1. Carnegie Mellon ICAPS-07 22-Sept, 2007 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

2. 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.

3. 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.

4. Carnegie Mellon ICAPS-07 22-Sept, 2007 Oversubscribed Problems Oversubscribed scheduling problems are characterized by the inability to accommodate all tasks given available resources.

5. 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.

6. 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.

7. Carnegie Mellon ICAPS-07 22-Sept, 2007 Motivation: A Tale of Two Studies * Barbulescu et al., (’04,’06) CSU studies AFSCN* 20022006 CMU studies AMC** 20022006 Repair-based methods perform poorly; GA, SWO well. Repair-based TaskSwap very efficient and effective. ** Kramer & Smith, (’04,’05) AFSCN + AMC Problem Fusion. 2006 - 2007 Teams at Carnegie Mellon and Colorado State have been studying different oversubscribed scheduling domains.

8. Carnegie Mellon ICAPS-07 22-Sept, 2007 Basic (AMC) Airlift Allocation Problem A B C W1 W2 Mission 1 : pick up cargo at A, deliver to B, then C. Decisions: Use resources (e.g., aircraft) from wing W1 or W2? Start at what time? Mission 2 … Mission n (Missions considered in strict priority order) Requests :

9. Carnegie Mellon ICAPS-07 22-Sept, 2007 Air Force Satellite Control Network (AFSCN) Access Scheduling GS1 GS2 Request 1 : Download data from satellite 1 to ground-station 1 in time window W. Decisions: Use resource (an antenna) from which ground station? Schedule at what time in the window? Request 2 … Request-n Input :

10. 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.

11. Carnegie Mellon ICAPS-07 22-Sept, 2007 Differences between AFSCN and AMC Domains are mainly of degree... except that of task priority. AFSCNAMC Hard Priority Constraint?NoYes Number of Tasks419 - 483983 Resource Capacity1 - 34 - 37 Average Temporal Flexibility (task duration/window size) (0.70 - 0.76) 0.50

12. 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.

13. 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)

14. Carnegie Mellon ICAPS-07 22-Sept, 2007 The Generated Problems (50 instances per problem set) Problem SetAverage SizeSlack dfCapacity cfpf = falsepf = true 1.14430034.171.2 1.288603127.7195.6 1.313290994.8170.3 2.14430.5025.144.3 2.28860.5381.6121.6 2.313290.5956.12106.6 3.14430.537.415.7 3.28860.5627.348.9 3.313290.5124765.4 4.14430.9011.622.6 4.28860.9337.965.3 4.313290.9932.345.4 5.1443054.0413.5 5.28860834.969.0 5.3132901547.880.5 6.14430.553.486.8 6.28860.5819.729.4 6.313290.51536.844.7 Avg. Unassignable Tasks, Initial Schedule

15. 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.

16. Carnegie Mellon ICAPS-07 22-Sept, 2007 References 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 (AAAI- 04). 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. 14 th 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).