NASA Technical Reports Server (NTRS) 20060015671: A Constraint-Based Planner for Data Production

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A Constraint-Based Planner for Data Production
Wanlin Pang' Keith Golden
NASA Ames Research Center
Moffett Field, CA 94035
{ wpang, kgo1den)Qemail. arc.nasa.g ov
Abstract We take the approach, like many other researchers
[van Beek & Chen, 1999; Lopez & Bacchus, 2003;
This paper presents a graph-based backtrack- Do & Kambhampati, 2001; Smith, Frank, & Jbnsson,
ing algorithm designed to support constraint- 20001, of translating the planning problem into a con-
based planning in data production domains. straint satisfaction problem (CSP). However, since data
This algorithm performs backtracking at two processing domains are substantially different from other
nested levels: the outer-b acktracking follow- planning domains that have been explored, our ap-
ing the structure of the planning graph to se- proach to translating planning problems to CSPs dif-
lect planner subgoals and actions to achieve fers as well. For example, [Do & Karrbhampati, 20011
them and the inner-backtracking inside a sub- use variables to represent goals and domains to repre-
problem associated with a selected action to sent available planner actions achieving the goals. Con-
find action parameter values. We show this al- straints are used to encode mutual exclusion relations.
gorithm works well in a planner applied to au- While this is an effective approach for propositional plan-
tomating data production in an ecological fore- ning problems, we also need variables to represent ob-
casting system. We also discuss how the idea of jects and action parameters, and constraints to rep-
multi-level backtracking may improve efficiency resent relations among them. Thus, our encoding is
of solving semi-structured constraint problems. somewhat more complex, and the CSPs resulting from
our encoding are hard to solve by the search methods
employed in other planners [van Beek & Chen, 1999;
1 Introduction Lopez & Bacchus, 2003; Do & Kambhampati, 2001;
Smith, Frank, & J6nsson, 20001.
Earth-science data processing (ESDP) at NASA is a data
production problem of transforming low-level observa- We have developed a constraint-based planner, called
tions of the Earth system, such as remote sensing data, DOPPLER, for data processing planner. From a data
into high-level observations or predictions, such as crop processing task, the planner constructs a Zified planning
failure or high fire risk. Given the large number of so- graph, from which it derives a CSP representation of the
cially and economically important variables that can be planning problem, and then searches the CSP for a so-
derived from the data, the complexity of the data pro- lution. Whereas a conventional planning graph [Blum &
cessing needed to derive them Ayd the maay teraby+es Furst, 19971 is a grounded representation, consisting of
of data that must be processed each day, there are great ground actions and propositions, a lifted planning graph
challenges and opportunities in processing the data in a contains variables. This is not only a much more concise
timely manner, and a need for more effective automation. representation than an ordinary planning graph, but it
Our approach to providing this automation is to cast it also is the only practical way that we know to repre-
as a planing problem: we represent data-processing op- sent potentially infinite sets of ground actions. Even
erations as planner actions and desired data products as though the CSP derived from a lifted planning graph is
planner goals, and use a planner to generate data-flow difficult to solve by many existing CSP search methods
programs that produce the requested data products. such as chronological backtracking (BT), forward check-
---
Many ofthe recent advances In pianning, such as state- ":'bn m (,aK 'vP,) nVrI mYYnYFIl;lrVtY-A u;^r-o.,rYt"oYAI h1-P-.r Ljiimpicg (QJ)it, h a
certain structural properties inherited from the planning
based heuristic search or reduction to satisfiability prob-
lems, are not readily adapted to ESDP problems, due graph. We have developed a search algorithm based the
structure of the planning graph to improve efficiency of
to some of its particular features, such as incomplete in-
solving the CSP.
formation, large and dynamic universes, complex data
types, and complex constraints, just to name a few. In this paper, we report our work on applying
DOPPLER to automating data production problem. We
'QSS Group Inc discuss how the data production problem is cast as a
planning problem which, in turn, is translated into a CY, does not support p. Initial graph construction ter-
CSP, and how the planning graph is used to improve minates when all preconditions have support or (more
backtracking in solving the CSP. Section 2 discusses data likely) a potential loop is detected.
processing as a planning task and our planning approach.
Seaion 3 describes a graph-based CSP search algorithm 2.2 horn Planning to Constraints
that outperforms the standard search on problems with A constraint satisfaction problem (CSP) representing the
certain structural properties. Section 4 describes the search space is incrementally built during the planning
graph-based planning search algorithm that is the main graph construction. The CSP contains: 1) boolean vari-
contribution of this paper. And Section 5 discusses re- ables for all arcs, nodes and conditions; 2) variables for
lated and future work. all parameters, input and output variables and function
values; 3) for every condition in the graph, a constraint
2 Planning for Data Processing specifying when that condition holds (for conditions sup-
ported by arcs, this is just the XOR of the arc variables);
Data processing is a task of transforming data products
into other data products. A common sequence of data 4) for conjunctive and disjunctive expressions, the con-
straint is the respective conjunction or disjunction of
processing step is: 1) gather data from multiple sources;
2) convert the data into a common representation; 3) the boolean variables corresponding to appropriate sub-
expressions; 5) for every arc in the graph, constraints
combine the data and perform other transformations; 4)
specifying the conditions under which the supported flu-
feed the data into science models and then run the mod-
els; 5) convert the output of the model into some form ents will be achieved (i.e., yp” 3 p, where rp” is the
suitable for visualization; 6) repeat some or all these precondition of a: needed to achieve p) ; 6) user-specified
steps depending on the requirements. To formalize data constraints; and 7) constraints representing structured
processing as a planning problem, we represent data- objects.
processing operations as planner actions, desired .data
2.3 Planning Search
products as planner goals, and available data sources as
part of the initial state. Guided by heuristic distance estimates extracted from
Planning in DOPPLER is a two-stage process. The the planning graph, the planner first selects planner sub-
first sta e consists of a Graphplan-style reachability goals to achieve and actions to achieve them, which form
analysisof131urn& first, 19971 to derive heuristic distance a lifted plan. After the subgoal and action selection,
estimates for the second stage, a constraint-based search. the the CSP solver finds values for variables representing
These stages are not entirely separate, however; con- planner action parameters. This is necessary to make ac-
straint propagation occurs in both graph-construction tions executable. During the search, propagation is per-
and constraint search stages, and the graph is refined formed whenever a value is assigned to a variable. The
during the constraint-search phase. search is an iterative process involving possible back-
tracks; that is, if there are no valid parameters for a cho-
2.1 Lifted Planning Graphs sen action, the planner has to search for another plan; if
From the planning problem specification, the planner it is impossible to extract a plan from the current plan-
incrementally constructs a directed graph, similar to a ning graph, the planning graph has to be extended, or
planning graph [Blum & first, 19971, but using a lifted the planner admits the failure of finding a plan.
representation (Le., containing variables). Arcs in the
graph are analogous to causal links [Penberthy & Weld, 2.4 A Simplified Example
19921. A causal link is triple (CY,, p,c yp), recording the .A typical data processing task consists of gathering data
decision to use action cy, to support precondition p of files, transforming them, feeding them into a science
action cyp. However? instead of an arc to record a com- model (e.g., a fire-risk model), and producing a find data
mitment of support, we use it to indicate the possibility file so that a decision maker can assess the fire risk of a
that, cy, supports p. The lifted graph contains multiple particular region. For simplicity, we ignore much of the
ways of supporting p; the choice of the actual supporter complexity of the data processing domain, and focus on
is left to constraint search. We add an extra term to one sub-problem: spatial aggregation. So a simplified
the arc for bookkeeping purposes - the condition 7s; task becomes to take some regions from thousands of
needed in order for as to achieve p. A link then becomes available regions and compose them to create a mosaic
(as7 7;s ,P , a,). that covers a specified region.
Given an unsupported precondition p of action CY^, our Specifically, a region is a pair of points (dI,T) where
is to idelltil’y di the actions that couid support
CII_L-L~ ~Lb,rd bqk ui is the upper-ieft corner and ir the lower-right corner.
p. Because the universe is large and dynamic, iaenti- A point is a pair of coordinates (z,y ). Normally z and y
fying all possible ground actions that could support p would be longitude and latitude, but as’ a further simpli-
would be impractical, so instead we use a lifted repre- fication, we will assume both x and y are non-negative
sentation, identifying all action schenias that could pro- integers. Further, we assume there are only 3 actions
vide support. Given an action schema CY, we determine the planner may take, compose two regions horizontally
whether it supports p by regressang p through CY,.T he (comp2h) and vertically (co~np&v)a,n d compose 4 re-
result of regression is the formula rp*.I f rFs =It,h en gions (compd) as in Figure 1.
assignment to a small number of variables in a very big
constraint problem; whereas finding values for action pa-
rameters is a difficult CSP search problem. To address
the issue, we developed a graph-based search algorithm,
which is discussed in the rest of the paper.
3 Graph-Based Backtracking
A constraint satisfaction problem (CSP) consists of vari-
ables, domains that contain possible values the variables
may take, and constraints that limit the values the vari-
Figure 1: The planner actions able can take simultaneously. In finite-domain CSPs
(that is, every variable has a finite domain), a constraint
over a variable subset can be represented extensionally
as a subset of the Cartesian product of the domains of
variables in the constraint. However, in the data pro-
cessing domain we are interested in, the CSPs obtained
from the planning problem contain variables that usually
have infinite domains [Golden & Frank, 20021. An infi-
nite domain is represented as an an interval (for numeric
types), regular expression (for string types) [Golden &
Pang, 20031, or symbolic set (for object types). Because
of infinite domains, the constraints are not represented
extensionally as relations, but as procedures [Jbnsson,
19961. A procedural constraint consists of a set of vari-
ables (the scope) and a procedure (i.e., an execute0
method) that can be executed to enforce the constraint
by eliminating inconsistent values from the domains of
variables in the scope. If execution of a constraint results
in an empty variable domain, execute0 returns failure,
indicating the violation of the constraint.
Solving a CSP, in general, is NP-complete. How-
ever, many practical problems possess certain proper-
ties that allow tractable solutions. A class of structure-
based CSP-solving algorithms, called decomposition al-
gorithms, has been developed [Gottlob, 2000; Gyssens,
Figure 2: A compact search space: objects in a dot-
Jeavons, & Cohen, 1994; Dechter, 1990; Dechter & Pearl,
ted rectangles are inputs to an action; an object divided
19891. Decomposition algorithms attempt to find solu-
by dashed lines is a composed object; single objects are
tions by decomposing a CSP into several simply con-
amilable in the initial state.
nected sils-CSPs based oii the under!ying censtr~int
graph and then solving them separately. Once a CSP
A problem instance we consider here consists of some is decomposed into a set of sub-CSPs, all solutions for
+
unit squares; that is, squares of (ul,I T) where u1.x 1 = each sub-CSP aze found. Then a new CSP is formed
IT.X and uZ.ij+ 1 = ~T.Y. For exLxple, ((G,!l),(1,2), or where the original variable set in each sub-CSP is taken
(2,3), (3,4)). The goal is to compose a region covering as a singleton variable. Usually the technique aims at
((0,o >,( 3,2)). decomposing a CSP into sub-CSPs such that the num-
The planning graph created by the planner is in ber of variables in the largest sub-CSP is minimal and
Figure 2. At a high level, the planner finds a lifted plan the newly formed CSP has a tree-structured constraint
by selecting subgoals and actions, shown in Figure 2 as a graph. In this way, the time and space complexity of
path from the initial state to the goal with dark arrows. finding ail soiutions for each sub-CSP is bouxded, and
This plan may not be executable because actions are not the newly formed CSP has backtrack-free solutions. The
grounded. For example, the action comp.4 is selected complexity of a decomposition algorithm is exponential
because it has support from the initiai state and ic in the size of the largest SU'U-CST.T lie class sf CSPs ih&
supports the action compZh, but its parameters are not can be decomposed into sub-CSPs such that their sizes
determined yet. The constraint solver then finds values are bounded by a fixed number IC is tractable and can be
for action parameters, which is shown in Figure 2 as solved by decomposition in polynomial time. This is the
groups of shaded rectangles. strength of CSP decomposition. A fatal weakness of CSP
decomposition, however, is that the decomposition is not
It turns out that finding a lifted plan is a relatively applicable to solving a CSP that is not decomposable,
easy task because it is a problem of finding a consistent that is, its decomposition is itself. A secondary draw-
back of CSP decomposition is that, even if the CSP is optimizing the constraint problem in terms of its size
decomposable, finding all solutions for all the sub-CSPs and structural properties.
is unnecessary and inefficient. As an alternative, we decompose the CSP into sub-
Graph based backtracking (GBT) [Pang L'A Goodwin, CsPs based on the planning graph instead of the con-
20031 was developed to address these issues. The idea of straint graph, each sub-CSP containing a group of vari-
the GBT algorithm is to decompose the constraint graph ables that are relevant to a node in the planning graph
into a tree of subgraphs (for example, non-separable corn- representing a lifted action. In most of the cases, the
ponents), and then search for a consistent assignment sub-CSPs may not form a tree, which makes the tradi-
to variables involved in a subgraph and extend it to its tional csp decomposition methods inapplicable. How-
children. At a subgraph where no consistent assignment ever, the GBT algorithm can be adapted easily: the
can be found, GBT backtracks to the parent, reinstan- outer-backtrackirig is performed to select the planner
tiates variables in that subgraph, and starts from there. subgods and actions, the inner-backtracking to find val-
Within a subgraph, GBT searches for a consistent as- ues for action parameters by solving the associated sub-
signment to the variables in the subgraph in a way sim- CSP. Even though the sub-CSPs do not form a tree, it is
ilar to standard backtracking, which may involve back- not a requirement for the graph based search approach
tracks but limited to within the subgraph. The algo- but a preferred property.
rithm stops when a solution is found or when it proves
that no solution exists. The detailed GBT algorithm 4.1 Algorithms
can be found in [Pang & Goodwin, 20031. h a simple
The graPh-based Planning search algorithm Outlined
way, the GBT algorithm performs backtracking at two
nested levels: the inner-backtracking inside a subgraph in 1 and 2. At a high level, the planner per-
forms Best-FirSt 'earch to 'elect the Planner subgoals
and outer-backtracking following the subgraph tree ob-
tained from the graph decomposition. and actions achieving the subgoals. Once an action is
csp chosen for a subgoal, it collects a subset of variables rel-
The GBT algorithm shares the merits of decem-
evant to the action and calls a constraint solver SBT to
position and OvercOmeSi t. webeAs s&hs ethes de.-
csp find a consistent assignment for the collected variables.
composition method, GBT decomposes the given
into sub-CSPs based on the underlying constraint graph SBT performs a local backtracking to search for a so-
lution to the sub-problem that is also consistent with
decomposition^ Unlike the decomposition how-
solutions to the sub-problems preceding the current one.
ever, GBT only tries to find one solution for a chosen
If SBT fails, the high-level search takes control, tries
sub-^^^, which is not separated from other sub-CSPs,
another action for the current selected subgoal or back-
and then tries to extend it to other sub-CSPs, If ,.he un-
derlying constraint graph can be decomposed, the corn- tracks to a previously subgoal. At the Of
selection of subgoals and actions, SBT is called again
plexity of GBT algorithm is bounded by the size of the
to find values for certain variables that may have been
largest sub-CSP; in the that the constraint graph
missed during the previous search.
is not decomposable, GBT degenerates to a standard
backtracking. Both algorithms interleave search with propagation,
The GBT algorithm, as with other decompos~t~oanl- which is a process of continuously executing constraints
gorithms, depends on the underlying constraint graph as long as variable domains change. The propagation
representation and its decomposition. For details on performs a partial generalized arc-consistency (GAC)l
graph representation and decomposition see [Gottlob, [Bessie= 8~ Ch, 1997; Katsirelos & Bacchus, 20011, and
2oool. F~~t he planning problem at hand, we adapt GBT it is an essential part of solving the constraint problem,
to utilize the planning graph structure for search heuris- not only because it reduces the search space by eliminat-
tics. ing some inconsistent values, but also because the con-
straint problem at hand contains variables with infinite
4 Graph-Based Planning Search domains which cannot be enumerated by search. If exe-
cuting a constraint fails, propagate 0 returns failure,
Intuitively, the CSP derived from the planning graph is which implies that the current value assignment to vari-
well structured due to the fact: i) the variables relevant ables is inconsistent. Because the propagation is not lim-
to each planner action along with the subgoal it sup- ited to a sub-problem even if it is invoked by the SBT
ports and the conditions enabling the action are tightly solving the sub-problem, it ensures the solutions to local
connected; ii) the constraints between variables of dif- sub-problems are globally consistent.
ferent actions are relatively sparse. Ideally, the CSP can Comparing to the GBT algorithm in Section 3, the
be decomposed based on the constraint graph decom- high-level BFS corresponds to the outer-backtracking;
position into sub-CSPs, each corresponding to a group it backtracks when the selected best subgoal or action
of variables associated with a planner action. However, achieving a subgoal based on the planning heuristics is
by experiments with a few graph decomposition meth-
not feasible; that is, either the immediate propagation
ods, we haven't been able to decompose the constraint
graph into a tree of subgraphs in a satisfactory way. It 'kve call it partial GAC for two reasons: 1) not every con-
is still an on-going research effort to evaluate the process straint procedure enforces the GAC; and 2) not every con-
of translating the planning problem to a CSP aiming at straint is executed in the propagation.
fails, or the subsequent SBT search fails. The lower-
level SBT is standard backtracking plus propagation for
solving a specified sub-problem. Whereas the GBT al-
gorithm and other graph-based decomposition methods
Algorithm 1 GBFS require that the CSPs to be solved can be decomposed
Given a set of subgoals in the lifted planning graph G into tree-structured sub-problems, the multi-level back-
and a family of action sets A = {A(g)lg E G}, each A(g) tracking algorithm presented here follows the structures
is a set of actions achieving subgoal g. Let G’ G be a of variable clusters, which may or may not form a tree,
set of active subgoals to be achieved (initially, the goals without an explicit decomposition. Such a multi-level
in the goal state), P = (X,D ,C ) the CSP derived from backtracking strategy is particularly well-suited for semi-
the lifted planning graph, and X’a subset of searchable structured problems; though, more empirical studies are
variables: needed.
GBFS(G, A,P ,G ’)
4.2 The Example Again
1. while (G’ # 0) do
We take a look at the simplified example again and de-
(a) g t a goal removed from G‘ scribe how the graph-based search algorithm works.
(b) for each action a E A(g) The task is to make a region covering ((O,O), (3,2)),
i. if (propagate(P, {a}) returns failure) which consists of regions B1,Bz ,. .., Bs,a ll available from
continue for the next action the initial state. At the beginning of the planning
ii. X’ t variables relevant to u search, the active goal set G’ contains only the top-
iii. while (SBT(P,X’) returns success) do level goal of making ((0,0 ), (3,2)).I gnoring the search
A. G, t conditions of a heuristics, we assume that the planner chooses the action
B. add G, to G’ and sort G‘ compth, which composes two regions horizontally. These
two regions are the parameters of the action, which are
C. if (GBFS(G, A, P,G ’)r eturns success)
not determined initially. The inner-backtracking solver
return SBT(P, X)
SBT is created with these parameters and it is called
iv. continue for the next action
to find values for them. It quickly finds two regions,
(c) return failure a)),
((O,O), (2,2)) and ((2,0),( 3, for output parameters
2. return success of action compth, and it also remembers its current sta-
tus so that when it backtracks, it can find the next so-
lution (the regions ((0,0),(1,2)) and ((1,0),( 3,2)),s ee
Figure 2) . The planner adds two subgoals, constructing
the regions ((O,O), (2,2))a nd ((2,0),( 3,2)),t o the active
goals, and then continues recursively with the next best
goal, which is one of the newly added two subgoals.
4.3 TOPS Application
M7e have applied the OoPPLEE planner to the Ter-
Algorithm 2 SBT
restrial Observation and Prediction System (TOPS,
, Given a CSP P = (X. D,C ), and let X’C X be a set of http://ecocast.arc.nasa.gov) [Nemani et al., 20021, an
searchable variables: ecological forecasting system that assimilates data from
SBT(P,X ‘) Earth-orbiting satellites and ground weather stations to
model and forecast conditions on the surface, such as soil
1. if (X’ = 0) return success moisture, vegetation growth and plant stress. The plan-
2. select 5%E X ner identifies the appropriate input files and sequences
of operations needed to satisfy a data request, executes
3. for each value v E d(xl)
those operations on a remote TOPS server, and displays
(a) ztt - v the results, quickly and reliably.
(b) if (propagate (P,C x,I> returns success) We have developed A TOPS planning domain, which
i. update X‘ specifies the data operations and data object types
ii. if (sBT(PX, ’j returns success) in TGPS. Daca operar;ions include I uririirlg siliidation-
return success based models, reprojection, scaling, and construction of
color composites, mosaics, and animations, etc. For ob-
4. return failure
ject types in TOPS, Figure 3 shows the input and output
objects to a TOPS model. To create a planning problem
instance (i.e., a TOPS task), the user needs only to spec-
ify the planner goal, which is a description of a desired
data product. A sample TOPS task would be something
c
for human interaction to be practical. Pegasus [Blythe
et al., 20031 is a workflow planning system for compu-
tation grids, a problem similar to ours, though their fo-
cus is on mapping pre-specified workflows onto a specific
grid environment, whereas our focus is on generating the
workflows.
References
[Bessiere & Ch, 19971 Bessiere, C., and Ch, J. 1997.
Arc-consistency for general constraint networks: Pre-
liminary results. In Proceedrnys of IJCAI-97, 398-404.
lBlum & Furst. 19971 Blum. A., and Furst, M. 1997.
, ,
Fast planning through planning graph analysis. AIJ
90(1-2):281-300.
Figure 3: Structured inputs and outputs to a TOPS
[Blythe et al., 20031 Blythe, J.; Deelman, E.; Gil, Y.;
model
Kesselman, C.; Agarwal, A,; Mehta, G.; and Vahi,
K. 2003. The role of planning in grid computing.
like “display Gross Primary Production (GPP) for con- In Proc. 13th Intl. Conf. on Automated Planning and
tinental US on May 5th, 2004”. Scheduling (ICAP S).
The motivation of developing the graph based plan-
[Chien et al., 19971 Chien, S.; Fisher, F.; LO, E.;
ning search is to speed up the search process so that the
Mortensen, H.; and Greeley, R. 1997. Using artificial
planner can produce the requested data product within
intelligence planning to automate science data analy-
a time limit acceptable to the user. Even though it is dif-
sis for large image database. In Proc. 1997 Conference
ficult for us to compare DOPPLER planner with publicly
on Knowledge Discovery and Data Mining.
available planners, which cannot handle data-processing
problem, we have compared DOPPLER to itself by turn- [Dechter & Pearl, 19891 Dechter, R., and Pearl, J. 1989.
ing on or off the inner-backtracking SBT. Without inner- Tree clustering for constraint networks. Artificial In-
backtracking SBT, for most of the TOPS tasks, it usu- telligence 38:353-366.
ally takes a few tries with different variable ordering [Dechter, 19901 Dechter, R.. 1990. Enhancement, schemes
hwrist>icst o solve a problem; sometimes it fails within for constraint processing: backjumping, learning, and
a specified time limit (e.g., 5 minutes). With inner- cutset, decomposition. Artaficial Intelligence 41:273-
backtracking SBT turned on, the same TOPS tasks can 312.
be solved quickly without trying the additional variable
[Do & Kambhampati, 2001] Do, M., and Kambham-
ordering heuristics. However, we are currently conduct-
pati, S. 2001. Planning as constraint satisfaction:
ing experiments on more TOPS tasks and artificial prob-
Solving the planning graph by compiling it into CSP.
lems like the one in Section 2.4.
Artificial Intelligence 132:1 51 -1 82.
5 Conclusions [Golden & Frank, 20021 Golden, K., and Frank, J. 2002.
Universal quantification in a constraint-based planner.
We have discussed the data production problem and how In AIPSO2.
we reduce it to planning and solve the planning problem
[Golden & Pang, 20031 Golden, K., and Pang, W. 2003.
with a constraint search and propagation approach. A
Constraint reasoning over strings. In Proceedings of
key element of our approach is the lifted planning graph,
which we use as a basis for our CSP encoding, and use the 9th International Conference on the Principles and
further to guide the planning and constraint search. The Practices of Constraint Programming.
graph-based backtracking algorithm presented here has [Gottlob, 20001 Gottlob, G. 2000. A comparison of
proved to be effective in our planner; it is also a gen- structural CSP decomposition methods. Artificial In-
eral CSP solver that we intend to evaluate further on telligence 124:243-282.
structured or semi-structured problems and to compare
[Gyssens, Jeavons, & Cohen, 19941 Gyssens, M.; Jeav-
to other search and decomposition methods. ons, P.; and Cohen, D. 1994. Decomposing constraint
There has been little work in planner-based automa- satisfaction problems using database techniques. Ar-
-
tion of data production. ‘lwo notable exceptions are tificial Intelligence 66:5 7-89.
Collage [Lansky, 19981 and MVP [Chien et al., 19971.
[J6nsson, 199G] J6nsson, A. 1996. Procedural Reasoning
Both of these planners were designed to provide assis-
in Constraint Satisfaction. P1i.D. Dissertation, Star-
tance with data analysis tasks, in which a human was in
ford University.
the loop, directing the planner. In contrast, our planner
does not require human interaction, which is appropriate IKatsirelos & Bacchus, 20011 Katsirelos, G., and Bac-
for domains like TOPS, in which data production must chus, F. 2001. GAC on conjiirictions of cowtrairits.
be entirely automated; there is simply too much data In CP-2001.
c
[Lansky, 19981 Lansky, A. 1998. Localized planning with
action-based constraints. Artificial Intelligence 98( 1-
2) A9-136.
[Lopez & Bacchus, 20031 Lopez, A., and Bacchus, F.
2003. Generalizing graphplan by formulating planning
as a CSP. In Proceedings of IJCAI-2003.
[Nemani et al., 20021 Nemani, R.; Votava, P.; Roads, J.;
White, M.; Thornton, P.; and Coughlan, J. 2002.
Terrestrial observation and predition system: Integra-
tion of satellite and surface weather observations with
ecosystem models. In Proceedings of the 2002 Inter-
national Geoscience and Remote Sensing Symposium
(IGARSS).
[Pang & Goodwin, 20031 Pang, W., and Goodwin, S. D.
2003. A graph based backtracking algorithm for gen-
eral CSPs. In Proceedings of 6th Canadian Conference
on Artificial Intelligence (CAI-2003), 114-128.
[Penberthy & Weld, 19921 Penberthy, J., and Weld, D.
1992. UCPOP: -4s ound, complete, partial order plan-
ner for ADL. In Proc. 3rd Int. Conf. Principles of
Knowledge Representation and Reasoning, 103-114.
[Smith, Frmk, & JBnsson, 20001 Smith, D.; Frank, J.;
and Jonssoq -4.2 000. Bridging the gap between plan-
ning and scheduling. Knowledge Engineering Review
15( 1): 61-94.
[van Beek & Chen, 19991 van Beek, P., and Chen, X.
1999. CPlan: A constraint programming approach
to planning. In Proceedings of AAAI-99.