Heuristic Planning with Single Action Goal Expansion Remo Christen - - PowerPoint PPT Presentation

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Heuristic Planning with Single Action Goal Expansion Remo Christen - - PowerPoint PPT Presentation

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Heuristic Planning with Single Action Goal Expansion Remo Christen Department of Mathematics and Computer Science University of Basel 5.7.2019 Introduction SAGE Results Conclusion Classical Planning Initial state Goal a 0 a 1 a 2 a n .

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Heuristic Planning with Single Action Goal Expansion

Remo Christen

Department of Mathematics and Computer Science University of Basel

5.7.2019

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Introduction SAGE Results Conclusion

Classical Planning

s0

Initial state

s1 s2 . . . sn

Goal

a0 a1 a2 an

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Introduction SAGE Results Conclusion

Blocksworld Domain

Initial state . . . Goal a0 an

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Introduction SAGE Results Conclusion

Forward Search

Initial state

pick up A pick up B pick up C

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Introduction SAGE Results Conclusion

Heuristics

◮ Estimate the distance from a state to the goal ◮ Assign every state a number indicating this estimate

<

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Introduction SAGE Results Conclusion

Heuristics

◮ Estimate the distance from a state to the goal ◮ Assign every state a number indicating this estimate Delete Relaxation Heuristic ◮ Find plan of simplified problem → Relaxed Plan ◮ Simplify by removing delete effects ◮ Relaxed plan length is heuristic value

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Introduction SAGE Results Conclusion

Heuristics

◮ Estimate the distance from a state to the goal ◮ Assign every state a number indicating this estimate Delete Relaxation Heuristic ◮ Find plan of simplified problem → Relaxed Plan ◮ Simplify by removing delete effects ◮ Relaxed plan length is heuristic value Pick up C pre = {clear C, ontable C, handempty} add = {holding C} del = {clear C, ontable C, handempty}

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Introduction SAGE Results Conclusion

Heuristics

◮ Estimate the distance from a state to the goal ◮ Assign every state a number indicating this estimate Delete Relaxation Heuristic ◮ Find plan of simplified problem → Relaxed Plan ◮ Simplify by removing delete effects ◮ Relaxed plan length is heuristic value Pick up C pre = {clear C, ontable C, handempty} add = {holding C} del = {clear C, ontable C, handempty}

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Introduction SAGE Results Conclusion

Starting Point

goals considered

g0 g1 g2 sz sx sy

Based on “Using Backwards Generated Goals for Heuristic Planning” by Alc´ azar et al. (2010): ◮ Use information from relaxed plan ◮ Generate intermediate goals ◮ Look for closest intermediate goal

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Introduction SAGE Results Conclusion

Starting Point

Based on “Using Backwards Generated Goals for Heuristic Planning” by Alc´ azar et al. (2010): ◮ Use information from relaxed plan ◮ Generate intermediate goals ◮ Look for closest intermediate goal Goals: ◮ Reduce depth of Heuristic Computation ◮ Reduce depth of Forward Search ◮ Handle difficulties close to the goal

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Introduction SAGE Results Conclusion

Single Action Goal Expansion

goal considered

g0 sz g1 g2 sx sy

Modify approach of Alc´ azar et al. by only expanding along a single sequence of actions: ◮ Introduce decision strategies about when to expand ◮ Limit generation of intermediate goals ◮ Search towards latest intermediate goal

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Introduction SAGE Results Conclusion

Single Action Goal Expansion

Modify approach of Alc´ azar et al. by only expanding along a single sequence of actions: ◮ Introduce decision strategies about when to expand ◮ Limit generation of intermediate goals ◮ Search towards latest intermediate goal Goals: ◮ Improve efficiency ◮ Preserve advantages of goal expansion

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Introduction SAGE Results Conclusion

Overview

Structure of the Goal Expansion Process

  • 1. State Decision
  • 2. Operator Ordering
  • 3. Check Operator for Legality
  • 4. Expand Goal with Legal Operator
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Introduction SAGE Results Conclusion

Goal Expansion

Original Goal

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Introduction SAGE Results Conclusion

Goal Expansion

New Goal Original Goal

stack C on B

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Introduction SAGE Results Conclusion

Goal Expansion

B on A C on B

New Goal Original Goal

stack C on B

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Introduction SAGE Results Conclusion

Goal Expansion

pre = {clear B, holding C} add = {C on B, clear C, hand empty} del = {clear B, holding C} B on A C on B

New Goal Original Goal

stack C on B

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Introduction SAGE Results Conclusion

Goal Expansion

pre = {clear B, holding C} add = {C on B, clear C, hand empty} del = {clear B, holding C} B on A C on B

New Goal Original Goal

stack C on B

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Introduction SAGE Results Conclusion

Goal Expansion

B on A clear B holding C pre = {clear B, holding C} add = {C on B, clear C, hand empty} del = {clear B, holding C} B on A C on B

New Goal Original Goal

stack C on B

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Introduction SAGE Results Conclusion

Goal Expansion

B on A clear B holding C pre = {clear B, holding C} add = {C on B, clear C, hand empty} del = {clear B, holding C} B on A C on B

New Goal Original Goal

stack C on B

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Introduction SAGE Results Conclusion

Overview

Structure of the Goal Expansion Process

  • 1. State Decision
  • 2. Operator Ordering
  • 3. Check Operator for Legality
  • 4. Expand Goal with Legal Operator
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Introduction SAGE Results Conclusion

State decision

Expand the goal when . . .

NewMinimum

. . . a state has the lowest heuristic value of all evaluated states.

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Introduction SAGE Results Conclusion

State decision

Expand the goal when . . .

NewMinimum

. . . a state has the lowest heuristic value of all evaluated states.

Accuracy

. . . the difference of a state’s heuristic value and the heuristic value

  • f the initial state is equal to the cost of reaching the state.
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Introduction SAGE Results Conclusion

State decision

Expand the goal when . . .

NewMinimum

. . . a state has the lowest heuristic value of all evaluated states.

Accuracy

. . . the difference of a state’s heuristic value and the heuristic value

  • f the initial state is equal to the cost of reaching the state.

Counter

. . . an operator appeared in the relaxed plan of a set percentage of previous evaluations, given that a minimum number of evaluations has been reached.

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Introduction SAGE Results Conclusion

Overview

Structure of the Goal Expansion Process

  • 1. State Decision
  • 2. Operator Ordering
  • 3. Check Operator for Legality
  • 4. Expand Goal with Legal Operator
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Introduction SAGE Results Conclusion

Operator Ordering

Collect all operators from the relaxed plan that satisfy a goal

  • proposition. Order them according to one of two criteria:

MostSatisfied

  • r

LowestLayer

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Introduction SAGE Results Conclusion

Operator Ordering

MostSatisfied

B on A clear B holding C pre = {clear B, holding C} add = {C on B, clear C, hand empty} del = {clear B, holding C} B on A C on B

New Goal Original Goal

stack C on B

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Introduction SAGE Results Conclusion

Operator Ordering

LowestLayer

B on A clear B holding C pre = {clear B, holding C} add = {C on B, clear C, hand empty} del = {clear B, holding C} B on A C on B

New Goal Original Goal

stack C on B

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Introduction SAGE Results Conclusion

Overview

Structure of the Goal Expansion Process

  • 1. State Decision
  • 2. Operator Ordering
  • 3. Check Operator for Legality
  • 4. Expand Goal with Legal Operator
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Introduction SAGE Results Conclusion

Legality Check

An operator is not legal if it meets one of these three conditions: ◮ Deletes goal proposition ◮ Mutual exclusion between goal propositions ◮ Dominated by previous goal

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Introduction SAGE Results Conclusion

Results

Coverage (Total 1827) NewMin Accuracy Counter Eager Greedy (FF) MostSatisfied 1051 1165 727 1503 LowestLayer 1027 1184 726

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Introduction SAGE Results Conclusion

Results

Coverage (Total 1827) NewMin Accuracy Counter Eager Greedy (FF) MostSatisfied 1051 1165 727 1503 LowestLayer 1027 1184 726 Goal Expansions Total NewMin Accuracy Counter Eager Greedy (FF) MostSatisfied 11699 7338 108636 LowestLayer 11986 6488 189694

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Introduction SAGE Results Conclusion

Results

Forward Expansions NewMin Accuracy Counter Eager Greedy (FF) blocks (32) 112.70 444.76 525.74 464.76 driverlog (14) 207.41 63.29 40.21 115.88 elevator-opt08-strips (19) 1379.44 2691.59 2154.87 3467.17 elevator-opt11-strips (12) 1462.71 2691.59 925.79 3516.75 gripper (17) 134.88 192.99 125.87 380.28 logistics00 (26) 153.92 34.04 25.35 42.20 miconic (130) 56.14 50.79 28.32 68.54 rovers (16) 111.78 104.46 153.03 225.05 scanalyzer-08-strips (23) 65.04 84.06 29.25 89.42 scanalyzer-opt11-strips (15) 71.71 45.73 19.00 48.49

Geometric mean of forward expansions for problems solved by all variants per domain. The operator order is LowestLayer.

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Introduction SAGE Results Conclusion

Unreachable Intermediate Goals

goal considered

g0 g1 g2 s5 s4 s3 s1 s0 s2

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Introduction SAGE Results Conclusion

Conclusion

◮ Negligable difference between operator orderings ◮ NewMinimum and Accuracy outperform Counter ◮ Visible potential in suitable domains ◮ Unreachable intermediate goals pose a problem

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Introduction SAGE Results Conclusion

Future Work

◮ Evaluate Counter with different settings ◮ What makes a domain suitable ◮ Find a strategy to avoid unreachable intermediate goals ◮ Improve implementation

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Introduction SAGE Results Conclusion

Questions