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Recent Advances in Computational Optimization pp 219–233Cite as

Genetic Algorithms for Constrained Tree Problems

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 655))

Abstract

Given an undirected weighted connected graph \(G=(V,E)\) with vertex set V, edge set E and a designated vertex \(r \in V\), this chapter studies the following constrained tree problems in G. The first problem, called Constrained Minimum Spanning Tree Problem (CMST), asks for a rooted tree T in G that minimizes the total weight of T such that the distance between the r and any vertex v in T is at most a given constant C times the shortest distance between the two vertices in G. The second problem, Constrained Shortest Path Tree Problem (CSPT) requires a rooted tree T in G that minimizes the maximum distance between r and all vertices in V such that the total weight of T is at most a given constant C times the minimum tree weight in G. It is easy to conclude from the literatures that the above problems are NP-hard. This chapter presents efficient genetic algorithms that return (as shown by our experimental results) high quality solutions for those two problems.

This work is partially supported by Alexander von Humboldt foundation.

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Authors and Affiliations

  1. Department of Mathematics, Suez Canal University, Ismailia, 41522, Egypt

    Riham Moharam & Ehab Morsy

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  1. Riham Moharam
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  2. Ehab Morsy
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Correspondence to Riham Moharam .

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Editors and Affiliations

  1. Department of Parallel Algorithms, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Moharam, R., Morsy, E. (2016). Genetic Algorithms for Constrained Tree Problems. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol 655. Springer, Cham. https://doi.org/10.1007/978-3-319-40132-4_13

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  • DOI: https://doi.org/10.1007/978-3-319-40132-4_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40131-7

  • Online ISBN: 978-3-319-40132-4

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