1. Validating Resources in Least Commitment Scheduling Nazma Ferdous & Mark Giuliano Space Telescope Science Institute October 24, 2006

2. Outline HST Observation Scheduling Process Resource Model Resource Model Limitations Plan Validation Tool Operational Results Summary & Future Directions

3. Outline HST Observation Scheduling Process Resource Model Resource Model Limitations Plan Validation Tool Operational Results Summary & Future Directions

4. HST Observation Scheduling Two Phased Approach Uncertainty in HST orbit. Big problem size (~ 2400 observations per year). Better long term HST usage. Year-based Long Range Planning (Assigns 8 week long window for start time) Week-based Short Term Scheduling (Assigns start time)

5. 1. Calculating Constraint Window Observation constraint windows are calculated from all physical and other constraints, which denotes the timeline of when the observation can be scheduled. 2. Generating Plan Window (PW) Using least commitment scheduler SPIKE, observations are assigned plan windows, which are the preferred window for scheduling. 3. Computing Resource Consumption Long Range Planning (LRP) Feb MarAprJunJulAugSepNov 0 1 Feb MarAprJunJulAugSepNov 0 1 Plan Window

6. Outline HST Observation Scheduling Process Resource Model Resource Model Limitations Plan Validation Tool Operational Results Summary & Future Directions

7. SPIKE Resources Total orbits per day (15 per day) South Atlantic Anomaly (SAA) related resources –SAA free orbits per day (6-7 per day) –SAA impacted orbits per day (8-9 per day) Sun Target

8. SPIKE Resource Model Equally distributes the total resource required by an observation over the range of the PW. Depicts general probability of resource contention/under usage. O1O1 O2O2 O3O3 Day 1 2 3 4 5 6 7 Plan Windows 2 Total Orbits Consumed 0 2 3 2 2 0 0 Available 2 0 -1 0 0 2 2 1 0 O1O1 O2O2 O3O3 Duration 234 234 State Day Over-subscribed 3 Leveled-subscribed 2,4,5 Under-subscribed 1,6,7

9. Outline HST Observation Scheduling Process Resource Model Resource Model LimitationsResource Model Limitations Plan Validation Tool Operational Results Summary & Future Directions

10. Resource Model Limitations Creates false positives. No oversubscribed days. Yet, no feasible schedule exists ! O1O1 O2O2 O3O3 Day 1 2 3 4 5 6 7 Plan Windows O4O4 Duration 33643364 O1O1 O2O2 O3O3 O4O4 2 Total Orbits Consumed 0 4 4 4 4 0 0 Available 4 0 0 0 0 4 4 1 0 4 3

11. Resource Model Limitation (cont.) Create false negatives. Day 3 and 4 are oversubscribed. Yet, a schedule can be generated ! O1O1 O2O2 O3O3 Day 1 2 3 4 5 6 7 Plan Windows O1O1 O2O2 O3O3 Duration 3 2 1 Total Orbits Consumed 0 1 2.5 2.5 1 0 0 Available 2 1 -0.5 -0.5 1 2 2 0.5 0 2 1.5 2.5

12. Initial Resource Profile Data from 2006 observation cycle Total Observations: 2389 Total Orbits Required: 3776 Total Orbits Oversubscription: 1029

13. Plan Window Generation ++ Short Term Scheduling LRP Plan Window Generation

14. Outline HST Observation Scheduling Process Resource Model Resource Model Limitations Plan Validation Tool Operational Results Summary & Future Directions

15. Short Term Scheduling Plan Window Generation Plan Validation Tool LRP Short Term Scheduling LRP Plan Window Generation Plan Validation Tool Given a Long Range Plan, Treat the plan windows for as the constraint windows. Assign 1 day-long scheduling window to the observations, essentially committing all resources required for the observation to that day. Analyze the resulting resource profile.

16. Validation Tool Implementation Initial Guess -Scheduling windows are assigned w/o violating the resource limit if possible. If not, window with least resource contention is chosen. Repair -A systematic repair (e.g. utilizes iterative deepening concept) is used to flatten the resource profile, minimizing false alarm as much as possible.

17. Iterative Deepening (ID) Repair Start at iteration 1 and progressively increase the iteration by 1. At iteration i, for each conflicted observation, perform a depth- first search, looking for chain of moves of length i, to resolve the conflict. The algorithm stops when max iteration (user specified) is reached or no resource contention exists. Iteration Operation 1 Oversubscribed  Undersubscribed 2 Oversubscribed  Leveled subscribed  Undersubscribed 3 Oversubscribed  Leveled subscribed  Leveled subscribed  Undersubscribed n Oversubscribed  Leveled subscribed  Leveled subscribed … (n-2 moves) …  Undersubscribed

18. ID : An example Resource Limit: 2 observations are allowed per day 1 2 3 4 5 6 7 8 9 10 11 U L O L U O L U O L L A F B C D E O : Over Subscribed Days L: Level Subscribed Days U: Under Subscribed Days Observations PW Conflicted? A 3 - 5 * B 5 - 7 * C 7 - 9 D 9 - 11 * E 4 - 10 F 1 - 4 AC BD F E

19. 1 2 3 4 5 6 7 8 9 10 11 U L O L U O L U O L L ID : Iteration 1 Oversubscribed  Undersubscribed Observation Chain: Actions Performed: 1 2 3 4 5 6 7 8 9 10 11 U L L L L O L U O L L A F B C D E A Move A from day 3 to day 5 AC BD F E A B D √ X X

20. ID: Iteration 2 Oversubscribed  Leveled subscribed  Undersubscribed Observation Chain: Actions Performed: 1 2 3 4 5 6 7 8 9 10 11 U L L L L O U L O L L B 1 2 3 4 5 6 7 8 9 10 11 U L L L L O L U O L L F B C D E A 1 2 3 4 5 6 7 8 9 10 11 U L L L L L L L O L L C Move C from day 7 to day 8 to create room for B Move B from day 6 to day 7. AC BD F E B, D,E AX X C√

21. 1 2 3 4 5 6 7 8 9 10 11 L L L L L L L L O U L D 1 2 3 4 5 6 7 8 9 10 11 L L L L L L L L L L L 1 2 3 4 5 6 7 8 9 10 11 L L L U L L L L O L L 1 2 3 4 5 6 7 8 9 10 11 U L L L L L L L O L L B F D E ACFE ID : Iteration 3 Oversubscribed  Leveled subscribed  Leveled subscribed  Undersubscribed Observation Chain: Action Performed: Move F from day 4 to day 1 to create room for E Move E from day 10 to day 4 to create room for D Move D from day 9 to day 10. AC BD F E D,E,AX B C F X X √

22. Outline HST Observation Scheduling Process Resource Model Resource Model Limitations Plan Validation Tool Operational Results Summary & Future Directions

23. Validation Tool Resource Profile For Total Orbits per day Resource False positives identified: 5 False negatives identified : 90 Total oversubscription : 495 (compared to 1029)

24. Extending Algorithms for PW Generation New initial guess and iterative deepening repair algorithms were extended for plan window generation. Resulting long range plan is more resource balanced. Validation tool identified fewer false positive/negatives and oversubscription. Short Term Scheduling Plan Window Generation Plan Validation Tool LRP

25. New Resource Profile Data from 2006 observation cycle Total Observations: 2389 Total Orbits Required: 3776 Total Orbits Oversubscription: 558 (compared to 1029)

26. Validation Tool Resource Profile For Total Orbits per day Resource False positives identified: 2 (compared to 5) False negatives identified : 179 (compared to 90) Total oversubscription : 142 (compared to 558)

27. Outline HST Observation Scheduling Process Resource Model Resource Model Limitations Plan Validation Tool Operational Results Summary & Future Directions

28. Summary An automated resource verification system is implemented for the long range planning. Streamlined the long range planning process. Significantly reduced human cost and saved time. Long range plan is more resource balanced.

29. Future Directions While repairing resource conflicts, knowledge gained in one iteration can be used in subsequent iterations. Couple “PW Generation” and “Validation Tool” more tightly so that resources are validated as the plan windows are laid out.

30. Thanks

31. Limitations Swapping observations is not allowed. Demonstrates diminishing return as the iteration increases. Using appropriate heuristics and utilizing domain knowledge is important. O1O1 O2O2 O3O3 Day 1 2 3 4 Plan Windows O1O1 O2O2 O3O3 Duration 2 1 1 0 Total Orbits 3 2 Consumed 0 3 1 0 Available 2 -1 1 2