Enhancing Search for Satisficing Temporal Planning with Objective-driven Decisions J. Benton Patrick EyerichSubbarao Kambhampati

g-value plateaus in Temporal Planning  Common temporal planning objective function (:metric (minimize (total-time)))  Makespan as the evaluation function is inefficient for satisificing search  g-value plateaus  Leads to worst case cost-variance between search operations  The usual approach: Use a Surrogate Search  Choose a surrogate evaluation function that allows for scalability, improving the cost-variance between search states  Objective Function ≠ Evaluation Function  We want to improve “keeping track” of objective function 2

Temporal Fast Downward  Temporal Fast Downward (TFD) 3 Objective Function Corresponding Evaluation Function Surrogate Evaluation Function

Temporal Fast Downward Search 4 end eff 4 6 end end eff 2 2

Temporal Fast Downward Search 5 end eff 4 6 end end eff 2 2 …

Find the Better Path  Force consideration of better-makespan path  Should maintain surrogate evaluation function’s scalability  Our idea: Determine whether operators are useful according to makespan and force their expansion 6

Useful Operators  Related to Wehrle et al.’s useless actions  At parent state s  Remove operator o from the domain  Find heuristic value for,  Apply operator o to generate  Find heuristic value for,  If then operator is possibly useful  Its degree of usefulness is 7

Makespan-Usefulness Example 8 Get all trucks to An optimal plan

Makespan-Usefulness Example 9

Lookahead on Useful Operators  Force expansion of most makespan-useful state before other states  Remove ‘best’ node from queue  Analyze for child states for makespan-usefulness  Expand state given by most useful operator  Evaluate each resulting grandchild state according to the surrogate evaluation function and push into queue 10

Useful Operator Lookahead 11 end eff 4 6 end end eff 2 2 …

Empirical Evaluation  4 Anytime search variations  TFD  TFD with useful lookahead,  TFD with lazy evaluation followed by TFD with useful lookahead (and without lazy evaluation),  TFD with lazy evaluation followed by TFD without lazy evaluation,  Makespan heuristic using STN  30 minute timeout  Compared on IPC score 12

Results Over Time 13

Results Over Time 14

At 30 Minutes 15

Quality Change 16

Summary  Used notion of operator usefulness  Lookahead on most useful operator  Use in combination with surrogate search  Shown to improve plan quality in some domains  Continues to help when combined with a portfolio-like approach 17

Future Work  Lookahead more than one step  k-deep local lookaheads on most useful operators combined with best-first search  Use relaxed solutions  YAHSP-style lookahead but stop when no makespan-useful operators are applicable 18