Planning as constraint satisfaction: Solving the planning graph by compiling it into CSP

The idea of synthesizing bounded length plans by compiling planning problems into a combinatorial substrate, and solving the resulting encodings has become quite popular in recent years. Most work to-date has however concentrated on compilation to satis ability (SAT) theories and integer linear programming (ILP). In this paper we will show that CSP is a better substrate for the compilation approach, compared to both SAT and ILP. We describe GP-CSP, a system that does planning by automatically converting Graphplan's planning graph into a CSP encoding and solving it using standard CSP solvers. Our comprehensive empirical evaluation of GP-CSP demonstrates that it is superior to both the Blackbox system, which compiles planning graphs into SAT encodings, and an ILP-based planner in a wide range of planning domains. Our results show that CSP encodings outperform SAT encodings in terms of both space and time requirements in various problems. The space reduction is particularly important as it makes GP-CSP less susceptible to the memory blow-up associated with SAT compilation methods. The paper also discusses various techniques in setting up the CSP encodings, planning speci c improvements to CSP solvers, and strategies for variable and value selection heuristics for solving the CSP encodings of di erent types of planning problems. 1 We thank Biplav Srivastava for explaining the inner workings of van Beek and Chen's constraint solver, and Terry Zimmerman for many useful comments on the earlier drafts of this paper. We also thank Peter van Beek for putting his CSP library in the public domain, and patiently answering our questions. This research is supported in part by NSF young investigator award (NYI) IRI-9457634, ARPA/Rome Laboratory planning initiative grant F30602-95-C-0247, AFOSR grant F20602-981-0182 and NSF grant IRI-9801676. The source code of the planner is available for downloading at http://rakaposhi.eas.asu.edu/gp-csp.html Preprint submitted to Elsevier Preprint 6 June 2001