PlanSIG, 15-16 Dec, 2005 1 Temporal Plans and Resource Management Pieter Buzing & Cees Witteveen Delft University of Technology.

PlanSIG, 15-16 Dec, 2005

1

Temporal Plans and Resource ManagementPieter Buzing & Cees Witteveen

Delft University of Technology

PlanSIG, 15-16 Dec, 2005 2

What about?

• Temporal planning in multi-agent systems• or: distributed issues in planning systems

• Plan repair (during tactical phase)• Introduce resource-based view• Use scheduling heuristic• Integrate it with multi agent temporal

planning

PlanSIG, 15-16 Dec, 2005 3

The Problem

• Many complex environments need planning and coordination of actions• Example: airport, harbor, factory, …

• Multiple (autonomous) parties involved• Issues: conflicting goals, communication,

coordination• Execution phase is error-prone:• Environment is unpredictable, partial

information

PlanSIG, 15-16 Dec, 2005 4

Example: Airport

PlanSIG, 15-16 Dec, 2005 5

Solution Requirements

• Respect individual planning tools:• Abstract temporal plan model

• Handle aberrations during plan execution:• Flexibility encoded in plan

• Respect and use agents’ intelligence:• No central planner• Smart coordination (negotiation)

PlanSIG, 15-16 Dec, 2005 6

[10, 20]

[15, 25] [5, 20] [14, 20]

[8, 23] [13, 26]

[12, 21] [15, 16]

[10, 15]

[12, 20]

[7, 21]

[10, 15]

[10, 12]

[8, 30]

[12, 25]

[11, 15]

[5, 24]

[7, 15]

[10, 40]

[12, 35]

[8, 30]

[1, 10] [5, 10]

[5, 30]

[10, 21]

[10, 20]

[4, 6]

[5, 15] [5, 20]

[5, 25]

PlanSIG, 15-16 Dec, 2005 7

Simple Temporal Problem (STP)

•Planning as CSP (Dechter et.al., 1991)•Temporal constraints between time point variables

•Path consistency = arc consistency = polynomial time: O(n^3)

•Extracting schedule is simple (read all lower bounds)•Flexibility is maintained

PlanSIG, 15-16 Dec, 2005 8

STPs and Preferences

• Duration action A is [10, 40]: hard constraint• In practice:• “A takes about 25 minutes, perhaps bit

more/less”• “25 would be ideal, but [15-30] is okay”

• Soft constraint expressed as preference function

• Repair opportunities

PlanSIG, 15-16 Dec, 2005 9

Preferences and Repair

• During planning:• Iteratively solve STPs at increasing p-levels• “Best plan” is selected

• During execution:• Some disruption causes a constraint change• Return to less-preferred (but feasible) STP

• Example:• Scheduled duration action A at p=3 is [23, 25]• Oops! Action A will take 28 minutes: conflict!• But we have a backup solution at p=1

PlanSIG, 15-16 Dec, 2005 10

STPs and Resources

• Planning = action ordering• Scheduling = resource assignment• Practical planning problems are mix of both…• Airport: gates, runways, taxiways• Example: 4 flights scheduled on 2 gates

PlanSIG, 15-16 Dec, 2005 11

[10, 20]

[15, 25] [5, 20] [14, 20]

[8, 23] [13, 26]

[12, 21] [15, 16]

[10, 15]

[12, 20]

[7, 21]

[10, 15]

[10, 12]

[8, 30]

[12, 25]

[11, 15]

[5, 24]

[7, 15]

[10, 40]

[12, 35]

[8, 30]

[1, 10] [5, 10]

[5, 30]

[10, 21]

[10, 20]

[4, 6]

[5, 15] [5, 20]

[5, 25]

PlanSIG, 15-16 Dec, 2005 12

[10, 20]

[15, 25] [5, 20] [14, 20]

[8, 23] [13, 26]

[12, 21] [15, 16]

[10, 15]

[12, 20]

[7, 21]

[10, 15]

[10, 12]

[8, 30]

[12, 25]

[11, 15]

[5, 24]

[7, 15]

[10, 40]

[12, 35]

[8, 30]

[1, 10] [5, 10]

[5, 30]

[10, 21]

[10, 20]

[4, 6]

[5, 15] [5, 20]

[5, 25]

PlanSIG, 15-16 Dec, 2005 13

[10, 20]

[15, 25] [5, 20] [14, 20]

[8, 23] [13, 26]

[12, 21] [15, 16]

[10, 15]

[12, 20]

[7, 21]

[10, 15]

[10, 12]

[8, 30]

[12, 25]

[11, 15]

[5, 24]

[7, 15]

[10, 40]

[12, 35]

[8, 30]

[1, 10] [5, 10]

[5, 30]

[10, 21]

[10, 20]

[4, 6]

[5, 15] [5, 20]

[5, 25]

PlanSIG, 15-16 Dec, 2005 14

Scheduling Heuristic for STPs

• Known scheduling heuristic: flexibility• Amount of slack

• Planning phase: • assign action a to resource s.t. flex(a) is max

• Plan repair:• Choose action a s.t. flex(a) is min• Move a to resource s.t. flex(a)’ becomes max

PlanSIG, 15-16 Dec, 2005 15

Example (Gate Scheduling)

• Aircraft has delay: can not dock before t=50• Inconsistency since flex value is negative• Find gate with highest flex: g2• Move aircraft to that gate

PlanSIG, 15-16 Dec, 2005 16

Conclusion

• Trying to bring together:• Multi agent system• (temporal) Planning• Scheduling aspects

• Application:• Collaborating with NLR (National Aerospace

Laboratory)

• Extending airport simulator with MA tools

PlanSIG, 15-16 Dec, 2005 17

PlanSIG, 15-16 Dec, 2005 18

Choices in STPs

• “either action A before B or action B before A”• Disjunctive Temporal Problem• MA voting protocol for decision making (B&W,

2004b)• Reordering actions as a means of plan repair