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Download Logic-Based 0–1 Constraint Programming by Peter Barth PDF

By Peter Barth

A good judgment view of 0-1 integer programming difficulties, delivering new insights into the constitution of difficulties that could lead the researcher to more advantageous resolution options looking on the matter category. Operations study ideas are built-in right into a common sense programming atmosphere. the 1st monographic therapy that starts to unify those methodological techniques.
Logic-based tools for modelling and fixing combinatorial difficulties have lately began to play an important position in either thought and perform. the applying of good judgment to combinatorial difficulties has a twin element. On one hand, constraint common sense programming permits one to declaratively version combinatorial difficulties over a suitable constraint area, the issues then being solved through a corresponding constraint solver. along with being a high-level declarative interface to the constraint solver, the common sense programming language permits one additionally to enforce these subproblems that can not be certainly expressed with constraints. nevertheless, logic-based equipment can be utilized as a constraint solving approach inside a constraint solver for combinatorial difficulties modelled as 0-1 integer programs.

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Extra info for Logic-Based 0–1 Constraint Programming

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When we abstract away the inference machine from the operational semantics, we see that the following operations provide the basis for an implementation for a constraint solver over a specific domain [JM94]. , whether ID ~ 3X': C, where X' is the set of free variables in C. , whether ID ~ VX' : C :::} C', where X'is the set of free variables in C and C'. projection: Let C be a set of constraints in 2 and X' be the set of free variables in C. Let y ~ X' be a set of variables that we want to project away.

Proof. Let h ~ t2 be an arbitrary non-linear pseudo-Boolean inequality. Obviously, h ~ t2 is equivalent to tl - t2 ~ O. 1 there is a unique normal form for the pseudo-Boolean term tl - t2. For the left-hand side of the pseudo-Boolean inequality the only additional restriction is that we require the index sets lEn to be non-empty. For an empty index set the pseudo-Boolean term c0 TIiE0 Xi is simply C0. By adding -c0 on both sides of the non-linear pseudo-Boolean inequality we obtain the desired normal form.

Since M = C1 = 1, the constraint C2 +S+M = 0 + lO·C1 reduces to C2 + S = 0 + 9 . Since 0 + 9 is greater than or equal to 9 in all possible assignments, we conclude that S must be greater than or equal to 8, because C2 is at most 1. Hence, the domain of S is reduced to {8,9}. Furthermore, the domain of 0 is reduced to {O}, since C2 + S is at most 10. Hence, 0 must be smaller than 2, but 1 is already eliminated from the domain. Proceeding further we obtain the following state before starting the enumeration.

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