CBR Applied to Planning

Abstract

Planning means constructing a course of actions to achieve a specified set of goals, starting from an initial situation. For example, determining a sequence of actions (a plan) for transporting goods from an initial location to some destination is a typical planning problem in the transportation domain. Many planning problems are of practical interest. The classical generative planning process consists mainly of a search through the space of possible operators to solve a given problem. For most practical problems, this search is intractable. Therefore, case-based reason-ing can be a useful idea because it transfers previous solutions rather than searching from scratch. Since the space of possible plans is typically vast, it is extremely unlikely that a case base contains a plan that can be reused without any modifica-tion. Modification has been addressed in Chef (Hammond 1986), one of the first case-based planners. It retrieves cooking recipes and adapts them to the new problem by using domain specific knowledge. As experience has shown, however, this kind of adaptation in realistic domains requires a large amount of very specific domain knowledge and lacks flexibility. Given that classical generative planning may involve a very great search effort and pure case-based planning may encounter insurmountable modifica-tion needs, several researchers have pursued a synergistic approach of gener-ative and case-based planning. In a nutshell, the case-based planner provides plans previously generated for similar situations and the generative planner is used as a source of modification. In this paper, we present four systems that integrate generative and case-based planning: Prodigy/Analogy de-veloped at the CMU, CAPlan/CbC and Paris developed at the University of Kaiserslautern, and Abalone developed at the Universities of Saarbrücken and Edinburgh. These systems are domain-independent case-based planners that accumulate and use planning cases to control the search. In these sys-tems, cases encode knowledge of which operators were used for solving prob-lems and why. In our synergistic systems, the workload imposed on the gen-erative planner depends on the amount of modification that is required to completely adapt a retrieved case. 170 7. Bergmann et al.: CBR Applied to Planning 7.2 Generative Planning Since the presented case-based planners are built on top of generative plan-ners, we briefly introduce generative planning here. Together, the initial state and a set of goals form a planning problem. A planning task consists of finding a plan, which is a sequence of actions that transform the initial state, into a final state in which the goals hold. The plan is a solution of the planning problem. Usually, a state is represented by a finite collection of logical clauses. Actions are described by so-called operators. Following the STRIPS representation of Fikes and Nilsson (1971), operators are data structures that consist of preconditions and effects. A precondition is a conjunctive formula that must hold in a current state for the operator to be applicable. The effects describe how the state changes when the operator is applied. For more detailed introduction to planning; see e.g., Russell and Norvig (1995). 7.2.1 The Logistics Transportation Domain