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

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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

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

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

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

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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

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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

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

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Makespan-Usefulness Example 9

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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

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

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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

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Results Over Time 13

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Results Over Time 14

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At 30 Minutes 15

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Quality Change 16

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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

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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

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