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Integrating Planning and Scheduling through Intensity Adaptation
Karen L. Myers1, Stephen F. Smith2,
David W. Hildum2, Peter A. Jarvis1, Raymond de Lacaze1
1 Artificial Intelligence Center
SRI International
Ravenswood Avenue
Menlo Park, California 94025
{myers,jarvis,delacaze}@ai.sri.com
2 The Robotics Institute
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
{sfs,hildum}@cs.cmu.edu
Abstract
We describe an incremental and adaptive approach to
integrating hierarchical task network planning and
constraint-based scheduling. The approach is grounded in
the concept of approximating the ‘resource intensity’ of
planning options. A given planning problem is decomposed
into a sequence of (not necessarily independent) subtasks,
which are planned and then scheduled in turn. During
planning, different operators are rated according to a
heuristic estimate of their expected resource requirements.
Options are selected that best match a computed ‘target
intensity’ for planning. Feedback from the scheduler is used
to adapt the target intensity after completion of each
subplan, thus guiding the planner towards solutions that are
tuned to resource availability. Experimental results from an
air operations domain validate the effectiveness of the
approach relative to typical “waterfall” models of
planner/scheduler integration.
Introduction
Goal-oriented activity in complex domains typically
requires a combination of planning and scheduling. A
manufacturing facility must develop process plans for
ordered parts that can be cost-effectively integrated with
current production operations. Military planners must
select courses of actions that achieve strategic objectives,
while making the most of available assets. Space
observatories must allocate viewing instruments to
maximize scientific return under a large and diverse set of
causal restrictions and dependencies. Though conceptually
decomposable, planning and scheduling processes in such
domains can be and often are highly interdependent.
Different planning options for achieving a given objective
can make quite different demands on system resources;
correspondingly, current resource commitments and
availability will impact the feasibility or desirability of
various planning options. The dynamics of the operating
environment complicate matters further, requiring efficient
response to continual unexpected changes to system
objectives and resource availability.
The effectiveness of goal-oriented activity is ultimately
tied to an ability to keep pace with evolving circumstances,
and one recognized obstacle in practice is poor integration
of “planning” and “scheduling” processes. In
manufacturing organizations, this problem has been
characterized as the “wall between engineering and
manufacturing”. Similar sorts of barriers can be found in
other large-scale enterprises. The crux of the problem is
lack of communication. Plans are developed with no
visibility of resource availability and operational status,
and likewise, schedules are developed and managed
without knowledge of objectives and dependencies.
Without such information exchange, planning and
scheduling processes are forced to each proceed in an
uninformed and inherently inefficient manner. In the
simplest case, the result is an iterative waterfall model of
integration, where planning and scheduling are performed
in sequential lockstep fashion and any problem
encountered during scheduling simply triggers the
generation of a new plan.
In this paper, we present a method for improving the
overall planning and scheduling process through a tighter
integration of these constituent activities. By planning, we
refer generally to the process of deciding what to do; i.e.,
the process of transforming strategic objectives into
executable activity networks. We use the term scheduling
to refer alternatively to the process of deciding when and
how; i.e., which resources to use to execute various
activities and over what time frames. Traditionally, AI
research has viewed planning and scheduling as distinct
activities, and different solution techniques and
technologies have emerged for each. Relatively few
attempts have been made to combine respective
technologies into larger integrated frameworks.
We take as our starting point previously developed
technologies for hierarchical task network (HTN) planning
and constraint-based scheduling. We describe and evaluate
an approach to their integration based on the idea of
approximating the resource requirements (called resource
intensity) of different planning options, and incrementally
exchanging and exploiting information about likely
resource shortfalls (and excesses) to settle on options that
best utilize available resources. Finally, we present
experimental results that compare an implementation of the
method to an iterative waterfall model of integration within
the air operations domain. These results show that the
intensity-based approach provides plans of comparable
quality for greatly reduced computation time.
Technology Foundations
Planning The CPEF system provides the planning
component for our work (Myers 98). CPEF embodies a
philosophy of plans as dynamic, open-ended artifacts that
evolve in response to a continuously changing
environment. CPEF provides a range of operations
required for continuous plan management, including plan
generation, plan execution, monitoring, and plan repair.
Plan generation within CPEF is based on the CHIP system
– an HTN planner derived from SIPE-2 (Wilkins 88) – and
the Advisable Planner (Myers 96). The Advisable Planner
provides an advice-taking layer on top of CHIP that
enables a user to guide and direct the plan generation
toward solutions that match his or her individual
preferences.
Scheduling ACS, a constraint-based scheduler, provides
the base scheduling capability. ACS is an air operations
scheduler constructed using OZONE (Smith, Lassila and
Becker 96), a customizable constraint-based modeling and
search framework for developing incremental scheduling
tools. OZONE consolidates the results of application
development experiences in a range of complex domains,
including one recently deployed system for day-to-day
management of airlift resources at the USAF Air Mobility
Command (AMC) (Becker and Smith 00).
The ACS scheduler adapts techniques underlying the
AMC application to the air operations domain. ACS can
be used to generate, incrementally extend and revise
assignments of aircraft and munitions to input target
demands over time, taking into account priorities, desired
levels of damage, time-on-target (TOT) windows, temporal
sequencing constraints, feasible resource alternatives, and
aircraft/munitions positioning and availability constraints.
Air Operations Domain Characteristics
Applications that require integrated planning and
scheduling will have individual characteristics that dictate
the relative importance of each capability. Much of the
work to date on combining AI planning and scheduling has
focused on resource-driven domains (such as satellite
observation scheduling (Muscettola et al 92)), which
emphasize optimization of resource usage in satisfying a
pool of tasks. In contrast, the air operations domain has a
more goal-driven flavor: while effective resource usage is
important, the key motivation is to identify and schedule
actions that will ensure attainment of stated objectives.
Objectives within the air operations domain reduce to
goals of neutralizing enemy capabilities (e.g., anti-aircraft
capability, electricity production, communications)
modeled as hierarchical networks that ground out at the
level of specific targets. We provide several strategies for
attacking networks, ranging from attacking all components
in a network, to attacking a coherent subset, or an isolated
node (Lee 98).
Resources are assigned to support prosecution of
individual targets. For a given target type, several
aircraft/munitions combinations might be viable, although
the numbers required to achieve the desired effect may
vary with each choice. Capacities of different resources are
positioned at various locations. The set of resources
assigned to fly against a target can vary in type and may
originate from multiple locations. This interchangeability
of resources allows higher-level abstraction of capacities
into intensity ‘dimensions’ (see below).
The style of planning within this domain differs
markedly from standard AI approaches. Here, the search
space is dense with solutions, making it easy to find a plan
that satisfies stated goals. The real challenge is to find
‘good’ plans rather than settling for any available solution.
While most AI planning systems seek to minimize plan
size, bigger plans tend to be better in this domain. For
example, eliminating more of an enemy’s missile sites
tends to improve the quality of a plan for neutralizing
enemy attack capability. Note that maximizing plan size is
not equivalent to maximizing resource usage: the planner
and scheduler must still decide how to allocate available
resources economically to support potential activities.
Air operations commanders generally apportion a set of
resources for a given set of high-level objectives; human
planners are expected to develop solutions that maximize
the likelihood of objective attainment while staying within
the resource allotment. Our planning models incorporate
this apportionment perspective into their design. In
particular, initial plans seek to capitalize on all available
resources; as resource problems arise, strategies are
adopted that decrease expected resource usage.
Technical Approach
Our integration method builds on an incremental model of
planning and scheduling that assesses resource feasibility
at the level of subplans for the overall set of objectives,
using a model of intensity to approximate resource
demand, and adaptation in response to scheduler feedback.
Incremental Planning and Scheduling
Within our domain model, actions with resource
requirements do not appear until the lowest levels of a deep
hierarchy. Approaches in which complete layers of a
hierarchical plan are forwarded to a scheduler for resource
allocation (e.g., (Wilkins and Myers 98)) do not provide
much value in this case, since most of the plan would have
to be completed before any scheduler feedback could be
obtained. Instead, we developed a hybrid top-
down/incremental model for planning and scheduling. The
approach involves planning in standard HTN fashion down
to a specified level of detail (the decomposition layer), and
then splitting into subplans that are planned separately.
The decomposition layer, defined implicitly in terms of
specific goals, separates the higher-level strategic decisions
that define overall plan structure from the planning of
(mostly independent) lower-level objectives.
After completion of each subplan, the scheduler
performs incremental resource allocation for the actions
introduced by the subplan, relative to resource assignments
made for previous subplans. In the event that the scheduler
is unable to produce a satisfactory resource assignment, the
planner will modify a completed subplan to reduce
resource demand, and then forward the revisions to the
scheduler for appropriate adjustments to the current
schedule. Once all outstanding resource problems have
been resolved, the planner continues with generation of
remaining subplans until completion of a full plan and
schedule. With this incremental approach, the integrated
plan and schedule is built in piecewise, incremental
fashion, with adjustments made in response to detected
resource problems.
Our incremental approach would be ineffective for
domains in which extensive strategic dependencies link
objectives. However, in our models for the Air Operations
domain, most dependencies occur at the level of resource
allocation, thus enabling the separation of the planning for
individual objectives. The incremental approach has the
added benefit that it can be used for dynamically extending
plans to include additional objectives as plan execution
unfolds.
Intensity Models of Resource Demand
In order to make informed decisions about its choices, a
planner requires some model of the resource impact of its
decisions. Although the specific actions that require
resources don’t appear until the lowest levels of our
hierarchical models, high-level decisions have a great
impact on resource requirements. For example, the
decision of whether to employ a passive or more proactive
approach to defending assets will greatly influence
resource requirements, although the actual missions that
require resources are planned at much lower levels of
detail. For this reason, our approach to linking planning
and scheduling builds on a heuristic characterization of
expected resource usage by a planning operator, which we
refer to as an operator’s intensity.
Our work to date has explored two models for intensity,
which vary both the dimensionality (single vs multi) and
the precision (qualitative vs quantitative).
Single-dimensional Qualitative Intensity Model In this
model, an operator intensity represents a qualitative
assessment of the operator’s expected resource usage
relative to alternatives for the same task. Our air
operations domain, for example, contains multiple
operators for neutralizing an enemy’s communication
capability, ranging from taking out a single site, to
destroying some select subset of communication devices,
to eliminating all communication nodes. When using an
intensity scale of [0 10], the first operator might be ranked
a 2, the second a 5, and the third a 10 to reflect their
relative levels of expected resource consumption.
Multidimensional Quantitative Intensity Model This
model captures expected resource usage at a finer level of
granularity. Resources are grouped into functional
categories intended to capture similarities in resource
applicability. These groupings provide an aggregation over
the individual resources classes, thus simplifying the
resource models inherent to the scheduler; however, the
aggregation has greater detail than the single-dimensional
intensity model and so would be expected to provide
improved predictive value for resource usage estimation.
Within our air operations domain, for example, aircraft and
munitions can be grouped according to the different types
of missions in which they can be used. Our
multidimensional intensity model for this domain groups 5
types of aircraft and 7 types of munitions into 4 distinct
resource dimensions.
This model further improves on the single-dimensional
qualitative approach by employing a situation-dependent
characterization of intensity for an operator. In particular,
operator intensities are defined by a heuristic function that
estimates resource demand based on the number of targets
that an operator is expected to introduce.
The single-dimensional model has the virtue of requiring
little effort to define the qualitative rankings within the
underlying planning models: such rankings should be
readily assessable by the knowledge engineer who
develops the planning operators (especially since they need
only be approximate). The multidimensional quantitative
model requires the identification and modeling of resource
abstractions. Such abstractions fall out naturally in the air
operations domain, but may be more problematic to define
in other domains.
The weakness of the single-dimensional approach lies in
its lack of granularity. Consider a situation with relatively
low overall resource demand, but where the class of
resources required for a key type of action has been almost
exhausted. The single-dimensional approach would be
unable to adjust strategy selection to adapt to the shortage
because of the overall abundance of resources. In contrast,
the multidimensional model can represent a lack of
capacity for specialized groups of resources, and hence
strategy selection can be adapted to prefer approaches with
minimal demand for the oversubscribed resource.
Intensity-based Adaptation
The incorporation of intensity information to guide
planning occurs at the level of subplans. For a given
subplan, the planner calculates a target intensity, denoted
by IT. This value represents the expected ‘ideal’ use of
resources for a particular subplan, relative to availability
and expected demand for remaining subplans. When
faced with a choice among multiple applicable operators Oi
for a subgoal, the intensity IOi for each is computed. Each
operator is assigned a rating Rating(Oi) based on how
closely its intensity matches the subplan’s target intensity,
with the planner then selecting the most highly rated
operator for application. Through appropriate definitions
for the target intensity, operator intensities, and the
operator rating strategy, the planner can adapt its strategy
to match changing resource availability.
For example, scheduler feedback could indicate a
shortage/excess of remaining resources, relative to the
subplans yet to be generated and scheduled. Such a
shortage/excess would be reflected in the setting of the
next target intensity at a lower/higher level; the planner
would then be biased towards selecting operators with
lower/higher intensity values to reduce/increase resource
consumption levels. In this way, the planner dynamically
adjusts its decision-making in response to scheduler
feedback.
Within this adaptive framework, different control
strategies can be defined for selecting the subplan to be
revised in response to schedulability problems. The
experiments reported on in this paper adopt a
chronological backoff strategy: when the scheduler
encounters a problem with a subplan, the planner
successively reduces the intensity of that subplan by some
factor until a successful subplan is found, or there is no
more room for intensity reduction. In the latter case, the
algorithm removes the unsuccessful subplan from the plan;
if the target intensity of the previous subplan can be
reduced, then planning and scheduling are tried at that
lower level; otherwise, the planner continues to remove
subplans until it reaches a point where it encounters a
subplan that is not yet at the minimal intensity value.
From that point, it tries to plan with the lower target
intensity and then restarts the generation process in the
forward direction.
Below, we provide the basic definitions for the target
intensity, operator intensity, and operator rating scheme for
the multidimensional case, followed by a discussion of
their definitions for the simpler single-dimensional case.
Target Intensity IT The target intensity for a given
intensity dimension is defined in terms of the ratio of the
resources available per remaining subplan to the resources
allotted originally to each subplan (assuming uniform
apportionment to each); this ratio is then normalized
relative to the interval of intensity values in use (namely,
[0,TopIntensity]).
More formally, let Capacity(Ij) be the overall capacity
for resources in dimension j and let Rji be the remaining
capacity for dimension j after the first i of n subplans have
been created and scheduled. The following equation
defines the target intensity IT for the i+1st subplan:
where
I
I
I
T
m
T
T=M
1
tyTopIntensi
Capacity
n
inT
jI
R
I
j
i
j↔
↔
↔
−
=)(
1
1
Provided that resource usage remains below allotment
levels, the value of IjT will exceed TopIntensity. Values
below TopIntensity indicate that planning choices should
seek to decrease demand for resources within that
dimension below the original allotment level.
Operator Intensity IOi The intensity IOi of a planning
operator Oi is defined by the equation:
where
O
O
O
I
I
I
i
i
i
m
=M
1 tyTopIntensi
Capacity
n
i
mandExpectedDe
O
I
I
O
I
j
j
j
i↔
↔
=)(
1
)( ,
The intensity for each dimension is defined to be the ratio
of the expected resource demands introduced by the
operator to the original allotment of resources for that
subplan and dimension (assuming uniform allotment).
For the air operations domain, the resource demands of
an operator are measured in terms of the expected
munitions and aircraft required to prosecute the targets
associated with the operator. These estimates are
calculated by summing the expected number of targets of a
given type multiplied by a capacity estimate for the type.
Operator Ranking Figure 1 presents our scheme for
ranking operators according to their proximity to the target
intensity values. The ranking method builds on the
intensity difference vector DOj= IT-IOi
, which gives the
difference between the target intensity and operator
intensity vectors. The operator rating, denoted by
Rating(Oi), is defined to be the sum of the magnitudes in
the intensity difference vector, adjusted by a penalty factor.
In cases where the difference value dj is positive (i.e., the
operator requires fewer resources than indicated by the
target intensity), the penalty is defined by P+; in cases
where dj<0 (i.e., the operator is expected to use more
resources than indicated by the target intensity), the penalty
is defined by P-
. Through appropriate settings of the ratio
of these penalty factors, different strategies can be defined
that penalize resource over/underutilization to different
degrees. With this rating scheme, the preferred operator
will be that with the lowest rating.
)()(
=
D
d
PenaltyRating
Oi
j
dO j
i
0
0
)(
)(
)( <
?
↔
↔
=−
+
d
d
for
for
dABS
dABS
denalty P
P
Figure 1: Operator Rating
Single-Dimension Case For the single-dimensional case,
the target intensity IT reduces to the following:
tyTopIntensi
Capacity
n
inT R
I
i
↔
↔
↔
−
=1
1
The operator intensity is simply the qualitative annotation
defined for the operator, while the rating is the difference
between the target and operator intensities.
Experimental Evaluation
We conducted a series of experiments to evaluate the
effectiveness of the intensity adaptation methods. For a
baseline, we adopted a loosely-coupled iterative waterfall
integration of the planner and scheduler in which the
planner generates complete plans and then passes them to
the scheduler for resource allocation and time-on-target
assignments. If the scheduler fails to produce an
acceptable schedule, the plan generation and scheduling
process repeats.
Our test problem yields plans with 8 subplans and 50-
724 actions, depending upon the aggressiveness of the
planning strategies applied. Experiments involved running
the test problem with different resource profiles, as shown
in Figure 2. The BIG profile contains a large amount of
resources relative to the maximal plan, while the 100%
profile provides just sufficient resources to enable the
maximum plan to be constructed; the profiles then decay
gradually until there are insufficient resources to support
the minimal plan.
Generation time constitutes one important criterion for
evaluating planner/scheduler behavior. Some measure of
plan quality must also be considered, otherwise the best
strategy is to generate the smallest plan that satisfies stated
objectives: because it contains fewer activities, it will
require fewer resources and so should be easier to
schedule. Plan quality can be difficult to assess as it
involves multiple dimensions and can be highly subjective
(Gil 98). As discussed above, air operations plans can
generally be
Figure 2: Experiment Resource Profiles
made more effective by adding additional actions to them.
For this reason, we use plan size as a rough indicator of
plan quality.
Our experiment compares the single- and
multidimensional approaches (with P+=P-=1) to the
iterative waterfall. For performance, we consider three
main factors: generation time, plan size, and number of
planner/scheduler interactions. Figure 3 shows the results.
The topmost graph displays generation times in log scale
for the three methods. As can be seen, the waterfall
method requires substantially more time when resources
become constrained, while the intensity-based methods
perform much better. The multidimensional approach also
outperforms the single dimensional approach. The middle
graph displays the number of interactions between the
planner and scheduler required to find a solution. As with
generation time, these results show that the
multidimensional method outperforms the single-
dimensional method, and that they both are far superior to
the waterfall method as resources become more limited.
These results show an impressive speed-up by the
intensity adaptation methods over the waterfall baseline.
The tests used a scaled-down version of the domain in
which goals that did not involve intensity decisions were
limited to a single applicable operator. As such, the
waterfall backtracking was limited to the same choices as
the intensity adaptation methods. An additional
experiment was run where non-intensity goals had 2
applicable operators. Runtimes for the intensity methods
were virtually identical to those in Figure 3, since the
intensity method backtracks at the level of intensity values
rather than operators (hence is not impacted by the
additional operators). In contrast, the waterfall method was
unable to find a solution below the 100% resource profile
after 239 trials and almost 30 hours of runtime. The
waterfall method fails so badly in this larger problem
because many planning decisions must be backtracked
through to reach one that impacts resource usage
significantly.
The waterfall approach produces larger plans than the
intensity-based methods for the 100% through 50%
profiles; as resource availability decreases though, it
produces smaller (i.e., less aggressive) plans. In comparing
the corresponding runtimes, it is clear that the small
1
10
100
1000
10000
100000
Big 100% 75% 50% 25% 15% 10%
Generation Time (log scale)
0
50
100
150
200
Big 100% 75% 50% 25% 1 5% 10%
Interactions
0
200
400
600
800
Figure 3: Comparison of Waterfall, Single-dimensional and
Multidimensional Methods
increase in plan size is obtained at the cost of an increase of
several orders of magnitude in planning/scheduling time.
While there is some variation between the single and
multidimensional methods, the difference is relatively
small. Overall, these results show that the performance
benefits realized by the multidimensional approach do not
adversely impact solution quality.
Additional experiments, documented in (Myers, Smith et
al 2001), provide further evidence of the effectiveness of
the intensity adaptation method for integrating strategic
planning and scheduling. One set considers variants to the
ground interdiction problem described here; a second set
employs an air superiority problem with related but
different structure. These experiments produced similar
results to those reported in this paper, thus providing
evidence for the generality of the method. We also
performed sensitivity analyses for the 2 key parameters to
the intensity adaptation method: the resource
over/underutilization ratio in the operator ranking scheme
(P+ /P-) and the distribution of resources among intensity
dimensions. These experiments show that the adaptive
Waterfall Single Multi
5
4
3
2
1
0
Number of Aircraft
Number of Aircraft
Aircraft Types
Resource Profiles (percentage of sufficient capacity)
0
1
2
3
4
5
H-1A
F-4
F-3
F-2
F-1
100%
95%
90%
85%
80%
75%
70%
65%
60%
55%
50%
45%
40%
35%
30%
25%
20%
15%
10%
5%
nature of the intensity method makes it robust in the face of
reasonable variations in these parameters.
Related Work
As mentioned earlier, much of the previous work in
integrated planning/scheduling systems has been motivated
by resource-driven applications. The early Hubble Space
Telescope scheduling application of the HSTS system
(Muscettola et.al 92) provides a representative example,
where a set of independent (or loosely coupled) requests
for telescope viewing time, each requiring a complex set of
spacecraft actions for setup, observation, and clean-up,
must be selected and sequenced for execution. Here, the
overriding concern is efficient allocation of system
resources, with planning decisions localized to
implementation of individual tasks. The Remote Agent
Planner/Scheduler (Jonsson et.al. 00) and the DCAPS
mission planner (Chien et.al.) also fall into this category, as
does IP3S (Sadeh et.al 98), a system that integrates process
planning and production scheduling.in the manufacturing
domain
The REALPLAN system places greater emphasis on
strategic planning (Srivastava, Kambhampati and Minh).
Like our approach, REALPLAN partitions a problem into
separate planning and scheduling subproblems rather than
solving the entire problem in a single integrated search
space (see (Smith, Frank, Jonsson 01) for a survey of
integrated search approaches). We similarly believe that
such partitioning provides essential computational
leverage. REALPLAN employs an iterative waterfall
control model, with feedback of failure information in the
most sophisticated variant. As shown in this paper, such an
approach can be intractable in nontrivial domains.
The planning and scheduling system described in
(McVey, et.al. 97) builds on an iterative waterfall model of
interaction, but incorporates a form of feedback from
scheduler to planner that is similar in spirit to our intensity
adaptation approach. Based on a probabilistic state model,
the planner generates control plans designed to prevent
runtime transition to failure states. Plans are generated
based on a specified probability threshold on states, with
higher thresholds resulting in consideration of fewer
eventualities and hence simpler plans. When the scheduler
is unable to meet the stated deadlines of all actions in a
generated plan, it recommends a higher probability
threshold as feedback to the planner for the next iteration.
Similarly, when schedules underutilize resources, the
scheduler suggests a lower probability threshold for the
planner to enable the incorporation of additional activities.
Conclusions
The two intensity-based methods defined in this paper
provide complementary methods for supporting effective
planner/scheduler integration in domains that require
significant strategic planning. The single-dimensional
qualitative approach provides a simple, easily implemented
method that shows significant performance gains over
waterfall-style methods. The multidimensional quantitative
approach provides even better results but requires more
modeling effort to operationalize.
This work represents one thrust of a larger effort to
develop an integrated planning and scheduling system for
management and control of large-scale enterprises (Myers
and Smith 99). Beyond the work on plan and schedule
generation described here, we are also developing
intensity-based methods to support efficient plan and
schedule repair in response to the addition or revision of
objectives and changes to resource availability.
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