## Abstract

We want to find a tree where the path length between any two vertices on this tree is as close as possible to their corresponding distance in the complete weighted graph of vertices upon which the tree is built. We use the residual sum of squares as the optimality criterion to formulate this problem, and use the Cholesky decomposition to solve the system of linear equations to optimize weights of a given tree. We also use two metaheuristics, namely Simulated Annealing (SA) and Iterated Local Search (ILS) to optimize the tree structure. Our results suggest that SA and ILS both perform well at finding the optimal tree structure when the dispersion of distances in the complete graph is large. However, when the dispersion of distances is small, only ILS has a solid performance.

Original language | English |
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Title of host publication | Proceedings of the 2020 Federated Conference on Computer Science and Information Systems, FedCSIS 2020 |

Editors | Maria Ganzha, Leszek Maciaszek, Marcin Paprzycki |

Place of Publication | Warsaw Poland |

Publisher | IEEE, Institute of Electrical and Electronics Engineers |

Pages | 271-275 |

Number of pages | 5 |

Volume | 21 |

ISBN (Electronic) | 9788395541674, 9788395541681 |

ISBN (Print) | 9789788395541698 |

DOIs | |

Publication status | Published - Sep 2020 |

Event | Federated Conference on Computer Science and Information Systems, 2020 - Virtual, Sofia, Bulgaria Duration: 6 Sep 2020 → 9 Sep 2020 Conference number: 15th https://fedcsis.org/2020/ |

### Publication series

Name | Annals of Computer Science and Information Systems |
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Volume | 21 |

ISSN (Print) | 2300-5963 |

### Conference

Conference | Federated Conference on Computer Science and Information Systems, 2020 |
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Abbreviated title | FedCSIS 2020 |

Country | Bulgaria |

City | Virtual, Sofia |

Period | 6/09/20 → 9/09/20 |

Other | The mission of the FedCSIS Conference Series is to provide a presentation, discussion and a reputable publication forum in computer science and information systems. The forum invites researchers and practitioners from around the world to contribute their research results focused on their scientific and professional interests in a chosen conference track. |

Internet address |