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Why is the additive heuristic inadmissible?

  • A.The relaxed problem is not a genuine relaxation of the original
  • B.The individual estimates are themselves overestimates
  • C.Summation is not defined when the costs are equal
  • D.A single action may achieve several goal atoms at once

Answer: D

If one action makes three goal atoms true, counting each separately triples the cost of that action and the total may exceed the true optimum. Ignoring positive interactions is exactly the assumption of independence. The relaxation is genuine and the individual estimates are themselves admissible. Recognising that combining admissible estimates by addition destroys admissibility, unless the subproblems are disjoint, is the same condition that governs additive pattern databases.

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