Constraint Relationships for Soft Constraints
Research and Development in Intelligent Systems XXX
We introduce constraint relationships as a means to define qualitative preferences on the constraints of soft constraint problems. The approach is aimed at constraint satisfaction problems (CSPs) with a high number of constraints that make exact preference quantizations hard to maintain manually or hard to anticipateespecially if constraints or preferences change at runtime or are extracted from natural language text. Modelers express preferences over the satisfaction of constraints with a
... semantics regarding preferred tuples without assigning priorities to concrete domain values. We show how a CSP including a set of constraint relationships can linearly be transformed into a k-weighted CSP as a representative of c-semirings that is solved by widely available constraint solvers and compare it with existing techniques. We demonstrate the approach by using a typical example of a dynamic and interactive scheduling problem in AI. P r e p r i n t O n l y Preprint only. Manuscript accepted for publication in Proc. SGAI 2013 can never give two lectures at the same time. We might prefer solutions that do not include Friday afternoon lectures. Real-world problems tend to become too rigid as problems become overconstrained due to additional constraints representing preferences. Pioneering approaches to this problem either change the problem by relaxing existing constraints by adding domain values as in Partial CSP  or look for solutions that fulfill as many constraints as possible as in MaxCSP  . Usually, we are interested in assignments that satisfy all mandatory constraints, and enable preferences as well as possible. We present a qualitative formalism that enables to make statements such as "We prefer a solution that violates constraint X and satisfies Y to another one that violates Y but satisfies X". Our contribution consists of two parts. First, we propose constraint relationships that provide a useful and time-saving modeling and elicitation tool to abstractly denote preferences. We illustrate their usage by analyzing scenarios for a typical example of the scheduling problem. Second, we give a transformation into a kweighted CSP that respects the dominance properties we formalized and can be used with off-the-shelf constraint solvers.