Increasing Planning Efficiency and Modelling Expressiveness through the Use of Pairs R.S.Aylett1, J.Soutter2, G.J.Petley1, P.W.H.Chung2, and D. W. Edwards2 1
Centre for Virtual Environments, Salford University, Salford, M5 4WT, UK
[email protected],
[email protected] 2 Chemical Engineering Dept., Loughborough University, Loughborough, UK, LE11 3TU
[email protected], {P.W.H.Chung, d.w.edwards}@lboro.ac.uk
Abstract. We discuss the use of variables during the planning process as means of extending the use of least commitment. We describe how static relationships can be treated as constraints between variables, which we call ‘pairs’, can improve both the efficiency of the planning process and the modelling expressiveness of planning operators.
1 Introduction We discuss what we see as a useful addition to a planner, the facility we call pairs, or a typed constraint between two planning variables. This arose as a result of applying planning to the domain of generating operating procedures for chemical process plant, using Chem. Eng. Planner (CEP) developed in [1] and latterly during the project INTOP [2]. However, while this domain poses specific planning problems [3], we believe pairs are a generic facility, which can be useful in many other planning domains.
2 Variables in Planning A basic facility of planning languages is the use of variables in the specification of planning operators. Intelligence that can be built into planning variables to help improve planning performance by supporting a new constraint between them. In a finite domain, associating a variable with a set of possible values is the same as giving that variable a type. For example, associating variable ?p with the type “person” is the same as restricting ?p to the finite set of people that are known to the planner. While the task of choosing acceptable values for typed non-codesignated variables is NPHard, this task is not performed very often in planning. Most planners are not concerned with the problem of assigning values to variables until the end of planning. At this point, there are usually very few unbounded variables and the task of satisfying these variables is not very difficult. Instead, the planner is simply concerned with whether a variable can bind to a particular value – e.g. whether a goal can be satisfied by an achiever. This simpler task can be completed in polynomial time even if typed non-codesignated variables are used. A relationship between variables may be static or dynamic in a given domain. Dynamic relationships can change over the length of a plan. Static relationships are not affected by any of the operators in the domain and so cannot change over the plan. In this case we can describe them as invariants [4].
3 Implementing Pairs Planning theory has been developed with dynamic predicates in mind. Static relationships are a special case. Complex modal truth criteria are not needed to reason about static relationships. However, most planners treat static relationships in the same way that they treat dynamic relationships. Often this is quite inefficient because plan reasoning carries a lot of baggage with it in order to deal with the difficult cases, though current work on plan compilation is now trying to take advantage of domain analysis to separate out simple from difficult cases [5]. We propose that all static relationships should also be treated as variable constraints. For most planners, this will allow static relationships to be satisfied in polynomial time using constraint satisfaction rather than being solved in exponential time using goal achievement. For super complex planners, that would otherwise satisfy these relationships intelligently in polynomial time, we still get the advantage of avoiding the baggage of goal achievement. In the data structure for a variable, a record is kept of the pairing constraints which apply to that variable. The record includes the list of pairs in the relationship, whether this relationship is positive or negative and which side of the pair should match the variable. Pairing constraints are applied when a variable is created. In planning, there is a risk that making planning operators more general will multiply the search effort required to instantiate them for a domain. Alternatively, if knowledge of the specific plant topology is incorporated into planning operators, they cease to be generic. Thus a mechanism is required which allows knowledge dependent on topology to be represented in generic planning operators. Pairs offer just such a mechanism. From a modelling perspective, the addition of extra expressiveness to a planning system can be a problem if it is difficult to acquire the extra knowledge now required. If the successful use of pairs requires detailed knowledge of the functioning of the planners instead of the domain, then it may make the definition of planning operators more difficult. Each generic pair defined in a planning operator requires the user must supply at least one plant-specific pair instantiating it.
4 Conclusions We have discussed a straightforward extension to the expressiveness of the STRIPS planning language and the ability to set up binary typed constraints between planning variables. In addition we believe that this extension may be generally useful in a planner and may have similar benefits in other planning domains. References 1. Soutter, J. “An Integrated Architecture for Operating Procedure Synthesis.” PhD thesis, Loughborough University, Loughborough, LE11 3TU, UK (1997) 2. Aylett, R.S; Petley, G.J; Chung, P.W.H; Soutter, J. & Rushton, A. “Planning and chemical plant operating procedure synthesis: a case study”. Proceedings, 4th European Conference on Planning, Toulouse, 1997. SpringerVerlag Lecture Notes in Artificial Intelligence (1997) 39-51 3. Aylett, R.S; Soutter, J; Petley, G.J; Chung, P.W.H. & Rushton, A. “AI Planning in a Chemical Plant Domain”. Proceedings, ECAI ’98, (1995) 622-626 4. Long, D. & Fox, M. “Domain-independent planner compilation” Proceedings, 16th Workshop UK Planning and Scheduling SIG, University of Durham, ISSN 1368-5708 (1997) 5. McLuskey, L. & Porteous, J. “Engineering and compiling domain models to promote validity and efficiency”. Artificial Intelligence, 95(1) (1997) 1-65
