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How can two admissible heuristics be combined?

  • A.Take their minimum at each state
  • B.Take their maximum at each state
  • C.Take their sum at each state
  • D.Take their average at each state

Answer: B

The maximum of two admissible heuristics is itself admissible, since neither exceeds the true cost, and it dominates both, so combining costs only the extra computation. The sum may overestimate and destroy admissibility unless the heuristics are additive over disjoint subproblems. Averaging and minimising both throw away information. Taking the maximum is a free improvement whenever several admissible estimates are available, which makes it the standard move.

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