Partially Ordered Constraint Optimization Problems

The Constraint Problems usually addressed fall into one of two models: the Constraint Satisfaction Problem (CSP) and the Constraint Optimization Problem (COP). However, in many real-life applications, more functions should be optimized at the same time, and solutions are ranked by means of a Partial Order. Also, when dealing with Null values, the solution set is ranked through a Partial Order, and only the non dominated solutions are interesting for the user. For example, in 3D visual recognition, from any viewpoint there are always hidden features: assignments that are less expressive (that take more Null values than others) should be discarded. For these reasons, we propose the model of Partially-Ordered Constraint Optimization Problem and provide an algorithm for solving it, derived from the widely used Branch and Bound.