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1392 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 TABLE V. RESULTS IN THE LOGISTICS DOMAIN Helpful implication paths Helpful actions T (s) S L T (s) S L 2-2-2 0.00 16 16 0.00 23 16 2-2-4 0.00 23 26 0.00 34 26 2-3-2 0.01 19 17 0.00 37 17 2-3-3 0.01 36 24 0.01 46 24 2-10-10 0.89 211 83 3.59 324 83 3-2-2 0.01 23 20 0.01 29 20 3-2-4 0.01 29 33 0.02 36 33 3-3-2 0.01 36 28 0.02 55 28 3-3-3 0.01 32 32 0.07 72 34 3-10-10 3.09 427 112 10.95 435 108 4-2-2 0.00 15 19 0.01 19 19 4-2-4 0.01 36 40 0.08 59 40 4-3-2 0.00 24 23 0.01 31 23 4-3-3 0.02 48 37 0.07 70 37 4-10-10 2.51 281 127 11.45 356 121 is a little longer only in two problems. In most of the time, our pruning of helpful implication paths finds exactly the same conformant plan as the situation of helpful actions pruning. All in all, from the experimental results above, we conclude that our pruning technique has the potential to reduce the size of search space and consequently improve the runtime efficiency. In this aspect we consider that our idea is clearly superior to helpful actions technique. V. CONCLUSION In this paper, we addressed the Conformant-FF planner which solves conformant planning problem by belief state space search. The size of search space has been a bottleneck to this method which could be ameliorated by using heuristic function and pruning. Based on our analysis of the implication paths in the relaxed planning heuristic function, we proposed the pruning technique of helpful implications paths to reduce the search space further. We run a number of conformant benchmarks to evaluate our idea and the experimental results indicate that our heuristic technique has two advantages: 1) An action sequence that integrates several helpful action branches together usually cuts down the branching factor of a search state. At the same time, considering helpful implication paths over other branches often finds a better state faster. 2) Executing a helpful implication path can get to a better state a few steps away within one search iteration, which relates with recent tread on obtaining long sequence of actions instead of applying one by one. Thus the evaluations of intermediate states on the helpful implication path are avoided, which leads to a considerable improvement of runtime efficiency. The planner Conformant-FF still has inherent limitations due to its implicit representation of belief states and incomplete information adding to the relaxation. These make the planner provide inaccurate heuristic sometimes and get trouble in situations where an action may contain many conditional effects or takes more complicated forms. It will be significant to propose promising ideas to overcome those disadvantages. In future, we will treat nondeterministic action effects and explore to use a similar pruning idea to solve the more general setting of contingent planning, i.e. to handle partially observable planning problems. We also plan to investigate the search spaces of other non-classical planning settings that can be formalized as search problems, in particular probabilistic planning and temporal planning. ACKNOWLEDGMENT The authors wish to thank Professor Dantong Ouyang for her comments, which was helpful to improve the paper. This work was Supported by the National Natural Science Foundation of China under Grant No. 61272208,61133011,60973089,61003101,61170092; Jilin Province Science and Technology Development Plan under Grant No. 20101501,20100185,201101039; Doctoral Fund of Ministry of Education of China under Grant No.20100061110031; REFERENCES [1] P. Bertoli, M. Pistore, P. Traverso, “Automated Composition of Web Services via Planning in Asynchronous Domains,” Artificial Intelligence, vol. 174, pp. 316-361, 2010, doi: 10.1016/j.artint.2009.12.002. [2] A. E. Gerevini, P. Haslum, D. Long, A. Saetti, Y. Dimopoulos, “Deterministic Planning in the Fifth International Planning Competition: PDDL3 and Experimental Evaluation of the Planners,” Artificial Intelligence, vol. 173, pp. 619-668, 2009, doi:10.1016/j.artint.2008.10.012. [3] A. L. Blum, M. L. Furst, “Fast Planning through Planning Graph Analysis,” Artificial Intelligence, vol. 90, pp. 279-298, 1997, doi: 10.1016/S0004-3702(96)00047-1. [4] D. Bryce, W. Cushing, S. Kambhampati, “State Agnostic Planning Graphs: Deterministic, Non-deterministic, and Probabilistic Planning,” Artificial Intelligence, vol. 175, pp. 848-889, 2011, doi:10.1016/j.artint.2010.12.002. [5] Y. Chen, R. Huang, Z. Xing, W. Zhang, “Long-distance mutual exclusion for planning,” Artificial Intelligence, vol. 173, pp. 365-391, 2009, doi: 10.1016/j.artint.2008.11.004. [6] N. Meuleau, E. Benazera, R. I. Brafman, E. A. Hansen, Mausam, “A Heuristic Search Approach to Planning with Continuous Resources in Stochastic Domains,” Journal of Artificial Intelligence Research, vol. 34, pp. 27-59, 2009, doi: 10.1613/jair.2529. [7] T. De la Rosa, S. Jimenez, R. Fuentetaja, D. Borrajo, “Scaling up Heuristic Planning with Relational Decision Trees,” Journal of Artificial Intelligence Research, vol. 40, pp. 767-813, 2011, doi: 10.1613/jair.3231. [8] J. Hoffmann, B. Nebel, “The FF Planning System: Fast Plan Generation through Heuristic Search,” Journal of Artificial Intelligent Research, vol. 14, pp. 253-302, 2001, doi: 10.1613/jair.855. [9] B. Bonet, “Conformant Plans and Beyond: Principles and Complexity,” Artificial Intelligence, vol. 174, pp. 245-269, 2010, doi: 10.1016/j.artint.2009.11.001. [10] D. Bryce, S. Kambhampati, D. E. Smith, “Planning Graph Heuristics for Belief Space Search,” Journal of Artificial Intelligence Research, vol. 26, pp. 35-99, 2006, doi: 10.1613/jair.1869. © 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1393 [11] A. Albore, M. Ramirez, H. Geffner, “Effective Heuristics and Belief Tracking for Planning with Incomplete Information,” in AAAI, F. Bacchus, C. Domshlak, S. Edelkamp, M. Helmert, Eds. 21st International Conference on Automated Planning and Scheduling, 2011, pp. 2-9. [12] H. Palacios, H. Geffner, “Compiling Uncertainty Away in Conformant Planning Problems with Bounded Width,” Journal of Artificial Intelligence, vol. 35, pp. 623-675, 2009, doi: 10.1613/jair.2708. [13] D. Tran, H. Nguyen, E. Pontelli, T. C. Son, “Improving performance of conformant planners: Static analysis of declarative planning domain specification,” in Springer, Practical Aspects of Declarative Languages, 11th International Symposium, 2009, pp. 239-253, doi: 10.1007/978-3-540-92995-6_17. [14] J. Hoffmann, R. Brafman, “Conformant Planning via Heuristic Forward Search: A New Approach,” Artificial Intelligence, vol. 170, pp. 507-541, 2006, doi: 10.1016/j.artint.2006.01.003. Wei Wei was born Dec. 28, 1984, in Jilin, China. She received the Master degree at College of Computer Science and Technology of Jilin University, China, in 2007. She is a Ph.D candidate at College of Computer Science and Technology of Jilin University. Her main research interests include automated planning and reasoning. Dantong Ouyang was born in 1968, Jilin, China. She received the Ph. D degree at College of Computer Science and Technology of Jilin University, China, in 1998. She is Professor, Ph.D. supervisor, Deputy Dean of College of Computer Science and Technology of Jilin University. Her main field of expertise is model-based diagnosis and automated reasoning. Tingting Zou was born Nov. 24, 1984, in Jilin, China. She received the Master degree at School of Computer Science and Information Technology of North East Normal University, China, in 2007. She is a Ph.D candidate at College of Computer Science and Technology of Jilin University. Her main research interest is description logic. Shuai LU was born Jul. 11, 1981, in Jilin, China. He received the Ph.D degree at College of Computer Science and Technology of Jilin University, China, in 2010. He is a lecturer at College of Computer Science and Technology of Jilin University. Her main research interests include automated planning and reasoning. © 2013 ACADEMY PUBLISHER
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Call for Papers and Special Issues
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(Contents Continued from Back Cover
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