Evolutionary Approach to the Euclidean Steiner Tree Problem in n-Space

This article presents the application of a genetic algorithm for solving the Euclidean Steiner problem in spaces of dimensionality greater than 2. The Euclidean Steiner problem involves finding the minimum spanning network that connects a given set of vertices, including the additional Steiner verti...

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Main Author: Michał Bereta
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Applied Sciences
Subjects:
Online Access:https://www.mdpi.com/2076-3417/15/3/1413
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author Michał Bereta
author_facet Michał Bereta
author_sort Michał Bereta
collection DOAJ
description This article presents the application of a genetic algorithm for solving the Euclidean Steiner problem in spaces of dimensionality greater than 2. The Euclidean Steiner problem involves finding the minimum spanning network that connects a given set of vertices, including the additional Steiner vertices, in a multi-dimensional space. The focus of this research is to compare several different settings of the method, including the crossover operators and sorting of the input data. The paper points out that significant improvement in results can be achieved through proper initialization of the initial population, which depends on the appropriate sorting of vertices. Two approaches were proposed, one based on the nearest neighbor method, and the other on the construction of a minimum spanning tree.
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spelling doaj-art-c289862f34ea4324a5ef57e7a63ea3f32025-08-20T02:12:40ZengMDPI AGApplied Sciences2076-34172025-01-01153141310.3390/app15031413Evolutionary Approach to the Euclidean Steiner Tree Problem in n-SpaceMichał Bereta0Department of Computer Science, Cracow University of Technology, 31-155 Kraków, PolandThis article presents the application of a genetic algorithm for solving the Euclidean Steiner problem in spaces of dimensionality greater than 2. The Euclidean Steiner problem involves finding the minimum spanning network that connects a given set of vertices, including the additional Steiner vertices, in a multi-dimensional space. The focus of this research is to compare several different settings of the method, including the crossover operators and sorting of the input data. The paper points out that significant improvement in results can be achieved through proper initialization of the initial population, which depends on the appropriate sorting of vertices. Two approaches were proposed, one based on the nearest neighbor method, and the other on the construction of a minimum spanning tree.https://www.mdpi.com/2076-3417/15/3/1413Euclidean Steiner problemevolutionary optimizationgenetic algorithmheuristics
spellingShingle Michał Bereta
Evolutionary Approach to the Euclidean Steiner Tree Problem in n-Space
Applied Sciences
Euclidean Steiner problem
evolutionary optimization
genetic algorithm
heuristics
title Evolutionary Approach to the Euclidean Steiner Tree Problem in n-Space
title_full Evolutionary Approach to the Euclidean Steiner Tree Problem in n-Space
title_fullStr Evolutionary Approach to the Euclidean Steiner Tree Problem in n-Space
title_full_unstemmed Evolutionary Approach to the Euclidean Steiner Tree Problem in n-Space
title_short Evolutionary Approach to the Euclidean Steiner Tree Problem in n-Space
title_sort evolutionary approach to the euclidean steiner tree problem in n space
topic Euclidean Steiner problem
evolutionary optimization
genetic algorithm
heuristics
url https://www.mdpi.com/2076-3417/15/3/1413
work_keys_str_mv AT michałbereta evolutionaryapproachtotheeuclideansteinertreeprobleminnspace