowledgments

This research was supported by the Ministry of Chinese Education, Humanities, and Social Sciences Project (Grant Number 17YJA630037); and Graduate teaching reform research project of Hefei University of Technology (Grant Number 2018YJG02).

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Authors and Affiliations

  1. School of Management, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Xiaoning Zang & Bin Ding

  2. School of Management, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Li Jiang

  3. Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, People’s Republic of China

    Li Jiang

  4. Sheldon B. Lubar School of Business, University of Wisconsin-Milwaukee, 3202 N Maryland Ave, Milwaukee, WI, 53201, USA

    Xiang Fang

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  1. Xiaoning Zang
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  2. Li Jiang
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  3. Bin Ding
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  4. Xiang Fang
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Correspondence to Li Jiang.

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Zang, X., Jiang, L., Ding, B. et al. A hybrid ant colony system algorithm for solving the ring star problem. Appl Intell 51, 3789–3800 (2021). https://doi.org/10.1007/s10489-020-02072-w

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