Implementing Semiring-Based Constraints using Mozart Alberto Delgado Carlos Alberto Olarte Jorge Andres Perez Camilo Rueda 1 1 Pontificia Universidad Javeriana-Cali Mozart/Oz Conference 2004 Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
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Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
C-semiring formalism
Defines a semiring structure 〈A,+,×, 0, 1〉 where :
A is the set of possible valuations× is used to combine constraints+ is the operator to order the elements in A (a ≥s biff a + b = a)0, 1 are the min and max elements in A
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
Soft Propagators
We provide propagators (soft ones) dealing with thec-semiring formalism concepts
They exploit standard mechanisms (CPI) for extending Mozartwith new constraint systems and user-defined constraints
Each propagator implements a filter and a valuation (def )function. The latter is computed only when the propagatorbecomes entailed, saving space and time.
Filter is written according to the valuation function
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
Imposing Preferences
Preferences
Given a variable, we can define preferences over elements inits domain. e.g.
Color : red � white � blue
And given two variables we can define conditional preferences.e.g.
Shape = circle : Color = blue � Color = white
In most cases, not all the preferences can be satisfied.Solution?: Use CP-Nets and solve a SCSP [Rossi et all, 2003]
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
Imposing Preferences (cont.)
A Simple CP-Net
Steak � Fish � Chicken
Red wine � White wine
Rise � Fries
Fish : White wine � Red wine
Chicken : Fries � Rise
The model
Choose the fuzzy or weighted c-semiring
Impose independent preferences by means of theUnaryPreference propagator
Impose conditional preferences by means of the nPreferencepropagator
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
Advantages
Advantages Using a semiring-based approach?
Avoids a double distribution process
Solution can be easily compared (by using +)
Allows to impose preferences and Soft Constraints by makingorthogonal changes in the model and source code
It is easy to make propagators harder or softer
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
Conclusions and Future Work
Conclusions
Soft, a new Mozart module to handle semiring-basedconstraints
We model hard constraints (i.e by using FDs propagators)without using soft constraint (i.e by using Scsp and thensolving a multicriteria problem)
Adding preferences and soft constraints can be achievedwithout change the core of the application and/or model.
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
Future Work
Future Work
Extend our set of soft propagators.
Include soft ideas into the distribution process.
Implement the abstraction scheme [Bistarelli,02], by usinginformation obtained from processing the abstract problem inthe distribution process of the concrete one.
Test our implementation on real-life applications.
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.
Thank you!
Delgado A., Olarte C., Perez J. and Rueda C. Implementing Semiring-Based Constraints using Mozart.