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From: Marco Gavanelli <marco.gavanelli_at_...17...>

Date: Fri, 15 Jun 2007 14:28:26 +0200

Date: Fri, 15 Jun 2007 14:28:26 +0200

Nicolas BERGER wrote: >> Nicolas BERGER wrote: >>> Hi everyone >>> >>> Is it possible to declare constants i.e. variable that are not reduced ? >>> For example, in the following problem, not reducing the domain of D but >>> only the domains of X and Y : >>> >>> [X,Y] $:: [-1.1..0.72], >>> D :: [1,4,7], >>> X + D #< 3, >>> Y + D #< 1. >> Hi Nicolas, >> >> What exactly do you mean with this? >> Maybe you mean that for each value in the domain of D, there exists a >> value in the domain of X such that the constraint X+D #< 3 is satisfied. >> >> If this is the case, you probably need a quantified CSP solver (QCSP). >> > > > Have a look at the following *real-life* (robot arm movement) CSP : > > Tx is 10.0, > Ty is 6.0, > X0 is 8, > Y0 is 4, > D $:: [1.99..2.01], > > A $:: [2.0..8.0], > B $:: [2.0..8.0], > Alpha $:: [0.. pi], > Beta $:: [0.. pi], > X $:: [0..Tx], > Y $:: [0..Ty], > I :: [2..5], > J :: [2..5] ; > > A * sin(Alpha) $= B * sin(Beta - Alpha) + Y, > A * cos(Alpha) $= X - (B * cos(Beta - Alpha)), > A * cos(Alpha) $=< Tx, > X $=< Tx, > A * sin(Alpha) $=< Ty, > Y $=< Ty, > (X - X0)^2 + (Y - Y0)^2 $=< 4, > A $= (I - 1) * D, > B $= (J - 1) * D. > > > D here is a constant term, it doesn't have to be reduced, it is just some > feature of the problem : 1.99 $=< D $=< 2.01. Actually, this problem comes > from a C++ constraint solving library (ELISA) where D can be declared as > of type "IntervalConstant"... > > Here what I have first thought of is excluding it from the "locate" var > list : > locate([A,B,Alpha,Beta,X,Y,I,J], > [A,B,Alpha,Beta,X,Y,I,J],1e-6,lin). > > > I suppose it means D is excluded from the search procedure (i.e. won't be > splitted) but I don't know if it excludes it from the propagation of > domain reductions raised by the constraints... Dear Nicolas, indeed the solver would propagate the constraints (thus reducing the domain of D), because D is an existentially quantified variable. The question is: what would you like the behaviour to be? If you need to declare a constant, you can easily do it, and you do not need propagation, but just unification: D = [1.99..2.01] Now D cannot be changed. But I suppose this is not what you need. For instance, what are the solutions of your previous example? X $:: [-1.1..0.72], D :: [1,4,7], X + D #< 3, Is X=0 a solution? Maybe yes, if you assume that D is equal to 1. But if D is equal to 7 it is not. So in the second case there is no point in leaving the value 7 in the domain of D. Cheers, Marco -- Marco Gavanelli, Ph.D. Computer Science Division Dipartimento di Ingegneria University of Ferrara Via Saragat 1 - 44100 Ferrara (Italy) Tel +39-0532-97-4833 Fax +39-0532-97-4870 http://www.ing.unife.it/docenti/MarcoGavanelli/Received on Fri Jun 15 2007 - 13:28:29 CEST

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