Steiner Tree

教育

免費 · 專為 iPad 設計

This app computes Steiner trees using an evolutionary algorithm. You can place, drag, and delete points of your tree. The optimal number and position of Steiner points is computed. A minimal spanning tree (MST) connects a given set of points in a plane so that the sum of all edges is minimal. Often this sum of all edges can be reduced, if additional points are added. These points are called Steiner points, and the corresponding minimal spanning tree Steiner tree. If more than 3 points are given, it is a hard optimization problem to compute the optimal number and position of Steiner points. This app uses a simple evolutionary algorithm for demonstration purposes. It uses a population of individuals. Each individual represents a MST containing some Steiner points. The population develops towards the optimal Steiner tree in an evolutionary loop: Initially, each individual sets random Steiner points, and constructs the corresponding Steiner tree. The minimal length of the Steiner tree in the population is stored. Each individual has now a fitness value, which is the higher, the closer its Steiner tree length is to the minimal length in the population. Fitter individuals have more descendants by reproduction, and less fit individuals die out. In order to explore better solutions, reproduction does not create descendants that are identical to the parent individual, i.e. do not have their Steiner points at the same position. Rather these positions are shifted randomly by mutation, using a Gaussian distribution. How far they are shifted on average is determined also by their fitness: Good individuals shift their Steiner points less than worse individuals. How fast a good solution is found, depends thus on the population size, and the mutation strength.

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Minor internal update for newer iOS versions

版本 4.3

開發者Reinhard MAENNER指出App的隱私權實務可能包含下方描述的資料處理。如需更多資訊，請參閱 開發者的隱私權政策 。

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    資訊

    • 銷售商
      • Reinhard MAENNER
    • 大小
      • 677.9 KB
    • 類別
      • 教育
    • 相容性
      需要 iOS 12.0 或以上版本。
      • iPhone
        需要 iOS 12.0 或以上版本。
      • iPad
        需要 iPadOS 12.0 或以上版本。
      • iPod touch
        需要 iOS 12.0 或以上版本。
      • Mac
        需要 macOS 11.0（或以上版本）以及配備 Apple M1（或以上版本）晶片的 Mac。
      • Apple Vision
        需要 visionOS 1.0 或以上版本。
    • 語言
      • 英文
    • 年齡分級
      4+
    • 版權
      • © zeh4soft
  • 隱私權政策

    • 更多Reinhard MAENNER的作品

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