Planning as satisfiability is one of the most efficient ways to solve classic automated planning problems. In SAT planning, the encoding used to convert the problem to a SAT formula is critical for the performance of the SAT solver. This paper presents a novel bit-encoding that reduces the number of bits required to represent actions in a SAT-based automated planning problem. To obtain such encoding we first build a conflict graph, which represents incompatibilities of pairs of actions, and bitwise encode the subsets of actions determined by a clique partition. This reduces the number of Boolean variables and clauses of the SAT encoding, while preserving the possibility of parallel execution of compatible (non-neighbor) actions. The article also describes an appropriate algorithm for selecting the clique partition for this application and compares the new encodings obtained over some standard planning problems.

1.
Ghallab
,
M.
,
Nau
,
D.
,
Traverso
,
P.
:
Automated Planning: Theory and Practice
,
Morgan Kaufmann Publishers
(
2004
)
2.
Russell
,
S. J.
,
Norvig
,
P
.:
Artificial Intelligence: A Modern Approach
. 3rd Ed.
Prentice Hall
(
2009
)
3.
Bylander
,
T.
,
1994
The computational complexity of propositional STRIPS planning
.
Artificial Intelligence
,
69
(
1-2
). pp.
165
204
4.
McDermott
,
D.
 et al 
1998
,
PDDL -- The Planning Domain Definition Language -- Version 1.2.
5.
Fox
,
M.
, &
Long
,
D.
,
2003
,
PDDL2.1: An extension of PDDL for expressing temporal planning domains
.
Journal of AI Research
,
20
, pp.
61
124
6.
Helmert
,
M.
,
2008
,
Changes in PDDL 3.1.
7.
Linares
,
C.
Jiménez
,
S.
,
García-Olaya
,
A.
, 2015,
The deterministic part of the seventh International Planning Competition
,
Artificial Intelligence
, Volume
223
, June
2015
, pp.
82
119
8.
Kautz
,
H. A.
,
Selman
,
B.
,
1992
,
Planning as Satisfiability (SAT - Plan
).
Proceedings of the 10th European Conference on Artificial Inteligence
,
9
.
9.
Kautz
,
H. A.
,
Selman
,
B.
,
1996
.
Pushing the envelope: Planning, propositional logic, and stochastic search
.
In Proc. 13th Nat. Conf. on AI
, pp.
1194
1201
.
10.
Ernst
,
M.D.
,
Millstein
,
T.D.
&
Weld
,
D.S.
,
1997
.
Automatic SAT-compilation of planning problems
.
IJCAI International Joint Conference on Artificial Intelligence
. pp.
1169
1176
.
11.
Kautz
,
H. A.
, and
Selman
,
B.
1999
.
Unifying sat-based and graph-based planning
.
IJCAI International Joint Conference on Artificial Intelligence
, pp.
318
325
.
12.
Robinson
,
N.
 et al,
2007
.
A Compact and Efficient SAT Encoding for Planning
.
Proceedings of the 18th International Conference on Automated Planning and Scheduling (ICAPS’08)
.
13.
Wehrle
,
M.
&
Rintanen
,
J.
,
2007
.
Planning as Satisfiability with relaxed \exists-step plans
.
Proceedings of 20th Australasian Joint Conference on Artificial Intelligence (AI-07)
,
Gold Coast
,
Australia
. pp.
244
253
.
14.
Helmert
,
M.
,
2009
.
Concise finite-domain representations for PDDL planning tasks
.
Artificial Intelligence
,
173
(
5-6
), pp.
503
535
.
15.
Huang
,
R.
,
Chen
,
Y.
&
Zhang
,
W.
,
2010
.
A Novel Transition Based Encoding Scheme for Planning as Satisfiability
.
AAAI Conference on Artificial Intelligence
, pp.
89
94
.
16.
Rintanen
,
J.
2011
.
Madagascar: efficient planning with sat
.
The 2011 International Planning Competition
, pp.
61
.
17.
Sideris
,
A.
, &
Dimopoulos
,
Y.
2010
,
Constraint Propagation in Propositional Planning
.
ICAPS
, pp.
153
160
.
18.
Jin
,
Y.
,
Hao
.
J.K.
,
Hybrid evolutionary search for the minimum sum coloring problem of graphs
,
Information Sciences, Elsevier
, vol.
352-353
.
2016
, pp.
15
34
.
19.
Wu
,
Q.
,
Hao
,
J.K.
,
Improved Lower Bounds for Sum Coloring via Clique Decomposition
,
2013
, arXiv:1303.6761.
20.
San Segundo
,
P.
,
Nikolaev
,
A.
,
Batsyn
,
M.
,
2015
.
Infra-chromatic bound for exact maximum clique search
,
Computers and Operations Research
, vol.
64
, C. Elsevier, pp.
293
303
.
21.
San Segundo
,
P.
,
Nikolaev
,
A.
,
Batsyn
,
M.
,
Pardalos
,
P. M.
,
2016
.
Improved Infra-Chromatic Bound for Exact Maximum Clique Search
.
Applied Intelligence
, vol.
45
issue
3
pp.
463
487
.
22.
Tapia
,
C.
,
San Segundo
,
P.
, &
Artieda
,
J.
,
2015
.
A PDDL-Bassed Simulation System
.
Proceedings of the IADIS International Conference Intelligent Systems and Agents
.
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