Benchmark Problems for Oversubscribed
Scheduling
Laura V. Barbulescu and Laurence A. Kramer
and Stephen F. Smith
Intelligent Coordination and Logistics Laboratory
The Robotics Institute
Carnegie Mellon University
Pittsburgh PA 15213
{laurabar,lkramer,sfs}@cs.cmu.edu
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Competition Benchmark Problems
• The problems should abstract features
that are present in real world domains.
• The real world domains should be
representative of the challenges faced by
human schedulers.
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Generalizing from a Set of Scheduling
Applications
• Evaluation of different approaches in the
expanded context of multiple
applications.
• Issues:
• Identifying similar applications.
• Synthesizing their common features.
• Imposing application specific features to
produce instances for that application.
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Oversubscribed Problems
• Oversubscribed scheduling problems are
characterized by the inability to accommodate
all tasks given available resources.
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Why Oversubscribed Scheduling
Problems?
• Present in many real world domains.
• Challenging problems - identifying the best
subset of tasks that can be scheduled is
difficult.
• Many oversubscribed real-world scheduling
applications exhibit similar characteristics
and can be modeled as a more abstract
problem class.
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Our Oversubscribed Scheduling
Benchmark Set
• We identify 2 oversubscribed scheduling
applications that share similar characteristics:
AFSCN and AMC scheduling.
• We implement a problem generator to produce a
more general class of problems.
• Generator parameter values control the
characteristics of the instances.
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Motivation: A Tale of Two Studies
CSU studies
AFSCN*
CMU studies
AMC**
2002
2006
Repair-based
methods perform
poorly; GA, SWO
well.
2006 - 2007
AFSCN + AMC
Problem Fusion.
2002
2006
Repair-based
TaskSwap very
efficient and
effective.
Teams at Carnegie Mellon and Colorado State have been studying different
oversubscribed scheduling domains.
*
**
Carnegie Mellon
Barbulescu et al., (’04,’06)
Kramer & Smith, (’04,’05)
ICAPS-07 22-Sept, 2007
Basic (AMC) Airlift Allocation Problem
Requests:
Mission1:
pick up
cargo at A,
deliver to
B, then C.
Mission2
…
Decisions:
B
C
A
Start at what time?
W2
W1
Missionn
(Missions considered in strict priority order)
Carnegie Mellon
Use resources (e.g.,
aircraft) from wing
W1 or W2?
ICAPS-07 22-Sept, 2007
Air Force Satellite Control Network
(AFSCN) Access Scheduling
Decisions:
Input:
Use resource (an antenna) from
which ground station?
Request1:
Download
data from satellite1 to
ground-station1 in
time window W.
Request2
…
Schedule at what time in the
window?
GS1
GS2
Request-n
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Exploring the AFSCN/AMC Problem Space
• Despite obvious domain differences, the two
applications share a common core problem
structure:
•
•
•
•
•
Required duration per task.
Multi-capacity resources.
Alternative resources.
Fixed duration time windows.
Basic objective of minimizing number of unassigned
tasks.
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Differences between AFSCN and AMC
Domains are mainly of degree
... except that of task priority.
Hard Priority Constraint?
Number of Tasks
Resource Capacity
Average Temporal Flexibility
AFSCN
AMC
No
Yes
419 - 483
983
1-3
4 - 37
(0.70 - 0.76)
0.50
(task duration/window size)
Carnegie Mellon
ICAPS-07 22-Sept, 2007
A Problem Set to Span the AFSCN/AMC
Problem Space
• We design a unified problem set to span the
characteristics of the AFSCN and AMC
domains.
• Initial problem set: five recent real-world
AFSCN problems, R1-R5.
• We generate 50 new AFSCN-like problems:
• We vary the placement of each task’s time window.
• For each instance in the R1-R5 set, we generate 10 new
instances.
Carnegie Mellon
ICAPS-07 22-Sept, 2007
A Problem Set to Span the
AFSCN/AMC Problem Space (cont.)
• Starting with the 50 AFSCN-like instances , we
generate new instances by varying:
• Problem size – same as the AFSCN instances, double or triple:
• For larger problems, we generate 1 or 2 new tasks for each task,
by randomly moving the time window later in time
• Temporal flexibility (task slack)
• Increasing the slack by shortening the duration
• Resource Capacity (resource slack)
• Increasing the capacity (using a random factor)
• Priority (on/off)
• Task priorities randomly sampled between 1 and 5 (priority
classes in AMC)
Carnegie Mellon
ICAPS-07 22-Sept, 2007
The Generated Problems
(50 instances per problem set)
Avg. Unassignable Tasks, Initial Schedule
Problem Set
Average Size
Slack df
Capacity cf
pf = false
pf = true
1.1
443
0
0
34.1
71.2
1.2
886
0
3
127.7
195.6
1.3
1329
0
9
94.8
170.3
2.1
443
0.5
0
25.1
44.3
2.2
886
0.5
3
81.6
121.6
2.3
1329
0.5
9
56.12
106.6
3.1
443
0.5
3
7.4
15.7
3.2
886
0.5
6
27.3
48.9
3.3
1329
0.5
12
47
65.4
4.1
443
0.9
0
11.6
22.6
4.2
886
0.9
3
37.9
65.3
4.3
1329
0.9
9
32.3
45.4
5.1
443
0
5
4.04
13.5
5.2
886
0
8
34.9
69.0
5.3
1329
0
15
47.8
80.5
6.1
443
0.5
5
3.48
6.8
6.2
886
0.5
8
19.7
29.4
6.3
1329
0.5
15
36.8
44.7
Carnegie Mellon
ICAPS-07 22-Sept, 2007
Summary
1. Oversubscribed scheduling applications
represent an important, practical class of
problems and should be considered for
inclusion in a scheduling competition.
2. Effective approach to generate test problems:
abstract and consolidate common features
from multiple domains.
Carnegie Mellon
ICAPS-07 22-Sept, 2007
References
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Barbulescu, L. and Howe, A. E. and Watson, J. P. and Whitley, L. D. 2002. Satellite Range Scheduling: A
Comparison of Genetic, Heuristic and Local Search. In Proceedings of The Seventh International
Conference on Parallel Problem Solving from Nature(PPSNVII).
Barbulescu, L. and Watson, J. P. and Whitley, L. D. and Howe, A. E. 2004. Scheduling Space-Ground
Communications for the Air Force Satellite Control Network. Journal of Scheduling.
Barbulescu, L.; Howe, A. E.; and Whitley, L. 2004. Leap before you look: An effective strategy in an
oversubscribed scheduling problem. In Proc. 19th National Conference on Artificial Intelligence (AAAI04).
Barbulescu, L. and Howe, A. E. and Whitley, L.D. and Roberts, M. 2004. Trading Places: How to
Schedule More in a Multi-Resource Oversubscribed Scheduling Problem. In Proc. 14th International
Conference on Automated Planning and Scheduling.
Barbulescu, L.; Howe, A.; Whitley, L.; and Roberts, M. 2006. Understanding algorithm performance on an
oversubscribed scheduling application. JAIR 27:577–615.
Cicirello, V., and Smith, S. 2002. Amplification of search performance through randomization of
heuristics. In Proc. 8th Int. Conf. on Principles and Practice of Constraint Programming. Ithaca NY:
Springer-Verlag.
Kramer, L., and Smith, S. 2003. Maximizing flexibility: A retraction heuristic for oversubscribed
scheduling problems. In Proceedings 18th International Joint Conference on Artificial Intelligence.
Kramer, L. A., and Smith, S. F. 2004. Task swapping for schedule improvement, a broader analysis. In
Proc. 14th Int’l Conf. on Automated Planning and Scheduling.
Kramer, L. A., and Smith, S. F. 2005a. The amc scheduling problem: A description for reproducibility.
Technical Report CMU-RI-TR-05-75, Robotics Institute, Carnegie Mellon University.
Kramer, L. A., and Smith, S. F. 2005b. Maximizing availability: A commitment heuristic for
oversubscribed scheduling problems. In Proc. 15th International Conference on Automated Planning and
Scheduling (ICAPS-05).
Carnegie Mellon
ICAPS-07 22-Sept, 2007