Modelling Search Strategies in Rules2CP

In this abstract, we present a rule-based modelling language for constraint programming, called Rules2CP [1], and a library PKML for modelling packing problems. Unlike other modelling languages, Rules2CP adopts a single knowledge representation paradigm based on logical rules without recursion, and a restricted set of data structures based on records and enumerated lists given with iterators. We show that this is su cient to model constraint satisfaction problems together with search strategies, where search trees are expressed by logical formulae, and heuristic choice criteria are de ned by preference orderings on variables and formulae. Rules2CP statements are compiled to constraint programs over nite domains (currently SICStus-prolog and soon Choco-Java) by term rewriting and partial evaluation. The Packing Knowledge Modelling Language (PKML) is a Rules2CP library developed in the European project Net-WMS for dealing with real size nonpure bin packing problems in logistics and automotive industry. PKML refers to shapes in Z . A point in this space is represented by the list of its K integer coordinates. A shape is a rigid assembly of boxes, represented by a record. A box is an orthotope in Z . An object , such as a bin or an item, is a record containing one attribute shapes for the list of its alternative shapes, one origin point, and some optional attributes such as weight, virtual reality representations or others. The alternative shapes of an object may be the discrete rotations of a basic shape, or di erent object shapes in a con guration problem. The end in one dimension and the volume of an object with alternative shapes are de ned with rei ed constraints. PKML uses Allen’s interval relations in one dimension, and the topological relations of the Region Connection Calculus in higher-dimensions, to express placement constraints. Pure bin packing problems can be de ned as follows: