Programmierung naturanaloger Verfahren. Soft Computing und by Jörn Schmidt

By Jörn Schmidt

In diesem Buch geht es um die Programmiertechniken, die zur Implementation sog. naturanaloger Verfahren erforderlich sind. Dabei handelt es sich um Zellularautomaten, Boolesche Netze, Evolutionäre Algorithmen, Simulated Annealing, Fuzzy-Methoden und Neuronale Netze. Der Band ist wegen seiner Konzentration auf Programmiertechniken ein Ergänzungsband zu dem Buch „Modellierung von Komplexität durch naturanaloge Verfahren“. Es werden keine speziellen Programmierkenntnisse vorausgesetzt, sondern nur die Kenntnis einer der heute üblichen Sprachen wie JAVA oder C#. Die Anleitungen für das Programmieren sind in einem Pseudocode geschrieben, der auch für Anfänger verständlich ist und keine bestimmte Sprache voraussetzt. Nach erfolgreicher Lektüre sind die Leser in der Lage, selbst die genannten Modelle zu programmieren.

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Dieses soll hier noch einmal als Programmskizze zusammengefasst werden: • • • • • • • • Feld-(Gitter-)Größe definieren (Vektor bzw. Matrix; ggf. zyklisch/toroidal) Zustand der Zellen definieren (binär, reelle Zahl oder Vektor) Anfangszustand des Systems S0 definieren (Vektor bzw. tmax) { o Zell-Scan: { Zellen zi werden in definierter Reihenfolge gemäß Ablaufmodus in Vektor/Matrix St durchlaufen und Zell-Zustand si,t abgefragt jeweils Zellzustände der Umgebung Ui abfragen Regel anwenden: liefert neuen Zellzustand si,t+1 neue Zellzustände in Systemzustand St+1 schreiben } o St+1 in Datei speichern o (Speicherplatz für St kann ggf.

Alternativ kann man die Zustände als Dezimalcode (oder Summe der Einsen) in klassischer Weise als Graph einer Funktion der Schrittzahl (Zeit) präsentieren (Abb. 2-4). Abbildung 2-4: Einfache Trajektorien des Netzes aus Abb. 2-4 und Tab. 2-5 Obere Kurve = Systemzustände als Dezimalcode; untere Kurve = Summe der Zustände 1 Bei einer weiteren Möglichkeit der Darstellung, die Studierenden in einer unserer Lehrveranstaltungen eingefallen ist, teilt man die Binärstrings der Zustände in zwei Hälften und trägt die Dezimalcodierung der beiden Teile (s.

Die folgenden Abbildungen 2-11 (a-d) zeigen verschiedene gebräuchliche Möglichkeiten der Umgebungen einer Zelle in ein- und zweidimensionalen Zellularautomaten. Abbildung 2-11a: Eindimensionaler Zellularautomat, jede Zelle hat zwei Nachbarn Abbildung 2-11b: Eindimensionaler Zellularautomat, jede Zelle hat vier Nachbarn 31 Man kann natürlich den schlichten Graphen hier auch als Digraphen ansehen, der jeweils "Doppelpfeile" als Kanten besitzt. 38 2 Boolesche Netze und Zellularautomaten Abbildung 2-11c/d: Zweidimensionaler Zellularautomat: (links) c.

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