COORDINATION OF PLANNING AND SCHEDULING

TECHNIQUES FOR A DISTRIBUTED, MULTI-LEVEL,

MULTI-AGENT SYSTEM

John S. Kinnebrew, Daniel L. C. Mack, Gautam Biswas and Douglas C. Schmidt

Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37203, U.S.A.

Keywords:

Planning and scheduling, Agent cooperation and coordination.

Abstract:

Planning and scheduling for agents operating in heterogeneous, multi-agent environments is governed by the

nature of the environment and the interactions between agents. Signiﬁcant efﬁciency and capability gains can

be attained by employing planning and scheduling mechanisms that are tailored to particular agent roles. This

paper presents such a framework for a global sensor web that operates as a two-level hierarchy, where the

mission level coordinates complex tasks globally and the resource level coordinates the operation of subtasks

on individual sensor networks. We describe important challenges in coordinating among agents employing

two different planning and scheduling methods and develop a coordination solution for this framework. Ex-

perimental results validate the beneﬁts of employing guided, context-sensitive coordination of planning and

scheduling in such sensor web systems.

1 INTRODUCTION

In large-scale, distributed, multi-agent systems

(MAS) that span multiple domains of agent operation,

choosing a single planning and scheduling mecha-

nism for all agents may be inefﬁcient and impractical.

For example, NASA’s Earth Science Vision calls for

the development of a global sensor web that provides

coordinated access to sensor network resources for re-

search and resolution of Earth science issues (Hilde-

brand et al., 2004). This global sensor web must se-

lect and coordinate an appropriate subset of hetero-

geneous, distributed sensors and computational re-

sources for user tasks that often require collaboration

among multiple constituent sensor networks. Com-

plex task execution with resource constraints and time

deadlines presents planning, scheduling, and coordi-

nation issues at multiple levels of the sensor web.

Our Multi-agent Architecture for Coordinated Re-

sponsive Observations (MACRO) platform provides

a powerful computational infrastructure for deploy-

ing, conﬁguring,and operating large sensor webs with

many constituent sensor networks (Suri et al., 2007).

MACRO is structured as a two-level agent hierar-

chy: (1) the mission level, where global coordina-

tion across sensor networks is achieved and planning

and scheduling is handled at an appropriate level of

abstraction to avoid computational intractability, and

(2) the resource level, where operations within a lo-

cal sensor network are coordinated and controlled us-

ing planning and scheduling methods that operate in

dynamic, uncertain and resource constrained environ-

ments. Therefore agents at these different levels of

the system operate in different contexts imply differ-

ent planning and scheduling requirements.

MACRO achieves efﬁcient and effective au-

tonomous planning by employing hierarchical task

network planning with distributed scheduling at the

mission level and decision theoretic planning with re-

source constraint propagation scheduling at the re-

source level. Developing such an agent architec-

ture, however, also presents challenges in coordinat-

ing among the agents . In particular,employing differ-

ent planning and scheduling mechanisms at the mis-

sion and resource levels requires an appropriate trans-

lation of the task, plan, and schedule representations

between levels. It also requires a coordination mech-

anism for deciding when to exchange information be-

tween levels during plan execution.

The remainder of the paper is organized as fol-

lows: Section 2 outlines the key capabilities pro-

vided by the MACRO agent framework; Section 3

summarizes the planning and scheduling coordination

challenges and the solutions we developed for this

184

S. Kinnebrew J., L. C. Mack D., Biswas G. and C. Schmidt D. (2010).

COORDINATION OF PLANNING AND SCHEDULING TECHNIQUES FOR A DISTRIBUTED, MULTI-LEVEL, MULTI-AGENT SYSTEM.

In Proceedings of the 2nd International Conference on Agents and Artiﬁcial Intelligence - Agents, pages 184-191

DOI: 10.5220/0002721001840191

 SciTePress

paper; Section 4 evaluates experimental results that

show the reduction in communication and computa-

tion achieved by using MACRO’s guided, context-

sensitive coordination mechanism for planning and

scheduling; Section 5 compares our work with related

research; and Section 6 presents concluding remarks.

2 OVERVIEW OF MACRO

To provide global coordination of the sensor web, the

MACRO mission level is comprised of broker agents,

user agents, and mission agents. Broker agents act as

the intelligent system infrastructure, providingmatch-

maker services, aggregating relevantdomain informa-

tion, tracking system performance, and mediating al-

location negotiations (Kinnebrew, 2009). User agents

generate the high-level tasks and are typically inter-

faces to mission scientists and wrappers for legacy

systems (e.g. weather modeling applications) that can

request execution of sensor web tasks. Each mission

agent represents an independent sensor network and

achieves its allocated tasks with the resources avail-

able in its sensor network.

As the representative of an entire sensor network,

a mission agent straddles the boundary between the

mission and resource levels. At the resource level,

mission agents divide tasks among the exec agents,

each of which controls a set of computational/sensor

resources within a sensor network and is supported by

additional domain-speciﬁc agents. An exec agent also

employs services for planning, scheduling, allocation,

and resource management of the hardware under its

control. These services are shared with any support-

ing agents under its direction, providing a centralized

control and environmental awareness for its set of re-

sources.

2.1 MACRO Mission Level

At the mission level of a sensor web MAS, user

tasks and scheduled plans spanning multiple sensor

networks have a high degree of complexity. Hi-

erarchical analysis helps deal with this complexity,

both for problem/task representation by domain ex-

perts and for coordinated planning and scheduling

among multiple agents. MACRO combines the OGC

SensorML (Botts et al., 2007) representation of sen-

sors and data processing with the Task Analysis, En-

vironment Modeling, and Simulation TÆMS hierar-

chically decomposable task representation (Horling

et al., 1999) for multi-agent planning and schedul-

ing. This combination provides standardized descrip-

tions of task/subtask requirements and effects across

sensor networks. The TÆMS representation also al-

lows the speciﬁcation of discrete probability distribu-

tions for task/subtask characteristics including poten-

tial outcome quality and duration (Lesser et al., 2004).

To coordinate and schedule TÆMS tasks across

sensor networks, MACRO mission agents employ the

Generalized Partial Global Planning (GPGP) (Lesser

et al., 2004) coordination mechanism, which works

in conjunction with a planning and scheduling mech-

anism that can generate an appropriate task decompo-

sition and schedule from a TÆMS task tree. For this

purpose, MACRO mission agents employ Design-

To-Criteria (DTC) (Wagner and Lesser, 2001) plan-

ning/scheduling, which has successfully been used in

conjunction with GPGP coordination (Lesser et al.,

2004). DTC scheduling is a soft real-time, heuristic

approach to solving the combinatorial problem of op-

timally decomposing and scheduling a TÆMS task.

DTC is particularly suited to the MACRO mission-

level because it can optimize plans and schedules

based on user-provided criteria, such as minimizing

execution time or maximizing expected quality.

2.2 MACRO Resource Level

Exec agents use the Spreading Activation Partial

Order Planner (SA-POP) (Kinnebrew et al., 2007),

which generates high utility, scheduled, partial or-

der plans that respect local resource constraints. SA-

POP allows the exec agents to use their limited com-

putational resources to maximize expected utility for

achieving local goals in the dynamic, uncertain en-

vironments at the resource level. Moreover, SA-

POP provides incremental re-planning/re-scheduling

that can quickly revise scheduled plans during ex-

ecution and prevent more expensive re-planning/re-

scheduling at the mission level. In conjunction with

SA-POP, exec agents also employ the Resource Allo-

cation and Control Engine (RACE) (Shankaran et al.,

2007) for resource allocation and management to

meet scheduled deadlines and required quality of ser-

vice (QoS) parameters for deployed applications and

hardware-based actions.

First-principles planning (Blum and Furst, 1997)

and scheduling with SA-POP requires a set of goal

conditions that correspond to the desired outcome.

These goal conditions are speciﬁed as desired en-

vironmental and system conditions with associated

utility values and time deadlines. Given these goal

conditions, SA-POP uses current/expected conditions

to generate a scheduled plan of high expected util-

ity (Kinnebrew et al., 2007).

COORDINATION OF PLANNING AND SCHEDULING TECHNIQUES FOR A DISTRIBUTED, MULTI-LEVEL,

MULTI-AGENT SYSTEM

185

Exec AgentMission Agent

Task T1

Subtask

T1.1

Subtask

T1.2

q_exactly_one()

Subtask

T1.2.1

q_sum_all()

enables

q_exactly_one()

Method

Quality: (70% 10) (30% 0)

Duration: (80% 43s) (20% 28s)

Quality: (75% 4) (25% 0)

Duration: (100% 30s)

Goal

Action

Plan M3

Utility: 100

Start Time: 0s

Deadline: 75s

SA-POP

Figure 1: Planning/Scheduling Representations in MACRO.

3 MACRO COORDINATION

As described in Section 2.1, mission agents must ef-

ﬁciently generate and coordinate plans and schedules

provided by the TÆMS task decomposition trees and

criteria-directed scheduling. As shown in Figure 1,

the leaves of a TÆMS task tree are methods, which

in standard TÆMS usage can be directly executed by

the agent. In MACRO, however, mission agents must

communicate these methods to their exec agents for

resource-level planning/scheduling and actual execu-

tion.

At the resource level, the decision-theoretic,

ﬁrst-principles planning and constraint-propagation

scheduling is efﬁciently performed by SA-POP for

achievement of goals in the dynamic sensor network

environment shown in Figure 1. Effectively employ-

ing both representations and forms of planning and

scheduling presents multiple challenges for coordina-

tion between MACRO mission and exec agents.

3.1 Translation: Top-Down

Problem. For an exec agent to implement a TÆMS

method, the mission agent must translate it into the

goal format used by SA-POP. SA-POP goals include

one or more goal conditions with associated utility

values and time deadlines. To plan for a goal accu-

rately, SA-POP requires knowledge of expected sys-

tem and environmental conditions at the time the plan

will be executed. Although current conditions and

other exec agent plans provide most of this informa-

tion, other expected conditions may be the result of

methods assigned to other exec agents in the mission

agent’s current plan (i.e., other methods that enable

the method in question by satisfying some of its pre-

conditions).

Solution → Cross-references in Task/Goal Mod-

eling. Domain experts (e.g., scientists and engi-

neers who design and deploy the sensor network)

use MACRO’s domain-speciﬁc modeling language

(based on GME (Karsai et al., 2003)) to specify

the TÆMS task tree for a mission agent. In this

model, TÆMS methods are associated with neces-

sary resource-levelpreconditionsand goal conditions,

which in turn are represented in the action network

model employed by the exec agent and SA-POP.

Moreover, the domain expert can automatically derive

method distributions for duration and outcome in this

model by providing potential initial condition settings

(with an associated probability) to SA-POP, which

produces scheduled plans and summarizes their prob-

ability of success, expected duration, and resource us-

age.

Instead of directly executing a method, the mis-

sion agent uses the encoded translation informa-

tion from the model to provide a goal to the exec

agent. This top-down translation is shown by the mis-

sion agent to exec agent information transfer in Fig-

ure 2. The mission agent awards overall task utility to

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186

Exec AgentMission Agent

Method

Method M3

Quality: (90% 10) (10% 0)

Duration: (100% 43s)

Avg Resource: R1=50%

Max Resource: R1=100%

Goal M3

Action

Plan M3

Utility: 100

Start Window: [30s, 30s]

Deadline: 75s

Goal Condition: C7=True

Goal Condition: C8=True

Initial Condition: C1=True

Probability Success: 90%

Duration: 43s

Avg Resource: R1=50%

Max Resource: R1=100%

Plan T1

Goal: C7=True

Goal: C8=True

Initial: C1=True

C1=True

Externally Provided/

Updated Information

Internally Encoded/

Derived Information

Utility: 100

Start Time: 30s

Deadline: 75s

Figure 2: Planning/Scheduling Translation in MACRO.

methods based on the quality aggregation functions

(QAFs) and expected quality in the TÆMS task tree.

In the chosen decomposition of the TÆMS task

tree, parents with a QAF that requires execution of

all child subtasks/methods pass the full parent utility

to each child, while QAFs that allow any subset of

children pass a percentage of parent utility based on

the child’s percentage of total expected quality for the

parent. For example, a task with an overall utility of

100 that is decomposed into two subtasks of expected

quality 3 and 7 with a sum QAF would assign util-

ity of 30 and 70, respectively, to its subtasks. Future

work will investigate more advanced methods of re-

ward assignment in the decomposition of TÆMS task

trees.

3.2 Translation: Bottom-Up

Problem. Another important challenge is codifying

the bottom-up translation between SA-POP plans and

TÆMS method parameters. Standard TÆMS meth-

ods include a priori probability distributions for dura-

tion and outcome quality, which are used during ini-

tial criteria-directed scheduling by the mission agent.

After an exec agent plans to achieve a goal, the re-

sultant scheduled plan may imply signiﬁcantly dif-

ferent probability distributions for the corresponding

method. Similarly, as a plan is being executed by

the exec agent, there may be further changes to the

expected duration or probability of outcomes for the

plan and its corresponding method. To improve the

efﬁciency of future criteria-directed scheduling and to

trigger appropriate mission-levelre-scheduling, infor-

mation about the exec agent’s plan must be commu-

nicated to the mission agent.

Solution → Summarize Resource-level Plans. In-

stead of providing the complete resource-level plan

to the mission agent (whose format is ill-suited to

its planning and scheduling capabilities), a MACRO

exec agent summarizes its plan by providing relevant

information only, including (1) expected duration, (2)

probability of achieving the goal, and (3) average

and maximum resource usage over expected execu-

tion. The mission agent uses these values to update

method parameters with more accurate information,

based on the resource-level planning and scheduling

for the current and expected environmental/system

conditions. The updated method parameters allow the

mission agent to more effectively perform any further

planning and scheduling for its task(s).

3.3 Context-Sensitive Updates

Problem. In addition to translating between the mis-

sion and exec agent planning/scheduling representa-

tions, MACRO agents must also decide when to up-

date and communicate the translated information. In

particular, during execution of exec agent plans, de-

viations may occur (e.g., differences between actual

and expected duration of actions). Only some vari-

COORDINATION OF PLANNING AND SCHEDULING TECHNIQUES FOR A DISTRIBUTED, MULTI-LEVEL,

MULTI-AGENT SYSTEM

187

ations, however, will impact the rest of the mission-

level plan—or other plans—in a manner that would

be of interest to the mission agent.

Solution → Leverage Mission-level Task Context.

Given the hierarchical relationship between mission

and exec agents, the top-down decision to commu-

nicate (i.e., when the mission agent should com-

municate information to an exec agent) is relatively

straightforward. Speciﬁcally, whenever a new task is

decomposed/scheduled or method parameters in the

plan are changed by re-planning/re-scheduling, the

mission agent communicates the new or revised goals

(translated from the methods) to the assigned exec

agents.

For bottom-up updates, however, an exec agent

can use its knowledge of a mission agent’s overall

goals/interests to guide its decision of when to com-

municate. Without mission agent guidance, an exec

agent would be forced to communicate on a peri-

odic basis or whenever the execution deviates from

the scheduled plan, which may happen frequently in

a dynamic sensor network environment. When task-

ing an exec agent with a goal, therefore, the MACRO

mission agents also provide guidance and contextual

information, such as the optimization criteria for the

related task. Knowledge of the optimization criteria

allows the exec agent to conﬁgure SA-POP’s planning

and scheduling to prefer plans based on that criteria.

In addition to optimization criteria, the mission

agent can specify acceptable deviations (in either di-

rection), success probability, expected utility, dura-

tion, and resource usage of an executing plan. This

information provides the exec agent with guidance

on the context for the corresponding method in the

mission agent’s plan, which allows the agent to more

intelligently determine when to update its scheduled

plan and provide the revised summary to the mission

agent. Speciﬁcally, during execution of a plan, the

exec agent will only re-plan and re-schedule if the ex-

pected utility falls below, or if the duration surpasses,

speciﬁed thresholds. When other thresholds are ex-

ceeded, the exec agent simply communicates updated

summary information to the mission agent.

Figure 3 shows the execution of the resource-level

plan from Section 3.2. To demonstrate the beneﬁt of

the guidance/context provided by the mission agent,

we focus on deviations of action duration from ex-

pected duration in the critical path (i.e., the linked

sequence of actions that requires the longest time to

complete). Although the planning and scheduling in

MACRO does not rely on identiﬁcation of the critical

path, such a path(s) always exist, and it constrains the

expected completion time of the plan.

Without the context provided by duration thresh-

E[T]: 10s

A[T]: 9s

E[T]: 5s

A[T]: 8s

E[T]: 8s

A[T]: 8s

E[T]: 14s

A[T]: 16s

E[T]: 6s

A[T]:4s

E[T]: 6s

A[T]: 9s

E[T]: 3s

A[T]:3s

39s 46s 54s 70s 74s30s

Finished Early

Finished Late

Deadline: 75s

Finished within

Time Window

Figure 3: A Resource-level Plan (Critical Path High-

lighted).

olds, the exec agent would have no knowledgeof what

deviations were important to the mission agent and

would have to communicate updates based on each

deviation. It would recalculate its schedule every time

an action did not complete with exactly its expected

duration. It would also transmit the new expected du-

ration of the plan either with every recalculation or at

least every time an action ﬁnished outside of its sched-

uled end window (either before or after that window).

The example execution in Figure 3 shows a typi-

cal case in which the mission agent provides an over-

threshold on duration equal to the difference between

the expected end-time of the plan and the original

deadline. In other words, the mission agent is only in-

terested in changes to the resource-level schedule that

would result in its ﬁnishing later than the deadline. In

this example, the exec agent would have to re-plan/re-

schedule only when execution of action A6 goes be-

yond its scheduled end window. Without the appro-

priate context (i.e., the duration threshold), the exec

agent would have also had to unnecessarily recalcu-

late or re-plan/re-schedule three times (after comple-

tion of A1, A4, and A3) and communicate unneces-

sary updates twice (after A1 and A4).

4 COORDINATION RESULTS

This section presents the results of mission and exec

agent coordination through the simulated execution of

randomly-generated resource-level plans with a vari-

ety of duration distributions for actions. These re-

sults validate our claims that MACRO’s use of guided,

context-sensitive coordination in planning/scheduling

can reduce communication and computation, while

still providing relevant information in a timely fash-

ion.

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4.1 Experimental Design

Our experiments simulate a scheduled, partial-order

plan generated by SA-POP for an exec agent at the

resource level of MACRO. These plans include a set

of actions with expected start and end time windows,

as well as ordering links. For these experiments, we

only simulate cases in which a valid plan can be gen-

erated.

One experimental parameter is the variability of

actual durations for actions, which requires differ-

ent probability distributions parameterized by a sigma

value. The experiments included both uniform dis-

tributions and Gaussian (Normal) distributions. The

uniform distributions showed the same trends ob-

served in the Gaussian distributions (results are omit-

ted due to the length constraints). The action duration

distributions have a mean of 100 seconds and “low”

and “high” variance scenarios providing a 95% like-

lihood (for the Gaussian) that durations are within 25

seconds or 75 seconds of the mean, respectively.

Another experimental variable is the length of the

critical path. The distributions provide all actions

with an expected duration of 100 seconds. The ex-

pected time for completion of the plan therefore de-

pends solely on the number of actions in the critical

path.

The ﬁnal experimental variable is the time thresh-

old provided by the mission agent in MACRO

context-sensitivecoordination, which determines how

far actions can surpass their expected end times be-

fore the mission agent must be notiﬁed for potential

mission-level re-planning and re-scheduling. To as-

sess computation and communication overhead of the

coordination mechanism, we employed random gen-

eration of plans across a range of parameters rather

than using a few example problems. These experi-

ments do not assess the quality or utility of plans or

potential plan changes during coordination. MACRO

coordination will not result in any degradation of plan

quality in comparison to the baseline coordination,

however, since plan and schedule information that

triggers mission-level re-planning and re-scheduling

is providedby both MACRO coordinationmechanism

and the baseline mechanism at the same time.

Since these experiments employ randomly-

generated plans to cover a range of potential applica-

tions, they do not allow changes to resource-level or

mission-level plans during execution. Whenever an

action execution exceeded its scheduled end window,

the schedule was updated and communicated to the

mission agent, but no changes to the plan or threshold

were made. Without re-planning, the MACRO

coordination overhead is an over-estimate of the real

overhead. After a critical path action’s end window is

exceeded, execution of further actions will continue

to exceed action end windows. Re-planning reduces

this possibility.

4.2 Experimental Results

Each experimental run included 10,000 trials with the

given parameter settings. In each trial, a series of (n)

actions formed the critical path, and each action had

an expected duration of 100 seconds. Using the cho-

sen distribution, random values are generated that cor-

respond to actual execution times. The number of up-

dates and messages are calculated using those values.

4.2.1 Investigating Critical Path Length

These experiments were performed under the assump-

tion that the mission agent simply requires a method

to be completed by the provided deadline and should

only be notiﬁed if the expected execution time will

exceed that deadline. The threshold value is therefore

set to the difference between the deadline and the ex-

pected duration of the plan. This threshold is varied

in the experiments between 0 and 200 seconds in 5

second increments.

y = 0.9839x - 0.9453

R² = 1

y = 0.4784x - 0.19

R² = 0.9998

y = 0.3142x - 1.2183

R² = 0.9926

y = 0.1769x - 1.1454

R² = 0.9654

0 10 20 30 40

Messages/Updates

Length of the Critical Path

Baseline

MACRO Thresh = 5s

MACRO Thresh = 50s

MACRO Thresh = 100s

Figure 4: The effect of critical path length with selected

thresholds with a low variance Gaussian.

Figure 4 shows the information from the mission

agent results in signiﬁcantly less computation and

communication than the baseline condition for all but

the smallest of critical paths The linear trend suggests

that in the worst case (i.e., a tight threshold/deadline),

MACRO sends about half as many messages as the

baseline machanism. As the threshold increases,

MACRO performs even better, whereas the baseline

performance does not change.

A comparison of the low variance action duration

distribution in Figure 4 to a high variance one in Fig-

ure 5 shows that with the smallest thresholds a ratio

COORDINATION OF PLANNING AND SCHEDULING TECHNIQUES FOR A DISTRIBUTED, MULTI-LEVEL,

MULTI-AGENT SYSTEM

189

y = 0.8815x - 0.8413

R² = 1

y = 0.4917x - 0.0522

R² = 0.9999

y = 0.4346x - 0.5674

R² = 0.9992

y = 0.3721x - 0.9923

R² = 0.997

0 10 20 30 40

Updates/Messages

Length of the Critical Path

Baseline

MACRO Thresh = 5s

MACRO Thresh = 50s

MACRO Thresh = 100s

Figure 5: The effect of critical path length with selected

thresholds with a high variance Gaussian.

of approximately 1 update per 2 actions in the critical

path is required for both distributions. The 1:2 ra-

tio is thus an approximate upper limit on the average

number of updates required in MACRO, even when

re-planning and re-scheduling is not possible.

The baseline mechanism shows a slight, relative

improvement in the high variance case, but MACRO’s

context-sensitive coordination still requires far fewer

updates. However, the number of updates required

in MACRO with different thresholds are much closer

in the high variance case than the low variance case.

This result suggests that when action durations are

less certain, the critical path length is signiﬁcantly

more important than the threshold, because even large

thresholds can be exceeded by a series of actions that

begins with an unexpectedly long-running action.

4.2.2 Investigating Time Thresholds

Figure 6 and Figure 7 show the trends in communi-

cation and computation with respect to the duration

threshold. The baseline results are not included in

these ﬁgures because they do not use of the thresh-

old value, therefore, they would produce a horizontal

line close to the number of actions in the critical path.

These results show that as the threshold increases,

the number of MACRO updates decreases. Figure 6,

shows a steep initial decrease which levels off. Qual-

itatively, this trend occurs since longer thresholds al-

low a series of actions to exceed their expected dura-

tion by a greater amount before requiring an update.

Extreme variation, however, from expected durations

can occur and will still require some updates, even

with relatively large thresholds. These results also

show, that even when uncertainty of action duration

is high, the exec agent can leverage the contextual in-

formation provided by the mission agent to minimize

coordination overhead.

y = 2.5e

-0.042x

R² = 0.9539

y = 5e

-0.027x

R² = 0.9777

y = 7.5e

-0.021x

R² = 0.9831

y = 10e

-0.018x

R² = 0.9865

0 25 50 75 100 125 150 175 200

Updates/Messages

MACRO Threshold

CP = 5 Tasks

CP = 10 Tasks

CP = 15 Tasks

CP = 20 Tasks

Figure 6: The effect of Slack with selected critical paths on

a low variance Gaussian.

y = 2.7609e

-0.011x

R² = 0.9945

y = 5.2883e

-0.007x

R² = 0.9958

y = 7.8007e

-0.006x

R² = 0.9956

y = 10.271e

-0.005x

R² = 0.9972

0 25 50 75 100 125 150 175 200

Updates/Messages

MACRO Threshold

CP = 5 Tasks

CP = 10 Tasks

CP = 15 Tasks

CP = 20 Tasks

Figure 7: The effect of Slack with selected critical paths on

a high variance Gaussian.

5 RELATED WORK

MACRO’s approach to planning and scheduling

builds upon and extends a signiﬁcant body of

related work. At the mission level, MACRO

agents employ Design-To-Criteria (DTC) plan-

ning/scheduling (Wagner and Lesser, 2001) operating

on an augmented TÆMS task tree to efﬁciently op-

timize for relevant criteria in generating a scheduled

plan to perform assigned subtasks. At the resource

level, exec agents employ SA-POP (Kinnebrew et al.,

2007) for decision-theoretic planning with constraint-

propagation scheduling.

MACRO Agents communicate the most useful in-

formation at an appropriate abstraction level and at

the right time. The translation from resource-level

plans to mission-level method parameters has some

similarities to research that uses plan summary in-

formation to coordinate between agents employing

HTN planning (e.g., (Clement and Durfee, 1999;

Clement and Durfee, 2000)). MACRO mission and

exec agents, however, employ different representa-

tions for planning and scheduling. Moreover, the re-

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190

source and scheduling constraints in MACRO require

summary information beyond the pre-, in-, and post-

conditions used in Clement’s task summary info ap-

proach (Clement and Durfee, 1999).

6 CONCLUDING REMARKS

This paper presented key research challenges for

coordinating planning and scheduling at two lev-

els of a hierarchical multi-agent system. We dis-

cussed MACRO’s solutions to coordinating HTN

task decomposition with criteria-directed scheduling

and ﬁrst-principles decision-theoretic planning with

constraint-propagation scheduling. We also report

the results of experiments that showcased the bene-

ﬁts gained by employing MACRO’s guided, context-

sensitive coordination of planning and scheduling.

Our experimental results quantiﬁed the effects of

different distributions from which average duration

information is derived for resource-level actions. The

experiments also showcase the effects of other plan-

ning/scheduling parameters, including the length of a

scheduled plan’s critical path and the restrictiveness

of the deadline. Moreover, our results verify the scal-

ability of MACRO planning/scheduling coordination

when execution time is the primary criteria of inter-

est to the mission agent. Our future work will explore

other forms of utility assignment in TÆMS task tree

decomposition and evaluate the beneﬁts of context-

sensitive coordination with thresholds on plan char-

acteristics other than execution time.

ACKNOWLEDGEMENTS

This work was supported in part by NASA Advanced

Information Systems Technology (AIST) program

under grants NNA04AA69C and NNX06AG97G.

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