Reasoning with Comparative Preferences in Combinatorial Problems

Many decision making problems involve choosing a preferred option amongst a large number of alternatives, which are structured in terms of a number of variables, with each alternative associating a value with each variable. The set of possible alternatives may be defined implicitly, as the (typically exponentially large) set of solutions of a Constraint Satisfaction Problem; or explicitly as a (still often very large) database of possibilities. The preference relation, specifying which alternatives are preferred to which, is over a very large set, so we cannot afford to explicitly represent it, but need a compact implicit representation. In the last few years there has been considerable interest in formalisms, such as CP-nets, for reasoning with comparative preferences in combinatorial problems. A comparative preference statement implies that certain alternatives are considered better than others. For example, the statement that I prefer blue cars to red cars might be interpreted as a preference for any blue car over a car which is similar except for being red; it is therefore a compact representation of a very large number of comparisons between alternatives. Important computational problems for comparative preferences include: finding an optimal complete assignment, finding an optimal solution of a constraint satisfaction problem, and inferring that one solution is preferred to another. In this talk I will discuss various kinds of comparative preference statement one may wish to represent, different semantics for such statements, and computational reasoning approaches.