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DD2380 HT24 (AIHT24_2) Q9: Planning

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Consider the following planning problem in PDDL š¼ š‘› š‘– š‘” ( š“ š‘” ( š‘ƒ 1 , šµ š‘™ š‘¢ š‘’ ) , š“ š‘” ( š‘ƒ 2 , šµ š‘™ š‘¢ š‘’ ) , š“ š‘” ( š‘ƒ 3 , š‘… š‘’ š‘‘ ) , š“ š‘” ( š‘ƒ 4 , š‘… š‘’ š‘‘ ) , š“ š‘” ( š‘ƒ 5 , šµ š‘™ š‘¢ š‘’ ) , š“ š‘” ( š‘ƒ 6 , š‘… š‘’ š‘‘ ) , š‘ š‘’ š‘„ š‘” ( š‘ƒ 1 , š‘ƒ 2 ) , š‘ š‘’ š‘„ š‘” ( š‘ƒ 2 , š‘ƒ 3 ) , š‘ š‘’ š‘„ š‘” ( š‘ƒ 3 , š‘ƒ 4 ) , š‘ š‘’ š‘„ š‘” ( š‘ƒ 4 , š‘ƒ 5 ) , š‘ š‘’ š‘„ š‘” ( š‘ƒ 5 , š‘ƒ 6 ) , š‘ š‘’ š‘„ š‘” ( š‘ƒ 6 , š‘ƒ 1 ) ) šŗ š‘œ š‘Ž š‘™ ( š“ š‘” ( š‘ƒ 1 , šµ š‘™ š‘¢ š‘’ ) , š“ š‘” ( š‘ƒ 2 , šµ š‘™ š‘¢ š‘’ ) , š“ š‘” ( š‘ƒ 3 , šµ š‘™ š‘¢ š‘’ ) , š“ š‘” ( š‘ƒ 4 , š‘… š‘’ š‘‘ ) , š“ š‘” ( š‘ƒ 5 , š‘… š‘’ š‘‘ ) , š“ š‘” ( š‘ƒ 6 , š‘… š‘’ š‘‘ ) ) š“ š‘ š‘” š‘– š‘œ š‘› ( š‘† š‘¤ š‘– š‘” š‘ ā„Ž ( š‘„ , š‘¦ , š‘“ š‘Ÿ š‘œ š‘š , š‘” š‘œ ) ) Ā  š‘ƒ š‘… šø š¶ š‘‚ š‘ š· : š“ š‘” ( š‘“ š‘Ÿ š‘œ š‘š , š‘„ ) ∧ š“ š‘” ( š‘” š‘œ , š‘¦ ) ∧ š‘ š‘’ š‘„ š‘” ( š‘“ š‘Ÿ š‘œ š‘š , š‘” š‘œ ) šø š¹ š¹ šø š¶ š‘‡ : š“ š‘” ( š‘“ š‘Ÿ š‘œ š‘š , š‘¦ ) ∧ ¬ š“ š‘” ( š‘“ š‘Ÿ š‘œ š‘š , š‘„ ) ∧ š“ š‘” ( š‘” š‘œ , š‘„ ) ∧ ¬ š“ š‘” ( š‘” š‘œ , š‘¦ ) ) Ignoring the precondition š‘ š‘’ š‘„ š‘” ( š‘“ š‘Ÿ š‘œ š‘š , š‘” š‘œ ) leads to defining a relaxed problem, whose solution can serve as a heuristic for solving the original problem via search. What holds for this heuristic?

Options
A.ā„Ž ( š‘› ) = 0
B.ā„Ž ( š‘› ) is the number of misplaced colors divided by two.
C.ā„Ž ( š‘› ) is the number of misplaced colors.
D.ā„Ž ( š‘› ) is the sum of the distances of misplaced colors to their right position.
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Step-by-Step Analysis
When evaluating a heuristic derived from solving a relaxed version of a planning problem, we look at how many goal conditions remain unsatisfied in the current state, under the relaxation. Option A: h(n) = 0. This would imply every state has a completed relaxed plan of length zero, which cannot be the case unless we are already at a goal state. In general, after ignoring preconditions, many goals remain unmet, so this option is not plausible as a descriptive heuristic for ......Login to view full explanation

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