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In heuristic search algorithms in Artificial Intelligence (AI), if a collection of admissible heuristics $h_1 \dots h_m$ is available for a problem and none of them dominates any of the others, which should we choose?

  1. $h(n)=max\{h_1(n), \dots , h_m(n)\}$
  2. $h(n)=min\{h_1(n), \dots , h_m(n)\}$
  3. $h(n)=avg\{h_1(n), \dots , h_m(n)\}$
  4. $h(n)=sum\{h_1(n), \dots , h_m(n)\}$
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If a collection of admissible heuristics is available for a problem, and none of them dominates any of the others, we can use the
composite function h(n) = max{h1(n),…,hm(n)}

Option (1) is correct.

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When multiple admissible heuristics are available for a problem, and none of them dominates any of the others, a common approach is to combine them. The idea is to create a new heuristic that benefits from the strengths of each individual heuristic. One such approach is to take the maximum (max) value of the individual heuristic

 

Therefore, the correct choice would be:

A. $h(n)=max((h_i(n),…,h_m(n))$

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