Constraint models for sequential planning

Abstract

Planning and constraint satisfaction are important areas of Artificial Intelligence, but surprisingly constraint satisfaction techniques are not widely applied to planning problems where dedicated solving algorithms dominate. Classical AI planning deals with finding a sequence of actions that transfer the initial state of the world into a desired state. One of the main difficulties of planning is that the size of the solution - the length of the plan - is unknown in advance. On the other hand, a constraint satisfaction problem needs to be fully specified in advance before the constraint model goes to the solver. As Kautz and Selman showed, the problem of shortest-plan planning can be translated to a series of SAT problems, where each SAT instance encodes the problem of finding a plan of a given length. First, we start with finding a plan of length 1 and if it does not exist then we continue with a plan of length 2 etc. until the plan is found. The same approach can be applied when constraint satisfaction is used instead of SAT. There exists a straightforward constraint model of this type but more advanced constraint models exploit the structure of a so called planning graph, namely GP-CSP and CSP-PLAN. There also exist hand-crafted constraint models for particular planning problems such as CPlan. All these models share the logical representation of the problem where Boolean variables describe whether a given proposition holds in a given state and whether a given action is applied to a given state. Constraints are in the form of logical formulae (frequently implications). In our opinion, these models do not exploit fully the potential of constraint satisfaction, namely domain filtering techniques and global constraints. Therefore, we suggested to use multi-valued representation of states based on the state variable formalism SAS∈+∈ that contributes to fewer variables with larger domains where domain filtering pays off. Also, we proposed to encapsulate the sets of logical constraints into combinatorial constraints with an extensionally defined set of admissible tuples. This extended abstract summarizes our recent results in the design of constraint models for planning problems presented in [1,2]. © 2009 Springer Berlin Heidelberg.