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A Steady-State Genetic Algorithm for the Tree t-Spanner Problem

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Soft Computing: Theories and Applications

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 742))

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Abstract

A tree t-spanner, in a given connected graph, is a spanning tree T in which the distance between every two vertices in T is at most t times their shortest distance in the graph, where the parameter t is called stretch factor of T. This paper studies the tree t-spanner problem on a given connected, undirected and edge-weighted graph G that seeks to find a spanning tree in G whose stretch factor is minimum among all tree spanners in G. This problem is \(\mathcal {NP}\)-Hard for any fixed \(t > 1\). In the domain of metaheuristic techniques, only genetic algorithm (GA) based on generational population model is proposed in the literature. This paper presents a steady-state genetic algorithm (SSGA) for this problem, which is quite different from the existing GA in the literature, not only in the population management strategy, but also in genetic operators. Genetic operators in SSGA use problem-specific knowledge for generating offspring, making SSGA highly effective in finding high-quality solutions in comparison to the existing GA. On a set of randomly generated instances, computational results justify the effectiveness of SSGA over the existing GA.

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Acknowledgements

This work is supported by the Science and Engineering Research Board—Department of Science & Technology, Government of India [grant no.: YSS/2015/000276].

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Authors and Affiliations

  1. Department of Computer Applications, National Institute of Technology Raipur, Raipur, 492010, CG, India

    Shyam Sundar

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  1. Shyam Sundar
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Correspondence to Shyam Sundar .

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Editors and Affiliations

  1. Department of Physics, Amity School of Applied Sciences, Amity University Rajasthan, Jaipur, Rajasthan, India

    Kanad Ray

  2. Department of Computer Science and Engineering, Amity School of Engineering and Technology, Amity University Rajasthan, Jaipur, Rajasthan, India

    Tarun K. Sharma

  3. Department of Electronics and Communication Engineering, SEEC, Manipal University Jaipur, Jaipur, Rajasthan, India

    Sanyog Rawat

  4. Institute of Basic Science, Bundelkhand University, Jhansi, Uttar Pradesh, India

    R. K. Saini

  5. Advanced Key Technologies Division, Nano Characterization Unit, Surface Characterization Group, National Institute for Materials Science, Tsukuba, Ibaraki, Japan

    Anirban Bandyopadhyay

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Sundar, S. (2019). A Steady-State Genetic Algorithm for the Tree t-Spanner Problem. In: Ray, K., Sharma, T., Rawat, S., Saini, R., Bandyopadhyay, A. (eds) Soft Computing: Theories and Applications. Advances in Intelligent Systems and Computing, vol 742. Springer, Singapore. https://doi.org/10.1007/978-981-13-0589-4_36

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