Transcription of A MiniZinc Tutorial
1 A MiniZinc TutorialKim Marriott and Peter J. Stuckeywith contributions from Leslie De Koninck and Horst SamulowitzContents1 Introduction22 Basic Modelling in Our First Example.. An Arithmetic Optimisation Example.. Datafiles and Assertions.. Real Number Solving.. Basic structure of a model.. 123 More Complex Arrays and Sets.. Global Constraints.. Conditional Expressions.. Complex Constraints.. Set Constraints.. Enumerated Types.. 364 Global Constraints.. Alldifferent.. Cumulative.
2 Table.. Regular.. Defining Predicates.. Reflection Functions.. Local Variables.. Domain Reflection Functions.. Scope.. 515 Finite Domain Search.. Search Annotations.. Annotations.. 566 Effective Modelling Practices in Variable Bounds.. Unconstrained Variables.. Effective Generators.. Redundant Constraints.. Modelling Choices.. Multiple Modelling and Channels.. 657 Boolean Satisfiability Modelling in Modelling Integers.. Modelling Disequality.. Modelling Cardinality.
3 69A MiniZinc Keywords77B MiniZinc Operators77C MiniZinc Functions7721 IntroductionMiniZinc is a language designed for specifying constrained optimization and decision prob-lems over integers and real numbers. A MiniZinc model does not dictate how to solve theproblem although the model can contain annotations which are used to guide the is designed to interface easily to different backend solvers. It does this by trans-forming an input MiniZinc model and data file into a FlatZinc model. FlatZinc models consistof variable declaration and constraint definitions as well as adefinition of the objective func-tion if the problem is an optimization problem.
4 The translation from MiniZinc to FlatZincis specializable to individual backend solvers, so they can control what form constraints endup in. In particular, MiniZinc allows the specification of global constraints by Basic Modelling in MiniZincIn this section we introduce the basic structure of a MiniZinc model using two simple Our First ExampleFigure 1: Australian our first example, imagine that we wish to colour a map of Australia as shown inFigure 1. It is made up of seven different states and territories each ofwhich must be givena colour so that adjacent regions have different can model this problem very easily in MiniZinc .
5 The model is shown inFigure 2. Thefirst line in the model is a comment. A comment starts with a % which indicates that therest of the line is a comment. MiniZinc has no begin/end comment symbols (such as C s/*and */comments).The next part of the model declares the variables in the model. The line3 AUST [DOWNLOAD]% Colouring Australia using nc coloursint: nc = 3; : wa; : nt; : sa; : q; : nsw; : v; : t;constraintwa != nt;constraintwa != sa;constraintnt != sa;constraintnt != q;constraintsa != q;constraintsa != nsw;constraintsa !
6 = v;constraintq != nsw;constraintnsw != v;solvesatisfy;output["wa=", show(wa),"\t nt=", show(nt),"\t sa=", show(sa),"\n","q=", show(q),"\t nsw=", show(nsw),"\t v=", show(v),"\n","t=", show(t),"\n"];Figure 2: A MiniZinc colouring the states and territories in : nc = 3;specifies aparameterin the problem which is the number of colours to be used. Parametersare similar to variables in most programming languages. They must be declared and given atype. In this case the type isint. They are given a value by anassignment. MiniZinc allowsthe assignment to be included as part of the declaration (as in the line above) or to be aseparate assignment statement.
7 Thus the following is equivalent to the single line aboveint: nc;nc = 3;Unlike variables in many programming languages a parameter can only begiven asinglevalue. It is an error for a parameter to occur in more than one basic parameter types are integers (int), floating point numbers (float), Booleans(bool) and strings (string). Arrays and sets are also models can also contain another kind of variable called adecision variables are variables in the sense of mathematical orlogical variables. Unlikeparameters and variables in a standard programming language, the modeller does not need4to give them a value.
8 Rather the value of a decision variable is unknown and it is only whenthe MiniZinc model is executed that the solving system determines if the decision variablecan be assigned a value that satisfies the constraints in the modeland if so what this our example model we associate adecision variablewith each region,wa,nt,sa,q,nsw,vandt, which stands for the (unknown) colour to be used to fill the each decision variable we need to give the set of possible values the variable can is called the variable sdomain. This can be given as part of the variable declaration andthe type of the decision variable is inferred from the type of the values in the MiniZinc decision variables can be Booleans, integers, floating point numbers, or supported are arrays whose elements are decision variables.
9 In our MiniZinc model weuse integers to model the different colours. Thus each of our decision variables is declared tohave the is an integer range expression indicating the set{1,2,..,nc}using thevardeclaration. The type of the values is integer so all of the variables in themodel are integer decision which are used to name parameters and variables are sequences of lower anduppercase alphabetic characters, digits and the underscore _ character. They must startwith a alphabetic character. ThusmyName_2is a valid identifier.
10 MiniZinc (and Zinc)keywordsare not allowed to be used as identifier names, they are listed inAppendix ANeither are MiniZincoperatorsallowed to be used as identifier names; they are listed inAppendix carefully distinguishes between the two kinds of model variables: parametersand decision variables. The kinds of expressions that can be constructed using decisionvariables are more restricted than those that can be built fromparameters. However, in anyplace that a decision variable can be used, so can a parameter ofthe same the distinction between parameters and decision variables is called theinstanti-ationof the variable.
