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New PDF release: Constraint and Integer Programming: Toward a Unified

By Michela Milano

ISBN-10: 144198917X

ISBN-13: 9781441989178

ISBN-10: 146134719X

ISBN-13: 9781461347194

Constraint and Integer Programming provides a number of the simple principles of constraint programming and mathematical programming, explores methods to integration, brings us brand new on heuristic tools, and makes an attempt to figure destiny instructions during this fast-moving box.

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Extra info for Constraint and Integer Programming: Toward a Unified Methodology

Sample text

As another example, if we have a cost associated to each variable-value assignment and we have to minimize the overall cost, in the model we introduce a cost variable Ci associated to each problem variable. The link between a cost variable and the corresponding problem variable is achieved through an element O; constraint. The objective function is Z = On the objective function, a minimization or a maximization predicate should be imposed. This predicate automatically posts a constraint, called bounding constraint each time a solution is found .

As soon as one constraint produces a modification on the domain of one variable, say X, all constraints involving X are triggered, and perform propagation on the basis of the current state of the variables' domains. At the end of the propagation, they are suspended until another event occur. 10] is always satisfied for all pairs of values in the domains of Xl and X2. Thus, if a constraint is solved it does not need to be triggered again. 1. 5] . Since X = Y + 1 is not solved it is suspended, since it could be triggered again after modifications of the domain of some variables.

This (unary) constraint states that variable Start can assume one of the integer values from 1 to 100. As another example, if a given variable Pos represents the position in a sequence of a given object, and positions available for the object are only 3, 5 and 9, we can express this constraint with a domain variable Po s :: [3,5, 9J. Thorough the book, other notations can be used for associating a domain to a variable. For instance the domain can be represented as a set like Pos E {3, 5, 9} or D{Pos) = {3, 5, 9}, but they all mean the same.

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Constraint and Integer Programming: Toward a Unified Methodology by Michela Milano

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