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  • Fachhochschule Brandenburg

    Informatik und Medien

    D I PL O MA R BE I T

    Lsung komplexer "Pickup and Delivery" Probleme unter Einbeziehungmoderner Constrainttechniken

    Vorgelegt von: Gutachter:Mathias Lhr Prof. Dr. Jochen HeinsohnInformatik / Intelligente Systeme Dipl.-Ing. (FH) Torsten StorrerMatrikelnummer: 972128

    Weberplatz 2014482 Potsdam

    Potsdam, den 22.04.2002

  • Seite I

    Inhaltsverzeichnis1 Einleitung..................................................................................................................12 Constraints................................................................................................................3

    2.1 Einleitung...........................................................................................................42.2 Constraintprobleme...........................................................................................42.3 Konsistenzprfungen und Constraintpropagierung...........................................9

    2.3.1 Knotenkonsistenz.......................................................................................92.3.2 Kantenkonsistenz.......................................................................................92.3.3 Pfadkonsistenz.........................................................................................14

    2.4 Suchverfahren.................................................................................................152.4.1 Backtracking.............................................................................................152.4.2 Tiefensuche..............................................................................................162.4.3 Limited Discrepancy Search.....................................................................172.4.4 Greedy Search.........................................................................................172.4.5 Min-Conflicts-Heuristik..............................................................................172.4.6 Hill-Climbing und Steepest-Descent Search............................................182.4.7 Tabu Search.............................................................................................182.4.8 Guided Local Search................................................................................192.4.9 Branch-and-Bound...................................................................................20

    2.5 Variablen-und Wertereihenfolge......................................................................212.6 Constrainterweiterungen..................................................................................22

    2.6.1 Partielle CSP............................................................................................222.6.2 Constrainthierarchien...............................................................................232.6.3 Fuzzy Constraints.....................................................................................232.6.4 Probabilistische Constraints.....................................................................24

    2.7 Trends.............................................................................................................242.8 Zusammenfassung..........................................................................................26

    3 Alternativen zur Constraintprogrammierung...........................................................263.1 Lineare Programmierung.................................................................................263.2 Simulation........................................................................................................313.3 Evolutionre Algorithmen.................................................................................333.4 Dynamische Programmierung.........................................................................343.5 Zusammenfassung..........................................................................................34

    4 Systembersicht und Auswahl................................................................................35

  • Seite II

    4.1 ECLiPSe .........................................................................................................354.2 ILOG Bibliotheken...........................................................................................364.3 CHIP................................................................................................................364.4 Mozart/OZ........................................................................................................374.5 StarFlip++........................................................................................................384.6 Fazit.................................................................................................................38

    5 Klassifizierung des Pickup and Delivery Problems...............................................406 Analyse der Aufgabenstellung................................................................................417 Funktionsweise der ILOG-Bibliotheken...................................................................468 Objektorientierte Analyse und Design.....................................................................50

    8.1 OOA.................................................................................................................508.2 OOD................................................................................................................53

    8.2.1 MlTimeWindow.........................................................................................538.2.2 MlNodes...................................................................................................548.2.3 MlBreaks..................................................................................................558.2.4 MlVisits.....................................................................................................558.2.5 MlVehicles................................................................................................568.2.6 MlOrders...................................................................................................578.2.7 MlManager...............................................................................................58

    8.3 Format der Eingangsdaten..............................................................................588.4 Bemerkungen zu OOA/OOD...........................................................................59

    9 Implementierung.....................................................................................................599.1 MlGeneratePlan...............................................................................................59

    9.1.1 Erster Schritt.............................................................................................629.1.2 Zweiter Schritt...........................................................................................639.1.3 Dritter Schritt............................................................................................639.1.4 Vierter Schritt............................................................................................649.1.5 Fnfter und sechster Schritt.....................................................................659.1.6 Siebenter Schritt.......................................................................................689.1.7 Achter Schritt............................................................................................699.1.8 Neunter Schritt.........................................................................................69

    9.2 MlProduct2ProductConstraint..........................................................................699.3 Constraints deklarieren....................................................................................749.4 Lsung berechnen...........................................................................................829.5 Erluterungen zur Delphi-Implementierung.....................................................85

  • Seite III

    10 Zusammenfassung und Fazit...............................................................................87 Anhang A Eingangsdaten..................................................................................91 Anhang B Klassendeklarationen........................................................................97 Anhang C UML-Klassendiagramm mit Kardinalitten......................................112 Literaturverzeichnis.............................................................................................113

  • Seite IV

    AbbildungsverzeichnisAbbildung 1 Graphenfrbeproblem..............................................................................5Abbildung 2 Graphenfrbeproblem (Lsung)...............................................................6Abbildung 3 Traveling Salesman Problem im vollstndigen Graphen.........................8Abbildung 4 einfaches CSP.......................................................................................10Abbildung 5 Backtracking..........................................................................................15Abbildung 6 Tiefensuche...........................................................................................16Abbildung 7 Zyklus im Greedy-Algorithmus...............................................................19Abbildung 8 Simplex (aus [Hillier & Lieberman 1997])...............................................28Abbildung 9 Entwurf UML-Klassendiagramm............................................................52Abbildung 10 erweitertes UML-Klassendiagramm.....................................................53Abbildung 11 Problem der Orderheuristik..................................................................66Abbild